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\begin{algorithm}[t]
\caption{Adv-NTK (Solving Eq.~(\ref{eq:adv-ntk-objective}) with SGD and GradNorm)}
\label{algo:advntk}
\begin{algorithmic}[1]
\Require
Training set $\mathcal{D}$, validation set size $M_{\mathrm{val}}$, learning rate $\zeta$, training iteration $T$, PGD function for finding adversarial validation data.
\Ensure An infinite-width adversarially robust DNN.
\State Randomly separate $\mathcal D$ into subsets $\mathcal D_{\mathrm{opt}}$ and $\mathcal D_{\mathrm{val}}$ such that $| \mathcal D_{\mathrm{val}} | = M_{\mathrm{val}}$.
\State Initialize trainable parameter $\varpi_0 \in \mathbb{R}^{|\mathcal D_{\mathrm{val}}| \cdot c}$ with zeros.
\For{$t$ \textbf{in} $1, \cdots, T$}
\State Sample a minibatch $(x, y) \sim \mathcal D_{\mathrm{val}}$.
\State $x' \leftarrow \mathrm{PGD}(x,y,f_{\varpi_{t-1}})$
\Comment{Finding adversarial validation examples.}
\State $g_t \leftarrow \partial_{\varpi} \frac{1}{2} \| f_{\varpi_{t-1}}(x') - y \|_2^2$
\State $\varpi_t \leftarrow \varpi_{t-1} - \zeta \cdot \frac{g_t}{\|g_t\|_2}$
\Comment{Update model parameter via SGD and $\ell_2$-GardNorm.}
\EndFor
\State \Return $f_{\varpi_T}$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[t]
\caption{Adv-NTK (Solving Eq.~(\ref{eq:adv-ntk-objective}) with SGD and GradNorm)}
\begin{algorithmic}
[1]
\Require
Training set $\mathcal{D}$, validation set size $M_{\mathrm{val}}$, learning rate $\zeta$, training iteration $T$, PGD function for finding adversarial validation data.
\Ensure An infinite-width adversarially robust DNN.
\State Randomly separate $\mathcal D$ into subsets $\mathcal D_{\mathrm{opt}}$ and $\mathcal D_{\mathrm{val}}$ such that $| \mathcal D_{\mathrm{val}} | = M_{\mathrm{val}}$.
\State Initialize trainable parameter $\varpi_0 \in \mathbb{R}^{|\mathcal D_{\mathrm{val}}| \cdot c}$ with zeros.
\For{$t$ \textbf{in} $1, \cdots, T$}
\State Sample a minibatch $(x, y) \sim \mathcal D_{\mathrm{val}}$.
\State $x' \leftarrow \mathrm{PGD}(x,y,f_{\varpi_{t-1}})$
\Comment{Finding adversarial validation examples.}
\State $g_t \leftarrow \partial_{\varpi} \frac{1}{2} \| f_{\varpi_{t-1}}(x') - y \|_2^2$
\State $\varpi_t \leftarrow \varpi_{t-1} - \zeta \cdot \frac{g_t}{\|g_t\|_2}$
\Comment{Update model parameter via SGD and $\ell_2$-GardNorm.}
\EndFor
\State \Return $f_{\varpi_T}$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2310.06112" | "2310.06112.tar.gz" | "2024-02-04" | {
"title": "theoretical analysis of robust overfitting for wide dnns: an ntk approach",
"id": "2310.06112",
"abstract": "adversarial training (at) is a canonical method for enhancing the robustness of deep neural networks (dnns). however, recent studies empirically demonstrated that it suffers from robust overfitting, i.e., a long time at can be detrimental to the robustness of dnns. this paper presents a theoretical explanation of robust overfitting for dnns. specifically, we non-trivially extend the neural tangent kernel (ntk) theory to at and prove that an adversarially trained wide dnn can be well approximated by a linearized dnn. moreover, for squared loss, closed-form at dynamics for the linearized dnn can be derived, which reveals a new at degeneration phenomenon: a long-term at will result in a wide dnn degenerates to that obtained without at and thus cause robust overfitting. based on our theoretical results, we further design a method namely adv-ntk, the first at algorithm for infinite-width dnns. experiments on real-world datasets show that adv-ntk can help infinite-width dnns enhance comparable robustness to that of their finite-width counterparts, which in turn justifies our theoretical findings. the code is available at https://github.com/fshp971/adv-ntk.",
"categories": "cs.lg stat.ml",
"doi": "",
"created": "2023-10-09",
"updated": "2024-02-04",
"authors": [
"shaopeng fu",
"di wang"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2310.06112"
} | "2024-03-15T07:33:05.157801" | {
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} | [] | "algorithm" | "241abda0-76ad-414a-9b6c-1ad836bfba2d" | 1161 | medium |
|
\begin{algorithmic}
\Require $X_{0}$ initial condition,
$t$ simulation horizon.
\State Sample a realisation for $B_t$\,.
\If{$B_t = 1$}
\State Compute $\phi_V(u,t)$.
\State Run Algorithm \ref{alg:simul1}, using
$\phi_V(u,t)$ as CF.
\Else
\State $X_{t} = X_{0} e^{-bt}$.
\EndIf
\end{algorithmic}
| \begin{algorithmic}
\Require $X_{0}$ initial condition,
$t$ simulation horizon.
\State Sample a realisation for $B_t$\,.
\If{$B_t = 1$}
\State Compute $\phi_V(u,t)$.
\State Run Algorithm \ref{alg:simul1}, using
$\phi_V(u,t)$ as CF.
\Else
\State $X_{t} = X_{0} e^{-bt}$.
\EndIf
\end{algorithmic} | "https://arxiv.org/src/2401.15483" | "2401.15483.tar.gz" | "2024-01-27" | {
"title": "fast and general simulation of l\\'evy-driven ou processes for energy derivatives",
"id": "2401.15483",
"abstract": "l\\'evy-driven ornstein-uhlenbeck (ou) processes represent an intriguing class of stochastic processes that have garnered interest in the energy sector for their ability to capture typical features of market dynamics. however, in the current state-of-the-art, monte carlo simulations of these processes are not straightforward for two main reasons: i) algorithms are available only for some particular processes within this class; ii) they are often computationally expensive. in this paper, we introduce a new simulation technique designed to address both challenges. it relies on the numerical inversion of the characteristic function, offering a general methodology applicable to all l\\'evy-driven ou processes. moreover, leveraging fft, the proposed methodology ensures fast and accurate simulations, providing a solid basis for the widespread adoption of these processes in the energy sector. lastly, the algorithm allows an optimal control of the numerical error. we apply the technique to the pricing of energy derivatives, comparing the results with existing benchmarks. our findings indicate that the proposed methodology is at least one order of magnitude faster than existing algorithms, all while maintaining an equivalent level of accuracy.",
"categories": "q-fin.cp q-fin.mf q-fin.pr",
"doi": "",
"created": "2024-01-27",
"updated": "",
"authors": [
"roberto baviera",
"pietro manzoni"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.15483"
} | "2024-03-15T05:30:23.512614" | {
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} | [] | "algorithm" | "8454da4e-1452-481d-9993-ad04f913b6c5" | 294 | easy |
|
\begin{algorithm}
\floatname{algorithm}{\bf Algorithm}
\caption{Qualitative Test}
\vspace{4pt}
\hrule
\vspace{4pt}
\label{alg:qualitative}
\begin{algorithmic}[1]
\State Perform Step 1 - 5 in \textbf{Algorithm} \ref{alg:EFT} to obtain the critical value of EFT, $\hat{q}_{n,1-\alpha}$.
\State Formulate a projection problem as in \eqref{eq:opt} and find the solution $\tilde{\Lambda}_{\mathbf{C}}(t)$.
\State For the Qualitative Test where $H_0: \Lambda_\mathbf{C}(t) \in \mathcal{N}_0, \quad t \in (0,1)$, reject the null hypothesis whenever $\max_{i_* \le j \le i^*}|\check{\Lambda}_{\mathbf{C}}(t_j) - \tilde{\Lambda}_{\mathbf{C}}(t_j)|_\infty > \hat{q}_{n,1-\alpha}/\sqrt{n}$.
\end{algorithmic}
\vspace{4pt}
\hrule
\end{algorithm}
| \begin{algorithm}
\floatname{algorithm}{\bf Algorithm}
\caption{Qualitative Test}
\vspace{4pt}
\hrule
\vspace{4pt}
\begin{algorithmic}
[1]
\State Perform Step 1 - 5 in \textbf{Algorithm} \ref{alg:EFT} to obtain the critical value of EFT, $\hat{q}_{n,1-\alpha}$.
\State Formulate a projection problem as in \eqref{eq:opt} and find the solution $\tilde{\Lambda}_{\mathbf{C}}(t)$.
\State For the Qualitative Test where $H_0: \Lambda_\mathbf{C}(t) \in \mathcal{N}_0, \quad t \in (0,1)$, reject the null hypothesis whenever $\max_{i_* \le j \le i^*}|\check{\Lambda}_{\mathbf{C}}(t_j) - \tilde{\Lambda}_{\mathbf{C}}(t_j)|_\infty > \hat{q}_{n,1-\alpha}/\sqrt{n}$.
\end{algorithmic}
\vspace{4pt}
\hrule
\end{algorithm} | "https://arxiv.org/src/2310.11724" | "2310.11724.tar.gz" | "2024-02-26" | {
"title": "simultaneous nonparametric inference of m-regression under complex temporal dynamics",
"id": "2310.11724",
"abstract": "the paper considers simultaneous nonparametric inference for a wide class of m-regression models with time-varying coefficients. the covariates and errors of the regression model are tackled as a general class of nonstationary time series and are allowed to be cross-dependent. we construct $\\sqrt{n}$-consistent inference for the cumulative regression function, whose limiting properties are disclosed using bahadur representation and gaussian approximation theory. a simple and unified self-convolved bootstrap procedure is proposed. with only one tuning parameter, the bootstrap consistently simulates the desired limiting behavior of the m-estimators under complex temporal dynamics, even under the possible presence of breakpoints in time series. our methodology leads to a unified framework to conduct general classes of exact function tests, lack-of-fit tests, and qualitative tests for the time-varying coefficients under complex temporal dynamics. these tests enable one to, among many others, conduct variable selection procedures, check for constancy and linearity, as well as verify shape assumptions, including monotonicity and convexity. as applications, our method is utilized to study the time-varying properties of global climate data and microsoft stock return, respectively.",
"categories": "stat.me math.st stat.th",
"doi": "",
"created": "2023-10-18",
"updated": "2024-02-26",
"authors": [
"miaoshiqi liu",
"zhou zhou"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2310.11724"
} | "2024-03-15T03:19:25.303660" | {
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} | [] | "algorithm" | "bf5fa5de-4a71-49da-a795-d4780ff193ae" | 710 | medium |
|
\begin{algorithmic} [1]
\State Initialize actor network $\mu_\theta$ and critic networks $Q_{\omega_1}$ and $Q_{\omega_2}$.
\State Initialize corresponding target networks: $\theta' \leftarrow \theta$, ${\omega'}_1 \leftarrow \omega_1$, ${\omega'}_2 \leftarrow \omega_2$ and choose $\rho_\text{p} \in (0, 1)$.
\State Initialize replay buffer $\mathcal{R}$.
\State Choose a batch size $K$, a gradient based optimization algorithm and a corresponding learning rate $\lambda_\text{actor}, \lambda_\text{critic} > 0$ for both optimization procedures, a time step size $\Delta t$ and a stopping criterion.
\State Choose standard deviation exploration noise $\sigma_\text{expl}$ and lower and upper action bounds $a_\text{low}, a_\text{high}$.
\Repeat
\State Select clipped action and step the environment dynamics forward.
\begin{equation*}
a= \text{clip}(\mu_\theta(s) + \epsilon, a_\text{low}, a_\text{high}), \quad \epsilon \sim \mathcal{N}(0, \sigma_\text{expl}).
\end{equation*}
\State Observe next state $s'$, reward $r$, and done signal $d$ and store the tuple $(s, a, r, s', d)$ in the replay buffer.
\If{$s'$ is terminal}
\State Reset trajectory.
\EndIf
\For{$j$ in range(\textit{update frequency})}
\State Sample batch $\mathcal{B} = \{(s^{(k)}, a^{(k)}, r^{(k)}, {s'}^{(k)}, d^{(k)})\}_{k=1}^K$ from replay buffer.
\State Compute targets (Clipped Double Q-learning and policy smoothing).
\begin{equation*}
y(r, s', d) = r + (1-d) \min\limits_{i=1, 2} \left\{ Q_{{\omega'}_i}(s', \tilde{a}) \right\}, \quad \tilde{a}= \text{clip}(\mu_{\theta'}(s) + \epsilon, a_\text{low}, a_\text{high}), \quad \epsilon \sim \mathcal{N}(0, \sigma_\text{target}).
\end{equation*}
\State Estimate critic gradient $\nabla_\omega L(Q_\omega^{\mu_\theta})$ by
\begin{equation*}
\nabla_{\omega_i} \Biggl(\frac{1}{K} \sum\limits_{k=1}^K \left(Q_{\omega_i}(s^{(k)}, a^{(k)}) - y(r^{(k)}, {s'}^{(k)}, d^{(k)}) \right)^2 \Biggr), \quad \text{for} \,\, i=1,2.
\end{equation*}
\State Update the critic parameters $\omega_i$ based on the optimization algorithm.
\If{$j \text{ mod } \textit{policy delay frequency} = 0$}
\State Estimate actor gradient $\nabla_\theta J(\mu_\theta)$ by
\begin{equation*}
\nabla_{\theta} \Biggl(\frac{1}{K} \sum\limits_{k=1}^K Q_{\omega_1}(s^{(k)}, \mu_\theta(s^{(k)})) \Biggr).
\end{equation*}
\State Update the actor parameters $\theta$ based on the optimization algorithm.
\State Update target networks softly:
\begin{equation*}
\theta' \leftarrow \rho_\text{p} \theta' + (1 - \rho_\text{p})\theta, \quad
{\omega'}_i \leftarrow \rho_\text{p} {\omega'}_i + (1 - \rho_\text{p})\omega_i, \quad \text{for} \, \, i=1, 2.
\end{equation*}
\EndIf
\EndFor
\Until{stopping criterion is fulfilled.}
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Initialize actor network $\mu_\theta$ and critic networks $Q_{\omega_1}$ and $Q_{\omega_2}$.
\State Initialize corresponding target networks: $\theta' \leftarrow \theta$, ${\omega'}_1 \leftarrow \omega_1$, ${\omega'}_2 \leftarrow \omega_2$ and choose $\rho_\text{p} \in (0, 1)$.
\State Initialize replay buffer $\mathcal{R}$.
\State Choose a batch size $K$, a gradient based optimization algorithm and a corresponding learning rate $\lambda_\text{actor}, \lambda_\text{critic} > 0$ for both optimization procedures, a time step size $\Delta t$ and a stopping criterion.
\State Choose standard deviation exploration noise $\sigma_\text{expl}$ and lower and upper action bounds $a_\text{low}, a_\text{high}$.
\Repeat
\State Select clipped action and step the environment dynamics forward.
\begin{equation*}
a= \text{clip}(\mu_\theta(s) + \epsilon, a_\text{low}, a_\text{high}), \quad \epsilon \sim \mathcal{N}(0, \sigma_\text{expl}).
\end{equation*}
\State Observe next state $s'$, reward $r$, and done signal $d$ and store the tuple $(s, a, r, s', d)$ in the replay buffer.
\If{$s'$ is terminal}
\State Reset trajectory.
\EndIf
\For{$j$ in range(\textit{update frequency})}
\State Sample batch $\mathcal{B} = \{(s^{(k)}, a^{(k)}, r^{(k)}, {s'}^{(k)}, d^{(k)})\}_{k=1}^K$ from replay buffer.
\State Compute targets (Clipped Double Q-learning and policy smoothing).
\begin{equation*}
y(r, s', d) = r + (1-d) \min\limits_{i=1, 2} \left\{ Q_{{\omega'}_i}(s', \tilde{a}) \right\}, \quad \tilde{a}= \text{clip}(\mu_{\theta'}(s) + \epsilon, a_\text{low}, a_\text{high}), \quad \epsilon \sim \mathcal{N}(0, \sigma_\text{target}).
\end{equation*}
\State Estimate critic gradient $\nabla_\omega L(Q_\omega^{\mu_\theta})$ by
\begin{equation*}
\nabla_{\omega_i} \Biggl(\frac{1}{K} \sum\limits_{k=1}^K \left(Q_{\omega_i}(s^{(k)}, a^{(k)}) - y(r^{(k)}, {s'}^{(k)}, d^{(k)}) \right)^2 \Biggr), \quad \text{for} \,\, i=1,2.
\end{equation*}
\State Update the critic parameters $\omega_i$ based on the optimization algorithm.
\If{$j \text{ mod } \textit{policy delay frequency} = 0$}
\State Estimate actor gradient $\nabla_\theta J(\mu_\theta)$ by
\begin{equation*}
\nabla_{\theta} \Biggl(\frac{1}{K} \sum\limits_{k=1}^K Q_{\omega_1}(s^{(k)}, \mu_\theta(s^{(k)})) \Biggr).
\end{equation*}
\State Update the actor parameters $\theta$ based on the optimization algorithm.
\State Update target networks softly:
\begin{equation*}
\theta' \leftarrow \rho_\text{p} \theta' + (1 - \rho_\text{p})\theta, \quad
{\omega'}_i \leftarrow \rho_\text{p} {\omega'}_i + (1 - \rho_\text{p})\omega_i, \quad \text{for} \, \, i=1, 2.
\end{equation*}
\EndIf
\EndFor
\Until{stopping criterion is fulfilled.}
\end{algorithmic} | "https://arxiv.org/src/2211.02474" | "2211.02474.tar.gz" | "2024-02-15" | {
"title": "connecting stochastic optimal control and reinforcement learning",
"id": "2211.02474",
"abstract": "in this paper the connection between stochastic optimal control and reinforcement learning is investigated. our main motivation is to apply importance sampling to sampling rare events which can be reformulated as an optimal control problem. by using a parameterised approach the optimal control problem becomes a stochastic optimization problem which still raises some open questions regarding how to tackle the scalability to high-dimensional problems and how to deal with the intrinsic metastability of the system. to explore new methods we link the optimal control problem to reinforcement learning since both share the same underlying framework, namely a markov decision process (mdp). for the optimal control problem we show how the mdp can be formulated. in addition we discuss how the stochastic optimal control problem can be interpreted in the framework of reinforcement learning. at the end of the article we present the application of two different reinforcement learning algorithms to the optimal control problem and a comparison of the advantages and disadvantages of the two algorithms.",
"categories": "math.oc",
"doi": "",
"created": "2022-11-04",
"updated": "2024-02-15",
"authors": [
"jannes quer",
"enric ribera borrell"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2211.02474"
} | "2024-03-15T04:03:02.445897" | {
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} | [] | "algorithm" | "64c02284-0165-4239-b815-a1defb3478dc" | 2714 | hard |
|
\begin{algorithmic}[1]
\Require{$\{\beta_i\}_{i=1}^N, \{\alpha_i\}_{i=1}^N, \text{csm}, \mathbf{\hat{y}}, \lambda_1, \lambda_2, r, N, M, \mathbf{M_u}$.} \Comment{$\text{csm} = \{\text{csm}_1, \cdots, \text{csm}_n\}$, $M_u$ is the undersampling mask}
\State{$\mathbf{x}_{N} \sim \mathcal{N}(\mathbf{F}^{-1}(\mathbf{M}_l\mathbf{y}), \boldsymbol{\mathcal{F}}_h)$}
\For{$i = N-1$ to $0$}
\State{$\mathbf{z} \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$}
\State{$\mathbf{g} \leftarrow \boldsymbol{\mathcal{F}}_h(\mathbf{s}_{\boldsymbol{\theta^*}}\left(\mathbf{x}_{i+1}, i+1\right)$})
\State{$\mathbf{G}=\sum_{j=1}^{n} \text{csm}_j^{*} \cdot \mathbf{F}^{-1}\left(\mathbf{F}(\text{csm} \cdot \mathbf{x}_i) \cdot \mathbf{M_u} - \mathbf{\hat{y}}\right)$}
\State{$\epsilon \leftarrow \lambda_1\left(\|\mathbf{g}\|_{2} /\|\mathbf{G}\|_{2}\right)$}
\State{$\mathbf{x}_{i} \leftarrow \mathbf{x}_{i+1}+\dfrac{1}{2}\beta_{i+1}\boldsymbol{\mathcal{F}}_h(\mathbf{x}_i)+\beta_{i+1}(\mathbf{g}-\epsilon\mathbf{G})+\sqrt{\beta_{i+1}}\boldsymbol{\mathcal{F}}_h(\mathbf{z})$}
\For{$k \gets 1$ to $M$}
\State{$\mathbf{z} \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$}
\State{$\mathbf{g} \leftarrow \boldsymbol{\mathcal{F}}_h(\mathbf{s}_{\boldsymbol{\theta}^*}\left(\mathbf{x}_{i}^{k-1}, i\right)$})
\State{$\mathbf{G}=\sum_{j=1}^{n} \text{csm}_j^{*} \cdot \mathbf{F}^{-1}\left(\mathbf{F}(\text{csm} \cdot \mathbf{x}_i^k) \cdot \mathbf{M_u} - \mathbf{\hat{y}}\right)$}
\State{$\epsilon_1 \leftarrow 2 \alpha_{i}\left(r\|\mathbf{z}\|_{2} /\|\mathbf{g}\|_{2}\right)^{2}$}
\State{$\epsilon_2 \leftarrow \|\mathbf{g}\|_{2} /(\lambda_2 \cdot \|\mathbf{G}\|_{2})$}
\State{$\mathbf{x}_{i}^{k} \leftarrow \mathbf{x}_{i}^{k-1}+\epsilon_1 (\mathbf{g}-\epsilon_2\mathbf{G})+\sqrt{2 \epsilon_1} \boldsymbol{\mathcal{F}}_h(\mathbf{z})$}
\EndFor
\State{$\mathbf{x}_{i-1}^{0} \leftarrow \mathbf{x}_{i}^{M}$}
\EndFor
\item[]
\Return{${\mathbf{x}}_0^0$} \Comment{$\mathbf{x}_0 = \mathbf{x}_i^0$}
\end{algorithmic}
| \begin{algorithmic}
[1]
\Require{$\{\beta_i\}_{i=1}^N, \{\alpha_i\}_{i=1}^N, \text{csm}, \mathbf{\hat{y}}, \lambda_1, \lambda_2, r, N, M, \mathbf{M_u}$.} \Comment{$\text{csm} = \{\text{csm}_1, \cdots, \text{csm}_n\}$, $M_u$ is the undersampling mask}
\State{$\mathbf{x}_{N} \sim \mathcal{N}(\mathbf{F}^{-1}(\mathbf{M}_l\mathbf{y}), \boldsymbol{\mathcal{F}}_h)$}
\For{$i = N-1$ to $0$}
\State{$\mathbf{z} \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$}
\State{$\mathbf{g} \leftarrow \boldsymbol{\mathcal{F}}_h(\mathbf{s}_{\boldsymbol{\theta^*}}\left(\mathbf{x}_{i+1}, i+1\right)$})
\State{$\mathbf{G}=\sum_{j=1}^{n} \text{csm}_j^{*} \cdot \mathbf{F}^{-1}\left(\mathbf{F}(\text{csm} \cdot \mathbf{x}_i) \cdot \mathbf{M_u} - \mathbf{\hat{y}}\right)$}
\State{$\epsilon \leftarrow \lambda_1\left(\|\mathbf{g}\|_{2} /\|\mathbf{G}\|_{2}\right)$}
\State{$\mathbf{x}_{i} \leftarrow \mathbf{x}_{i+1}+\dfrac{1}{2}\beta_{i+1}\boldsymbol{\mathcal{F}}_h(\mathbf{x}_i)+\beta_{i+1}(\mathbf{g}-\epsilon\mathbf{G})+\sqrt{\beta_{i+1}}\boldsymbol{\mathcal{F}}_h(\mathbf{z})$}
\For{$k \gets 1$ to $M$}
\State{$\mathbf{z} \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$}
\State{$\mathbf{g} \leftarrow \boldsymbol{\mathcal{F}}_h(\mathbf{s}_{\boldsymbol{\theta}^*}\left(\mathbf{x}_{i}^{k-1}, i\right)$})
\State{$\mathbf{G}=\sum_{j=1}^{n} \text{csm}_j^{*} \cdot \mathbf{F}^{-1}\left(\mathbf{F}(\text{csm} \cdot \mathbf{x}_i^k) \cdot \mathbf{M_u} - \mathbf{\hat{y}}\right)$}
\State{$\epsilon_1 \leftarrow 2 \alpha_{i}\left(r\|\mathbf{z}\|_{2} /\|\mathbf{g}\|_{2}\right)^{2}$}
\State{$\epsilon_2 \leftarrow \|\mathbf{g}\|_{2} /(\lambda_2 \cdot \|\mathbf{G}\|_{2})$}
\State{$\mathbf{x}_{i}^{k} \leftarrow \mathbf{x}_{i}^{k-1}+\epsilon_1 (\mathbf{g}-\epsilon_2\mathbf{G})+\sqrt{2 \epsilon_1} \boldsymbol{\mathcal{F}}_h(\mathbf{z})$}
\EndFor
\State{$\mathbf{x}_{i-1}^{0} \leftarrow \mathbf{x}_{i}^{M}$}
\EndFor
\item[]
\Return{${\mathbf{x}}_0^0$} \Comment{$\mathbf{x}_0 = \mathbf{x}_i^0$}
\end{algorithmic} | "https://arxiv.org/src/2208.05481" | "2208.05481.tar.gz" | "2024-01-20" | {
"title": "high-frequency space diffusion models for accelerated mri",
"id": "2208.05481",
"abstract": "diffusion models with continuous stochastic differential equations (sdes) have shown superior performances in image generation. it can serve as a deep generative prior to solving the inverse problem in magnetic resonance (mr) reconstruction. however, low-frequency regions of $k$-space data are typically fully sampled in fast mr imaging, while existing diffusion models are performed throughout the entire image or $k$-space, inevitably introducing uncertainty in the reconstruction of low-frequency regions. additionally, existing diffusion models often demand substantial iterations to converge, resulting in time-consuming reconstructions. to address these challenges, we propose a novel sde tailored specifically for mr reconstruction with the diffusion process in high-frequency space (referred to as hfs-sde). this approach ensures determinism in the fully sampled low-frequency regions and accelerates the sampling procedure of reverse diffusion. experiments conducted on the publicly available fastmri dataset demonstrate that the proposed hfs-sde method outperforms traditional parallel imaging methods, supervised deep learning, and existing diffusion models in terms of reconstruction accuracy and stability. the fast convergence properties are also confirmed through theoretical and experimental validation. our code and weights are available at https://github.com/aboriginer/hfs-sde.",
"categories": "eess.iv cs.cv cs.lg",
"doi": "10.1109/tmi.2024.3351702",
"created": "2022-08-10",
"updated": "2024-01-20",
"authors": [
"chentao cao",
"zhuo-xu cui",
"yue wang",
"shaonan liu",
"taijin chen",
"hairong zheng",
"dong liang",
"yanjie zhu"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2208.05481"
} | "2024-03-15T09:17:42.639884" | {
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} | [] | "algorithm" | "f40fb3f7-924b-4656-9ff3-dbe66c209e55" | 1965 | hard |
|
\begin{algorithm}
State Smoothing
\end{algorithm}
| \begin{algorithm}
State Smoothing
\end{algorithm} | "https://arxiv.org/src/2402.08051" | "2402.08051.tar.gz" | "2024-02-12" | {
"title": "on bayesian filtering for markov regime switching models",
"id": "2402.08051",
"abstract": "this paper presents a framework for empirical analysis of dynamic macroeconomic models using bayesian filtering, with a specific focus on the state-space formulation of dynamic stochastic general equilibrium (dsge) models with multiple regimes. we outline the theoretical foundations of model estimation, provide the details of two families of powerful multiple-regime filters, imm and gpb, and construct corresponding multiple-regime smoothers. a simulation exercise, based on a prototypical new keynesian dsge model, is used to demonstrate the computational robustness of the proposed filters and smoothers and evaluate their accuracy and speed for a selection of filters from each family. we show that the canonical imm filter is faster and is no less, and often more, accurate than its competitors within imm and gpb families, the latter including the commonly used kim and nelson (1999) filter. using it with the matching smoother improves the precision in recovering unobserved variables by about 25 percent. furthermore, applying it to the u.s. 1947-2023 macroeconomic time series, we successfully identify significant past policy shifts including those related to the post-covid-19 period. our results demonstrate the practical applicability and potential of the proposed routines in macroeconomic analysis.",
"categories": "econ.em",
"doi": "",
"created": "2024-02-12",
"updated": "",
"authors": [
"nigar hashimzade",
"oleg kirsanov",
"tatiana kirsanova",
"junior maih"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.08051"
} | "2024-03-15T04:21:14.605813" | {
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} | [] | "algorithm" | "4769e97e-aa4f-4112-8549-c210514be07f" | 49 | easy |
|
\begin{algorithm}
\label{subalg}
\begin{description}
\item[{\sc Input:}]
Three integers $m$, $n$, and $r$ satisfying $0<2r \le n\le m$;
an $m\times n$ matrix $M$, given explicitly or implicitly.
\item[{\sc Initialization:}]
\begin{enumerate}
\item Generate a pair of independent abridged SRHT matrices $F$ and $H$ of length 3 and sizes $2r\times m$ and $n\times r$, respectively
(see Appendix \ref{spreprmlt});
\item Compute the sketches $FM$ and $MH$.
\end{enumerate}
\item[{\sc Computations:}]
\begin{enumerate}
\item
Compute matrix $Q$ as the Q factor of the thin QR factorization\footnote{Recall the
uniqueness of the thin QR factorization of an $m\times k$ matrix
where an $k\times k$ upper triangular factor
$R$ has positive diagonal entries
\cite[Thm. 5.3.2]{GL13}.} of $EH$.
\item
Compute the matrices $U$ and $T$ of the thin QR factorization $UT$ of $FQ$.
\item
Compute and output the matrix $\Delta = QT^+U^T(FM)$, an LRA of $M$.
\end{enumerate}
\end{description}
\end{algorithm}
| \begin{algorithm}
\begin{description}
\item[{\sc Input:}]
Three integers $m$, $n$, and $r$ satisfying $0<2r \le n\le m$;
an $m\times n$ matrix $M$, given explicitly or implicitly.
\item[{\sc Initialization:}]
\begin{enumerate}
\item Generate a pair of independent abridged SRHT matrices $F$ and $H$ of length 3 and sizes $2r\times m$ and $n\times r$, respectively
(see Appendix \ref{spreprmlt});
\item Compute the sketches $FM$ and $MH$.
\end{enumerate}
\item[{\sc Computations:}]
\begin{enumerate}
\item
Compute matrix $Q$ as the Q factor of the thin QR factorization\footnote{Recall the
uniqueness of the thin QR factorization of an $m\times k$ matrix
where an $k\times k$ upper triangular factor
$R$ has positive diagonal entries
\cite[Thm. 5.3.2]{GL13}.} of $EH$.
\item
Compute the matrices $U$ and $T$ of the thin QR factorization $UT$ of $FQ$.
\item
Compute and output the matrix $\Delta = QT^+U^T(FM)$, an LRA of $M$.
\end{enumerate}
\end{description}
\end{algorithm} | "https://arxiv.org/src/1906.04223" | "1906.04223.tar.gz" | "2024-01-06" | {
"title": "superfast escalators for near-optimal low rank approximation of a matrix",
"id": "1906.04223",
"abstract": "a superfast (aka sublinear cost) algorithm only accesses a small fraction of all entries of an input matrix. we seek such algorithms for low rank approximation (lra) of a matrix, but for some matrix families any such algorithm at best halves the large error of the trivial approximation by the matrix filled with 0s. nevertheless, our simple superfast escalating algorithms compute near optimal lras of a new large class of real-world matrices according to our analysis and numerical tests.",
"categories": "math.na cs.na",
"doi": "",
"created": "2019-06-10",
"updated": "2024-01-06",
"authors": [
"soo go",
"qi luan",
"victor y. pan"
],
"affiliation": [],
"url": "https://arxiv.org/abs/1906.04223"
} | "2024-03-15T06:33:14.119039" | {
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} | [] | "algorithm" | "0c384e20-7482-42f6-a13b-fd99b46b8db8" | 974 | medium |
|
\begin{algorithm}[h!]
\caption{Regression-Tree}\label{alg:rt}
\begin{algorithmic}
\State {\textbf{Input:}} $\{X_i,T_i,Y_i\}_{i=1}^n$, bandwidth $h$, tree depth $K$, number of features $L$
\If{K=1}
\State Return $(\arg\max_p\sum_{i=1}^nK(\frac{T_i-p}{h})\frac{Y_i}{f(T_i\mid X_i)}, \max_p\sum_{i=1}^nK(\frac{T_i-p}{h})\frac{Y_i}{f(T_i\mid X_i)})$.
\Else
\State Initialize Reward $=0$, tree = $\emptyset$
\State Draw $l_1,\dots,l_L$ randomly from $d$ total features without replacement
\For{$l = l_1,\dots,l_L$}
\State Sort the data along $x_l$
\For{$i=1,\dots,n$}
\State (Tree\_left, Reward\_left) = \text{Regression-Tree}($\{X_j,T_j,Y_j\}_{j=1}^i,L-1$)
\State (Tree\_right, Reward\_right) = \text{Regression-Tree}($\{X_j,T_j,Y_j\}_{j=i}^n,L-1$)
\If{Reward\_left+Reward\_right$>$Reward}
\State Reward = Reward\_left+Reward
\State Tree = $[l,\frac{X_{l,i}+X_{l,i+1}}{2},\text{Tree\_left},\text{Tree\_right}]$
\EndIf
\EndFor
\EndFor
\State Return (Tree, Reward)
\EndIf
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[h!]
\caption{Regression-Tree}\begin{algorithmic}
\State {\textbf{Input:}} $\{X_i,T_i,Y_i\}_{i=1}^n$, bandwidth $h$, tree depth $K$, number of features $L$
\If{K=1}
\State Return $(\arg\max_p\sum_{i=1}^nK(\frac{T_i-p}{h})\frac{Y_i}{f(T_i\mid X_i)}, \max_p\sum_{i=1}^nK(\frac{T_i-p}{h})\frac{Y_i}{f(T_i\mid X_i)})$.
\Else
\State Initialize Reward $=0$, tree = $\emptyset$
\State Draw $l_1,\dots,l_L$ randomly from $d$ total features without replacement
\For{$l = l_1,\dots,l_L$}
\State Sort the data along $x_l$
\For{$i=1,\dots,n$}
\State (Tree\_left, Reward\_left) = \text{Regression-Tree}($\{X_j,T_j,Y_j\}_{j=1}^i,L-1$)
\State (Tree\_right, Reward\_right) = \text{Regression-Tree}($\{X_j,T_j,Y_j\}_{j=i}^n,L-1$)
\If{Reward\_left+Reward\_right$>$Reward}
\State Reward = Reward\_left+Reward
\State Tree = $[l,\frac{X_{l,i}+X_{l,i+1}}{2},\text{Tree\_left},\text{Tree\_right}]$
\EndIf
\EndFor
\EndFor
\State Return (Tree, Reward)
\EndIf
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2402.02535" | "2402.02535.tar.gz" | "2024-02-04" | {
"title": "data-driven policy learning for a continuous treatment",
"id": "2402.02535",
"abstract": "this paper studies policy learning under the condition of unconfoundedness with a continuous treatment variable. our research begins by employing kernel-based inverse propensity-weighted (ipw) methods to estimate policy welfare. we aim to approximate the optimal policy within a global policy class characterized by infinite vapnik-chervonenkis (vc) dimension. this is achieved through the utilization of a sequence of sieve policy classes, each with finite vc dimension. preliminary analysis reveals that welfare regret comprises of three components: global welfare deficiency, variance, and bias. this leads to the necessity of simultaneously selecting the optimal bandwidth for estimation and the optimal policy class for welfare approximation. to tackle this challenge, we introduce a semi-data-driven strategy that employs penalization techniques. this approach yields oracle inequalities that adeptly balance the three components of welfare regret without prior knowledge of the welfare deficiency. by utilizing precise maximal and concentration inequalities, we derive sharper regret bounds than those currently available in the literature. in instances where the propensity score is unknown, we adopt the doubly robust (dr) moment condition tailored to the continuous treatment setting. in alignment with the binary-treatment case, the dr welfare regret closely parallels the ipw welfare regret, given the fast convergence of nuisance estimators.",
"categories": "econ.em",
"doi": "",
"created": "2024-02-04",
"updated": "",
"authors": [
"chunrong ai",
"yue fang",
"haitian xie"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.02535"
} | "2024-03-15T05:00:53.749181" | {
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} | [] | "algorithm" | "221f65db-97b3-4ab7-879f-0d36d700380f" | 985 | medium |
|
\begin{algorithm}
\caption{VS-BO}
\begin{algorithmic}[1]
\State \textbf{Input}: $f(\mathbf{x})$, $\mathcal{X}=[0,1]^{D}$, $N_{init}$, $N$, $N_{vs}$
\State \textbf{Output}: Approximate maximizer $\mathbf{x}^{max}$
\State Initialize the set of $\mathbf{x}_{ipt}$ to be all variables in $\mathbf{x}$, $\mathbf{x}_{ipt}=\mathbf{x}$, and $\mathbf{x}_{nipt}=\emptyset$
\State Uniformly sample $N_{init}$ points $\mathbf{x}^{i}$ and evaluate $y^{i}=f(\mathbf{x}^{i})$, let $\mathcal{D}=\{(\mathbf{x}^{i},y^{i})\}_{i=1}^{N_{init}}$
\State Initialize the distribution $p(\mathbf{x}\mid \mathcal{D})$
\For {$t=N_{init}+1,N_{init}+2,\ldots N_{init}+N$}
\If {mod($t-N_{init}$, $N_{vs}$) = 0}
\State Variable selection to update $\mathbf{x}_{ipt}$ and let $\mathbf{x}_{nipt}=\mathbf{x}\setminus \mathbf{x}_{ipt}$ (Algorithm~\ref{alg:VS_detail})
\State Update $p(\mathbf{x}\mid \mathcal{D})$, then derive the conditional distribution $p(\mathbf{x}_{nipt}\mid \mathbf{x}_{ipt},\mathcal{D})$
\EndIf
\State Fit a GP to $\mathcal{D}_{ipt}:=\{(\mathbf{x}_{ipt}^{i},y^{i})\}_{i=1}^{t-1}$
\State Maximize the acquisition function to obtain $\mathbf{x}_{ipt}^{t}$.
\State Sample $\mathbf{x}_{nipt}^{t}$ from $p(\mathbf{x}_{nipt}\mid \mathbf{x}_{ipt}^{t},\mathcal{D})$
\State Evaluate $y^{t}=f(\mathbf{x}^{t})+\epsilon^{t}=f(\{\mathbf{x}_{ipt}^{t},\mathbf{x}_{nipt}^{t}\})+\epsilon^{t}$ and update $\mathcal{D}=\mathcal{D}\cup \{(\mathbf{x}^{t},y^{t})\}$
\EndFor
\State\Return $\mathbf{x}^{max}$ which is equal to $\mathbf{x}^{i}$ with maximal $y^{i}$
\end{algorithmic}
\label{alg:VSBO}
\end{algorithm}
| \begin{algorithm}
\caption{VS-BO}
\begin{algorithmic}
[1]
\State \textbf{Input}: $f(\mathbf{x})$, $\mathcal{X}=[0,1]^{D}$, $N_{init}$, $N$, $N_{vs}$
\State \textbf{Output}: Approximate maximizer $\mathbf{x}^{max}$
\State Initialize the set of $\mathbf{x}_{ipt}$ to be all variables in $\mathbf{x}$, $\mathbf{x}_{ipt}=\mathbf{x}$, and $\mathbf{x}_{nipt}=\emptyset$
\State Uniformly sample $N_{init}$ points $\mathbf{x}^{i}$ and evaluate $y^{i}=f(\mathbf{x}^{i})$, let $\mathcal{D}=\{(\mathbf{x}^{i},y^{i})\}_{i=1}^{N_{init}}$
\State Initialize the distribution $p(\mathbf{x}\mid \mathcal{D})$
\For {$t=N_{init}+1,N_{init}+2,\ldots N_{init}+N$}
\If {mod($t-N_{init}$, $N_{vs}$) = 0}
\State Variable selection to update $\mathbf{x}_{ipt}$ and let $\mathbf{x}_{nipt}=\mathbf{x}\setminus \mathbf{x}_{ipt}$ (Algorithm~\ref{alg:VS_detail})
\State Update $p(\mathbf{x}\mid \mathcal{D})$, then derive the conditional distribution $p(\mathbf{x}_{nipt}\mid \mathbf{x}_{ipt},\mathcal{D})$
\EndIf
\State Fit a GP to $\mathcal{D}_{ipt}:=\{(\mathbf{x}_{ipt}^{i},y^{i})\}_{i=1}^{t-1}$
\State Maximize the acquisition function to obtain $\mathbf{x}_{ipt}^{t}$.
\State Sample $\mathbf{x}_{nipt}^{t}$ from $p(\mathbf{x}_{nipt}\mid \mathbf{x}_{ipt}^{t},\mathcal{D})$
\State Evaluate $y^{t}=f(\mathbf{x}^{t})+\epsilon^{t}=f(\{\mathbf{x}_{ipt}^{t},\mathbf{x}_{nipt}^{t}\})+\epsilon^{t}$ and update $\mathcal{D}=\mathcal{D}\cup \{(\mathbf{x}^{t},y^{t})\}$
\EndFor
\State\Return $\mathbf{x}^{max}$ which is equal to $\mathbf{x}^{i}$ with maximal $y^{i}$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2109.09264" | "2109.09264.tar.gz" | "2024-02-12" | {
"title": "computationally efficient high-dimensional bayesian optimization via variable selection",
"id": "2109.09264",
"abstract": "bayesian optimization (bo) is a method for globally optimizing black-box functions. while bo has been successfully applied to many scenarios, developing effective bo algorithms that scale to functions with high-dimensional domains is still a challenge. optimizing such functions by vanilla bo is extremely time-consuming. alternative strategies for high-dimensional bo that are based on the idea of embedding the high-dimensional space to the one with low dimension are sensitive to the choice of the embedding dimension, which needs to be pre-specified. we develop a new computationally efficient high-dimensional bo method that exploits variable selection. our method is able to automatically learn axis-aligned sub-spaces, i.e. spaces containing selected variables, without the demand of any pre-specified hyperparameters. we theoretically analyze the computational complexity of our algorithm and derive the regret bound. we empirically show the efficacy of our method on several synthetic and real problems.",
"categories": "cs.lg stat.ml",
"doi": "",
"created": "2021-09-19",
"updated": "2024-02-12",
"authors": [
"yihang shen",
"carl kingsford"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2109.09264"
} | "2024-03-15T06:47:05.818231" | {
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} | [] | "algorithm" | "262efc37-f989-4cd7-afaf-cbb3afc5eae1" | 1563 | hard |
|
\begin{algorithm}[H]
\begin{enumerate}
\item Fix a degree $d$, starting from $d=1$.
\item Find all curves at degree $d$, and form the set $\mathcal{S}:=\{\mathcal{C}\in \mathcal{M}_X|\text{deg}(\mathcal{C})=d\}$. Since at linear order $\psi^{\vec{n}}=q^{\vec{n}}$, the GW or GV invariants can be read off from the coefficient of the corresponding monomial in $\mathcal{F}_a^{\text{inst.}}$, cf.~\eqref{eq:rerepeatperturbative_GV_formula}. Thus, we extract all invariants from the curves in $S$.
\item Compute either $q^{\vec{n}}$ or $\text{Li}_2(q^{\vec{n}})$ for all curves in $\mathcal{S}$ in parallel. This is the most expensive step in the entire algorithm, as it involves many polynomial multiplications. To improve efficiency, we keep some intermediate results, so that subsequent computations require fewer polynomial multiplications.
\item Subtract the computed terms, multiplied by the appropriate factor, so as to eliminate the corresponding monomials in $\mathcal{F}_a^{\text{inst.}}$.
\item Increment $d$ by one, and repeat from the first step, until the maximum degree is reached.
\end{enumerate}
\caption{Find enumerative invariants iteratively.}
\end{algorithm}
| \begin{algorithm}
[H]
\begin{enumerate}
\item Fix a degree $d$, starting from $d=1$.
\item Find all curves at degree $d$, and form the set $\mathcal{S}:=\{\mathcal{C}\in \mathcal{M}_X|\text{deg}(\mathcal{C})=d\}$. Since at linear order $\psi^{\vec{n}}=q^{\vec{n}}$, the GW or GV invariants can be read off from the coefficient of the corresponding monomial in $\mathcal{F}_a^{\text{inst.}}$, cf.~\eqref{eq:rerepeatperturbative_GV_formula}. Thus, we extract all invariants from the curves in $S$.
\item Compute either $q^{\vec{n}}$ or $\text{Li}_2(q^{\vec{n}})$ for all curves in $\mathcal{S}$ in parallel. This is the most expensive step in the entire algorithm, as it involves many polynomial multiplications. To improve efficiency, we keep some intermediate results, so that subsequent computations require fewer polynomial multiplications.
\item Subtract the computed terms, multiplied by the appropriate factor, so as to eliminate the corresponding monomials in $\mathcal{F}_a^{\text{inst.}}$.
\item Increment $d$ by one, and repeat from the first step, until the maximum degree is reached.
\end{enumerate}
\caption{Find enumerative invariants iteratively.}
\end{algorithm} | "https://arxiv.org/src/2303.00757" | "2303.00757.tar.gz" | "2024-01-19" | {
"title": "computational mirror symmetry",
"id": "2303.00757",
"abstract": "we present an efficient algorithm for computing the prepotential in compactifications of type ii string theory on mirror pairs of calabi-yau threefolds in toric varieties. applying this method, we exhibit the first systematic computation of genus-zero gopakumar-vafa invariants in compact threefolds with many moduli, including examples with up to 491 vector multiplets.",
"categories": "hep-th",
"doi": "",
"created": "2023-03-01",
"updated": "2024-01-19",
"authors": [
"mehmet demirtas",
"manki kim",
"liam mcallister",
"jakob moritz",
"andres rios-tascon"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2303.00757"
} | "2024-03-15T07:37:52.714955" | {
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|
\label{alg:expansionrange}\begin{algorithmic}[1]
\State Input:
\begin{enumerate}
\item[1] Difference equation system $\Sigma$ with algebraic or analytic transcendental functions.
\item[2] For each parameter $\mu_i$ appearing as an argument of a transcendental function, user-specified acceptable domains for each $\mu_i$, denoted $R_{\mu_i}$.
\item[3] Observed data $\bar{y}(t_0),\bar{y}(t_1),\ldots,\bar{y}(t_r)$
\end{enumerate}
\State Output: Domains $R_{G_{j}}$ over which each transcendental function $G_j$ in $\Sigma$ is expanded.
\Procedure{Expansion range}{} By substitution of maximums and minimums (modulus) of \phantom{-----} $R_{\mu_i}$ into arguments of $G_j$, as relevant, determine radii of discs $R_{L_t}$.
\State Call the argument of $G_j$ as $\tilde{G}_j=:\tau_j$.
\For{$j=1\to r$, $t$ fixed}
\State $\displaystyle R_{G_{j,t}}:=\left\{\min_{R
_{\mu_i^*,i=1,\ldots,s} }|\tilde{G}_j|\le |\tau_j| \le\max_{R
_{\mu_i^*,i=1,\ldots,s} }|\tilde{G}_j|\right\}$
\EndFor
\EndProcedure
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Input:
\begin{enumerate}
\item[1] Difference equation system $\Sigma$ with algebraic or analytic transcendental functions.
\item[2] For each parameter $\mu_i$ appearing as an argument of a transcendental function, user-specified acceptable domains for each $\mu_i$, denoted $R_{\mu_i}$.
\item[3] Observed data $\bar{y}(t_0),\bar{y}(t_1),\ldots,\bar{y}(t_r)$
\end{enumerate}
\State Output: Domains $R_{G_{j}}$ over which each transcendental function $G_j$ in $\Sigma$ is expanded.
\Procedure{Expansion range}{} By substitution of maximums and minimums (modulus) of \phantom{-----} $R_{\mu_i}$ into arguments of $G_j$, as relevant, determine radii of discs $R_{L_t}$.
\State Call the argument of $G_j$ as $\tilde{G}_j=:\tau_j$.
\For{$j=1\to r$, $t$ fixed}
\State $\displaystyle R_{G_{j,t}}:=\left\{\min_{R
_{\mu_i^*,i=1,\ldots,s} }|\tilde{G}_j|\le |\tau_j| \le\max_{R
_{\mu_i^*,i=1,\ldots,s} }|\tilde{G}_j|\right\}$
\EndFor
\EndProcedure
\end{algorithmic} | "https://arxiv.org/src/2401.16220" | "2401.16220.tar.gz" | "2024-01-29" | {
"title": "symbolic-numeric algorithm for parameter estimation in discrete-time models with $\\exp$",
"id": "2401.16220",
"abstract": "determining unknown parameter values in dynamic models is crucial for accurate analysis of the dynamics across the different scientific disciplines. discrete-time dynamic models are widely used to model biological processes, but it is often difficult to determine these parameters. in this paper, we propose a robust symbolic-numeric approach for parameter estimation in discrete-time models that involve non-algebraic functions such as exp. we illustrate the performance (precision) of our approach by applying our approach to the flour beetle (lpa) model, an archetypal discrete-time model in biology. unlike optimization-based methods, our algorithm guarantees to find all solutions of the parameter values given time-series data for the measured variables.",
"categories": "q-bio.qm cs.sc cs.sy eess.sy math.ac math.ds",
"doi": "",
"created": "2024-01-29",
"updated": "",
"authors": [
"yosef berman",
"joshua forrest",
"matthew grote",
"alexey ovchinnikov",
"sonia rueda"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.16220"
} | "2024-03-15T06:38:23.919697" | {
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} | [] | "algorithm" | "dd97095e-8c9d-408a-b12f-02545fcf6309" | 984 | medium |
|
\begin{algorithm}[htpb]
\caption{Randomized $r$-sets-Douglas-Rachford with momentum (mRrDR) \label{r-mRDRK}}
\begin{algorithmic}
\Require
$A\in \mathbb{R}^{m\times n}$, $b\in \mathbb{R}^m$, $r\in\mathbb{Z}_{+}$, $k=1$, extrapolation/relaxation parameter $\alpha$, the heavy ball momentum parameter $\beta$, and initial vectors $x^1,x^0\in \mathbb{R}^{n}$.
\begin{enumerate}
\item[1:] Set $z^{k}_0:=x^k$.
\item[2:] {\bf for $\ell=1,\ldots,r$ do}
\item[3:] \ \ \ Select $j_{k_{\ell}}\in\{1,\ldots,m\}$ with probability $\mbox{Pr}(\mbox{row}=j_{k_{\ell}})=\frac{\|a_{j_{k_{\ell}}}\|^2_2}{\|A\|_{F}^2}$.
\item[4:] \ \ \ Compute
$$
z_{\ell}^{k}:=z_{\ell-1}^k-2\frac{\langle a_{j_{k_{\ell}}},z_{\ell-1}^k\rangle-b_{j_{k_{\ell}}}}{\|a_{j_{k_\ell}}\|^2_2}a_{j_{k_{\ell}}}.
$$
\item[5:] {\bf end for}
\item[6:] Update
$$
x^{k+1}:=(1-\alpha) x^k+\alpha z_{r}^k+\beta(x^k-x^{k-1}).
$$
\item[7:] If the stopping rule is satisfied, stop and go to output. Otherwise, set $k=k+1$ and return to Step $1$.
\end{enumerate}
\Ensure
The approximate solution $ x^k $.
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[htpb]
\caption{Randomized $r$-sets-Douglas-Rachford with momentum (mRrDR) }
\begin{algorithmic}
\Require
$A\in \mathbb{R}^{m\times n}$, $b\in \mathbb{R}^m$, $r\in\mathbb{Z}_{+}$, $k=1$, extrapolation/relaxation parameter $\alpha$, the heavy ball momentum parameter $\beta$, and initial vectors $x^1,x^0\in \mathbb{R}^{n}$.
\begin{enumerate}
\item[1:] Set $z^{k}_0:=x^k$.
\item[2:] {\bf for $\ell=1,\ldots,r$ do}
\item[3:] \ \ \ Select $j_{k_{\ell}}\in\{1,\ldots,m\}$ with probability $\mbox{Pr}(\mbox{row}=j_{k_{\ell}})=\frac{\|a_{j_{k_{\ell}}}\|^2_2}{\|A\|_{F}^2}$.
\item[4:] \ \ \ Compute
$$
z_{\ell}^{k}:=z_{\ell-1}^k-2\frac{\langle a_{j_{k_{\ell}}},z_{\ell-1}^k\rangle-b_{j_{k_{\ell}}}}{\|a_{j_{k_\ell}}\|^2_2}a_{j_{k_{\ell}}}.
$$
\item[5:] {\bf end for}
\item[6:] Update
$$
x^{k+1}:=(1-\alpha) x^k+\alpha z_{r}^k+\beta(x^k-x^{k-1}).
$$
\item[7:] If the stopping rule is satisfied, stop and go to output. Otherwise, set $k=k+1$ and return to Step $1$.
\end{enumerate}
\Ensure
The approximate solution $ x^k $.
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2207.04291" | "2207.04291.tar.gz" | "2024-01-09" | {
"title": "randomized douglas-rachford methods for linear systems: improved accuracy and efficiency",
"id": "2207.04291",
"abstract": "the douglas-rachford (dr) method is a widely used method for finding a point in the intersection of two closed convex sets (feasibility problem). however, the method converges weakly and the associated rate of convergence is hard to analyze in general. in addition, the direct extension of the dr method for solving more-than-two-sets feasibility problems, called the $r$-sets-dr method, is not necessarily convergent. to improve the efficiency of the optimization algorithms, the introduction of randomization and the momentum technique has attracted increasing attention. in this paper, we propose the randomized $r$-sets-dr (rrdr) method for solving the feasibility problem derived from linear systems, showing the benefit of the randomization as it brings linear convergence in expectation to the otherwise divergent $r$-sets-dr method. furthermore, the convergence rate does not depend on the dimension of the coefficient matrix. we also study rrdr with heavy ball momentum and establish its accelerated rate. numerical experiments are provided to confirm our results and demonstrate the notable improvements in accuracy and efficiency of the dr method, brought by the randomization and the momentum technique.",
"categories": "math.oc",
"doi": "",
"created": "2022-07-09",
"updated": "2024-01-09",
"authors": [
"deren han",
"yansheng su",
"jiaxin xie"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2207.04291"
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} | [] | "algorithm" | "73720df1-3f10-487a-81bc-3caecb06dd30" | 1066 | medium |
|
\begin{algorithm}
\caption{Rejection Sampling algorithm to draw $y^{PS = S4}|x$}\label{alg:one}
\begin{algorithmic}
\State \textbf{Input:} $x, \alpha, z, y$
\For{$i = 1 \text{ to } 8000$}
\State Draw $u_i$ from Uniform(0,1)
\State Draw $y^i_N$ from Normal(1.5, 4)
\State $C \gets \frac{f(y^i_N|PS = S4,x,a,z)}{M*f_{Y_N}(y^i_N)}$
\If{$u_i < C$}
Accept $y^i_N$
\ElsIf{$u_i > C$}
Reject $y^i_N$
\EndIf
\EndFor
\State \textbf{Output:} $y^{PS = S4}|x = $ the mean of the accepted $y^i_N$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Rejection Sampling algorithm to draw $y^{PS = S4}|x$}\begin{algorithmic}
\State \textbf{Input:} $x, \alpha, z, y$
\For{$i = 1 \text{ to } 8000$}
\State Draw $u_i$ from Uniform(0,1)
\State Draw $y^i_N$ from Normal(1.5, 4)
\State $C \gets \frac{f(y^i_N|PS = S4,x,a,z)}{M*f_{Y_N}(y^i_N)}$
\If{$u_i < C$}
Accept $y^i_N$
\ElsIf{$u_i > C$}
Reject $y^i_N$
\EndIf
\EndFor
\State \textbf{Output:} $y^{PS = S4}|x = $ the mean of the accepted $y^i_N$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2207.08964" | "2207.08964.tar.gz" | "2024-02-20" | {
"title": "sensitivity analysis for constructing optimal regimes in the presence of treatment non-compliance",
"id": "2207.08964",
"abstract": "the current body of research on developing optimal treatment strategies often places emphasis on intention-to-treat analyses, which fail to take into account the compliance behavior of individuals. methods based on instrumental variables have been developed to determine optimal treatment strategies in the presence of endogeneity. however, these existing methods are not applicable when there are two active treatment options and the average causal effects of the treatments cannot be identified using a binary instrument. in order to address this limitation, we present a procedure that can identify an optimal treatment strategy and the corresponding value function as a function of a vector of sensitivity parameters. additionally, we derive the canonical gradient of the target parameter and propose a multiply robust classification-based estimator for the optimal treatment strategy. through simulations, we demonstrate the practical need for and usefulness of our proposed method. we apply our method to a randomized trial on adaptive treatment for alcohol and cocaine dependence.",
"categories": "stat.me",
"doi": "",
"created": "2022-07-18",
"updated": "2024-02-20",
"authors": [
"cuong t. pham",
"kevin g. lynch",
"james r. mckay",
"ashkan ertefaie"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2207.08964"
} | "2024-03-15T04:28:35.761087" | {
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} | [] | "algorithm" | "27b9cf55-cedc-40b2-bbe1-d571efbc07f6" | 500 | easy |
|
\begin{algorithmic}
\Require {$\mathfrak{c} \in [4, 14]$, P} \Comment{P is the pattern set}
\State$i \gets 0,$
\State$sum\_{d_2} = 0$
\While{$i \leq |P|,$}
\State$\mathbf{x} \gets \mathfrak{b}^{(i)}$
\State$sum\_{d_1} = 0$
\While{$j\leq \mathfrak{K}$}
\State\Comment{$\mathfrak{K}$ : calculating the avg.}
\State$\mathfrak{\bar{b}^{(i)}} \gets$ invert polarities of $\mathfrak{E}\%$ of $\mathfrak{b}^{(i)}$
\State$\mathbf{y} \gets CAM(\mathfrak{c}, \mathfrak{\bar{b}}^{(i)})$
\State$d_1 \gets \mathfrak{D}(\mathbf{x,y})$
\State$sum\_{d_1} \gets sum_{d_1} + d_1$
\EndWhile
\State$d_2 \gets \textbf{mean}(sum_{d_1})$
\State$sum\_{d_2} \gets sum\_{d_2} + d_2$
\EndWhile
\State$\textbf{avg\_Hamming\_dist} = mean(sum\_{d_2})$
\Return{\textbf{avg\_Hamming\_dist}}
\end{algorithmic}
| \begin{algorithmic}
\Require {$\mathfrak{c} \in [4, 14]$, P} \Comment{P is the pattern set}
\State$i \gets 0,$
\State$sum\_{d_2} = 0$
\While{$i \leq |P|,$}
\State$\mathbf{x} \gets \mathfrak{b}^{(i)}$
\State$sum\_{d_1} = 0$
\While{$j\leq \mathfrak{K}$}
\State\Comment{$\mathfrak{K}$ : calculating the avg.}
\State$\mathfrak{\bar{b}^{(i)}} \gets$ invert polarities of $\mathfrak{E}\%$ of $\mathfrak{b}^{(i)}$
\State$\mathbf{y} \gets CAM(\mathfrak{c}, \mathfrak{\bar{b}}^{(i)})$
\State$d_1 \gets \mathfrak{D}(\mathbf{x,y})$
\State$sum\_{d_1} \gets sum_{d_1} + d_1$
\EndWhile
\State$d_2 \gets \textbf{mean}(sum_{d_1})$
\State$sum\_{d_2} \gets sum\_{d_2} + d_2$
\EndWhile
\State$\textbf{avg\_Hamming\_dist} = mean(sum\_{d_2})$
\Return{\textbf{avg\_Hamming\_dist}}
\end{algorithmic} | "https://arxiv.org/src/2401.10922" | "2401.10922.tar.gz" | "2024-01-15" | {
"title": "a chaotic associative memory",
"id": "2401.10922",
"abstract": "we propose a novel chaotic associative memory model using a network of chaotic rossler systems and investigate the storage capacity and retrieval capabilities of this model as a function of increasing periodicity and chaos. in early models of associate memory networks, memories were modeled as fixed points, which may be mathematically convenient but has poor neurobiological plausibility. since brain dynamics is inherently oscillatory, attempts have been made to construct associative memories using nonlinear oscillatory networks. however, oscillatory associative memories are plagued by the problem of poor storage capacity, though efforts have been made to improve capacity by adding higher order oscillatory modes. the chaotic associative memory proposed here exploits the continuous spectrum of chaotic elements and has higher storage capacity than previously described oscillatory associate memories.",
"categories": "q-bio.nc nlin.cd",
"doi": "",
"created": "2024-01-15",
"updated": "",
"authors": [
"nurani rajagopal rohan",
"sayan gupta",
"v. srinivasa chakravarthy"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.10922"
} | "2024-03-15T07:01:32.792233" | {
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} | [] | "algorithm" | "534721e6-f901-46e1-b8d7-927fb0df9d3c" | 776 | medium |
|
\begin{algorithm}[H]
\caption{$\alpha$ upper bound}%标题
\label{alpha-upperbound}%标签
\begin{algorithmic}[1]
\State $\boldsymbol{J}$ = $\emptyset$
\For{$i$ in range(0,$n-1$)}
\State $S_1(\alpha) = F_i^{-1}(1-\alpha/2)$,
\State $S_2(\alpha) = F_{i+1}^{-1}(\alpha/2)$,
\State Let $S_1(\alpha) = S_2(\alpha)$, solve for solution $\alpha_i'$.
\If{$\alpha_i' \geq \alpha^a*$}
\State $ \boldsymbol{J} = \boldsymbol{J}\cup \{i\}$
\EndIf
\EndFor
\State $\alpha' = min\{\alpha_i\}_{i \in \boldsymbol{J}}$.
\State The upper bound of $\alpha$ is $\alpha'$, $\alpha \in (0,\alpha')$.
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[H]
\caption{$\alpha$ upper bound}%标题
%标签
\begin{algorithmic}
[1]
\State $\boldsymbol{J}$ = $\emptyset$
\For{$i$ in range(0,$n-1$)}
\State $S_1(\alpha) = F_i^{-1}(1-\alpha/2)$,
\State $S_2(\alpha) = F_{i+1}^{-1}(\alpha/2)$,
\State Let $S_1(\alpha) = S_2(\alpha)$, solve for solution $\alpha_i'$.
\If{$\alpha_i' \geq \alpha^a*$}
\State $ \boldsymbol{J} = \boldsymbol{J}\cup \{i\}$
\EndIf
\EndFor
\State $\alpha' = min\{\alpha_i\}_{i \in \boldsymbol{J}}$.
\State The upper bound of $\alpha$ is $\alpha'$, $\alpha \in (0,\alpha')$.
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2401.12237" | "2401.12237.tar.gz" | "2024-01-19" | {
"title": "a distribution-guided mapper algorithm",
"id": "2401.12237",
"abstract": "motivation: the mapper algorithm is an essential tool to explore shape of data in topology data analysis. with a dataset as an input, the mapper algorithm outputs a graph representing the topological features of the whole dataset. this graph is often regarded as an approximation of a reeb graph of data. the classic mapper algorithm uses fixed interval lengths and overlapping ratios, which might fail to reveal subtle features of data, especially when the underlying structure is complex. results: in this work, we introduce a distribution guided mapper algorithm named d-mapper, that utilizes the property of the probability model and data intrinsic characteristics to generate density guided covers and provides enhanced topological features. our proposed algorithm is a probabilistic model-based approach, which could serve as an alternative to non-prababilistic ones. moreover, we introduce a metric accounting for both the quality of overlap clustering and extended persistence homology to measure the performance of mapper type algorithm. our numerical experiments indicate that the d-mapper outperforms the classical mapper algorithm in various scenarios. we also apply the d-mapper to a sars-cov-2 coronavirus rna sequences dataset to explore the topological structure of different virus variants. the results indicate that the d-mapper algorithm can reveal both vertical and horizontal evolution processes of the viruses. availability: our package is available at https://github.com/shufeige/d-mapper.",
"categories": "math.at cs.lg q-bio.qm",
"doi": "",
"created": "2024-01-19",
"updated": "",
"authors": [
"yuyang tao",
"shufei ge"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.12237"
} | "2024-03-15T07:04:57.607207" | {
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} | [] | "algorithm" | "f4ae2a51-cd74-47ef-8cf2-e956a4a80198" | 580 | easy |
|
\begin{algorithm}
\caption{\texttt{Offline$\_$iCID(D,w,$\Psi$)}}
\label{shCHalgorithm}
\begin{algorithmic}[1]
\Statex \textbf{Input:} Dataset $D$;
Window Size $w$; Subsample Size List $\Psi$
\Statex \textbf{Output:} $C_{\psi^*}$ - a set of $N$ Interval Scores
\State Split $D$ into $N$ non-overlapping time intervals, each having $w$ points, i.e.,
\Statex $D \rightarrow \{X_i, i=1, \dots ,N\}$, where $N=\lfloor length(D)/w \rfloor $
\State Search the best $\psi^*$ from the $\Psi$, i.e.,
\Statex $\psi^* = \mathop{\mathrm{argmin}}\limits_{\psi}{\Bar{E}(C_{\psi})}$
\State \textbf{Return} $C_{\psi^*}$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{\texttt{Offline$\_$iCID(D,w,$\Psi$)}}
\begin{algorithmic}
[1]
\Statex \textbf{Input:} Dataset $D$;
Window Size $w$; Subsample Size List $\Psi$
\Statex \textbf{Output:} $C_{\psi^*}$ - a set of $N$ Interval Scores
\State Split $D$ into $N$ non-overlapping time intervals, each having $w$ points, i.e.,
\Statex $D \rightarrow \{X_i, i=1, \dots ,N\}$, where $N=\lfloor length(D)/w \rfloor $
\State Search the best $\psi^*$ from the $\Psi$, i.e.,
\Statex $\psi^* = \mathop{\mathrm{argmin}}\limits_{\psi}{\Bar{E}(C_{\psi})}$
\State \textbf{Return} $C_{\psi^*}$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2212.14630" | "2212.14630.tar.gz" | "2024-01-18" | {
"title": "detecting change intervals with isolation distributional kernel",
"id": "2212.14630",
"abstract": "detecting abrupt changes in data distribution is one of the most significant tasks in streaming data analysis. although many unsupervised change-point detection (cpd) methods have been proposed recently to identify those changes, they still suffer from missing subtle changes, poor scalability, or/and sensitivity to outliers. to meet these challenges, we are the first to generalise the cpd problem as a special case of the change-interval detection (cid) problem. then we propose a cid method, named icid, based on a recent isolation distributional kernel (idk). icid identifies the change interval if there is a high dissimilarity score between two non-homogeneous temporal adjacent intervals. the data-dependent property and finite feature map of idk enabled icid to efficiently identify various types of change-points in data streams with the tolerance of outliers. moreover, the proposed online and offline versions of icid have the ability to optimise key parameter settings. the effectiveness and efficiency of icid have been systematically verified on both synthetic and real-world datasets.",
"categories": "cs.lg",
"doi": "10.1613/jair.1.15762",
"created": "2022-12-30",
"updated": "2024-01-18",
"authors": [
"yang cao",
"ye zhu",
"kai ming ting",
"flora d. salim",
"hong xian li",
"luxing yang",
"gang li"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2212.14630"
} | "2024-03-15T08:43:19.846400" | {
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} | [] | "algorithm" | "92cb38f5-2745-468d-9a05-031354d35734" | 615 | easy |
|
\begin{algorithm}[!ht]
\caption{Integer Linear Programming for 3d Subroutine of 4d Sieve}
\begin{algorithmic}
\Require
\State \hspace{5mm}Boundary $[-B,B[\times[-B,B[\times[-B,B[\times[-B,B[$,
\State Plane $P$ defined by $u=(u_1,u_2,u_3,u_4),v=(v_1,v_2,v_3,v_4),R=(x,y,z,t)$
\State \hspace{5mm} such that $R \in P$, but $R$ not necessarily in boundary.
\Ensure
\State \hspace{5mm}$(a,b)$ such that $p_0 = R + a\cdot u + b\cdot v$ contained in
both $P$ and boundary.
\Procedure{}{}
\vspace{1mm}
\State $U \gets \{ u_1,u_2,u_3,u_4,-u_1,-u_2,-u_3,-u_4 \}^T$
\State $V \gets \{ v_1,v_2,v_3,v_4,-v_1,-v_2,-v_3,-v_3 \}^T$
\State $C \gets \{ B-x-1,B-y-1,B-z-1,B-t-1,B+x,B+y,B+z,B_t \}^T$
\State $L \gets \lvert \text{LCM}\left(u_1,u_2,u_3,u_4\right) \rvert$
\State Normalize system - multiply all entries by $L$, divide $U_i,V_i,C_i$ by original $\lvert U_i \rvert$
\State $a \gets B, b \gets B$
\For {all pairs of rows $(i,j)$}
\If {$U_i = 0$ and $V_i > 0$}
\State $b_{_{TRIAL}} = \left\lfloor C_i / V_i \right\rfloor$
\State if $b_{_{TRIAL}} < b$ then $b \gets b_{_{TRIAL}}$
\Else
\If {$U_i < 0$ and $U_j > 0$ and $\lvert i - j \rvert \neq 4$ }
\State $D \gets V_i + V_j$
\If {$D > 0$}
\State $b_{_{TRIAL}} = \left\lfloor \left(C_i + C_j\right)/D \right\rfloor$
\State if $b_{_{TRIAL}} < b$ then $b \gets b_{_{TRIAL}}$
\EndIf
\EndIf
\EndIf
\EndFor
\State for the best value of $b$, compute $a$ by back substitution.
\State Return $(a,b)$
\State\EndProcedure
\end{algorithmic}\label{alg2}
\end{algorithm}
| \begin{algorithm}
[!ht]
\caption{Integer Linear Programming for 3d Subroutine of 4d Sieve}
\begin{algorithmic}
\Require
\State \hspace{5mm}Boundary $[-B,B[\times[-B,B[\times[-B,B[\times[-B,B[$,
\State Plane $P$ defined by $u=(u_1,u_2,u_3,u_4),v=(v_1,v_2,v_3,v_4),R=(x,y,z,t)$
\State \hspace{5mm} such that $R \in P$, but $R$ not necessarily in boundary.
\Ensure
\State \hspace{5mm}$(a,b)$ such that $p_0 = R + a\cdot u + b\cdot v$ contained in
both $P$ and boundary.
\Procedure{}{}
\vspace{1mm}
\State $U \gets \{ u_1,u_2,u_3,u_4,-u_1,-u_2,-u_3,-u_4 \}^T$
\State $V \gets \{ v_1,v_2,v_3,v_4,-v_1,-v_2,-v_3,-v_3 \}^T$
\State $C \gets \{ B-x-1,B-y-1,B-z-1,B-t-1,B+x,B+y,B+z,B_t \}^T$
\State $L \gets \lvert \text{LCM}\left(u_1,u_2,u_3,u_4\right) \rvert$
\State Normalize system - multiply all entries by $L$, divide $U_i,V_i,C_i$ by original $\lvert U_i \rvert$
\State $a \gets B, b \gets B$
\For {all pairs of rows $(i,j)$}
\If {$U_i = 0$ and $V_i > 0$}
\State $b_{_{TRIAL}} = \left\lfloor C_i / V_i \right\rfloor$
\State if $b_{_{TRIAL}} < b$ then $b \gets b_{_{TRIAL}}$
\Else
\If {$U_i < 0$ and $U_j > 0$ and $\lvert i - j \rvert \neq 4$ }
\State $D \gets V_i + V_j$
\If {$D > 0$}
\State $b_{_{TRIAL}} = \left\lfloor \left(C_i + C_j\right)/D \right\rfloor$
\State if $b_{_{TRIAL}} < b$ then $b \gets b_{_{TRIAL}}$
\EndIf
\EndIf
\EndIf
\EndFor
\State for the best value of $b$, compute $a$ by back substitution.
\State Return $(a,b)$
\State\EndProcedure
\end{algorithmic}\end{algorithm} | "https://arxiv.org/src/2212.04999" | "2212.04999.tar.gz" | "2024-02-06" | {
"title": "an implementation of the extended tower number field sieve using 4d sieving in a box and a record computation in fp4",
"id": "2212.04999",
"abstract": "we report on an implementation of the extended tower number field sieve (extnfs) and record computation in a medium characteristic finite field $\\mathbb{f}_{p^4}$ of 512 bits size. empirically, we show that sieving in a 4-dimensional box (orthotope) for collecting relations for extnfs in $\\mathbb{f}_{p^4}$ is faster than sieving in a 4-dimensional hypersphere. we also give a new intermediate descent method, `descent using random vectors', without which the descent stage in our extnfs computation would have been difficult/impossible, and analyze its complexity.",
"categories": "cs.cr",
"doi": "",
"created": "2022-12-09",
"updated": "2024-02-06",
"authors": [
"oisin robinson"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2212.04999"
} | "2024-03-15T07:40:23.873860" | {
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} | [] | "algorithm" | "746699e6-dbc0-4491-b2b5-8e540f97fd92" | 1486 | hard |
|
\begin{algorithm}[t]
\caption{Successive elimination procedure for a static bandit with source data}
\label{alg:EA-TL-tabular}
\begin{algorithmic}[1]
\State{\textbf{Input:} state $s$, set of arms $\mathcal{I}$, source data $\mathcal{D}^{P}$.}
\State{Set $n_{k}^{P}(s)$ and $\overline{Y}_{k}^{P}(s)$ as in (\ref{eq:n-k-B-Pdata-tabular}) and (\ref{eq:Y-bar-k-B-Pdata-tabular}), respectively, $\forall k\in\mathcal{I}$.}
\State{Set $n_{k}^{P} \gets n_{k}^{P}(s)$ and $\overline{Y}_{k} \gets \overline{Y}_{k}^{P}(s)$, $\forall k\in\mathcal{I}$.}
\State{Initialize $t\gets0$.}
\State{Initialize $\tau_{k} \gets 0, \forall k\in\mathcal{I}$.}
\Comment{initialize pull counts}
\State{Initialize $\underline{Y}^{\star}\gets\max_{k\in\mathcal{I}}\big\{\overline{Y}_{k}-U_{k}(0,s)\big\}$.}
\Comment{initialize largest reward lower bound}
\Loop
\For{$k\in\mathcal{I}$}
\If{$\overline{Y}_{k}+ U_{k}(\tau_{k},s) \geq\underline{Y}^{\star}$}
\Comment{eliminate arm s.t.~reward upper bound is smaller than largest reward lower bound}
\State{Set $t \gets t+1$.}
\State{Select arm $\widetilde{\pi}_{t}\gets k$ and receive reward $Y^{Q,(k)}$.}
\State{Set $\tau_{k}\gets\tau_{k} + 1$.}
\Comment{update pull count}
\State{Set $\overline{Y}_{k}\gets\frac{1}{n_{k}^{P}+\tau_{k}}\big(Y^{Q,(k)}+(n_{k}^{P}+\tau_{k}-1)\overline{Y}_{k}\big)$.}
\Comment{update estimated reward}
\State{Set $\underline{Y}^{\star}\gets\max_{k\in\mathcal{I}}\big\{\overline{Y}_{k}-U_{k}(\tau_{k},s)\big\}$.}
\Comment{update largest reward lower bound}
\Else \State{Eliminate arm $k$ from active arm set: $\mathcal{I} \gets\mathcal{I}\setminus\{k\}$.}
\EndIf
\EndFor
\EndLoop
\State{\textbf{Output:} policy $\{\widetilde{\pi}_{t}\}_{t\geq1}$.}
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[t]
\caption{Successive elimination procedure for a static bandit with source data}
\begin{algorithmic}
[1]
\State{\textbf{Input:} state $s$, set of arms $\mathcal{I}$, source data $\mathcal{D}^{P}$.}
\State{Set $n_{k}^{P}(s)$ and $\overline{Y}_{k}^{P}(s)$ as in (\ref{eq:n-k-B-Pdata-tabular}) and (\ref{eq:Y-bar-k-B-Pdata-tabular}), respectively, $\forall k\in\mathcal{I}$.}
\State{Set $n_{k}^{P} \gets n_{k}^{P}(s)$ and $\overline{Y}_{k} \gets \overline{Y}_{k}^{P}(s)$, $\forall k\in\mathcal{I}$.}
\State{Initialize $t\gets0$.}
\State{Initialize $\tau_{k} \gets 0, \forall k\in\mathcal{I}$.}
\Comment{initialize pull counts}
\State{Initialize $\underline{Y}^{\star}\gets\max_{k\in\mathcal{I}}\big\{\overline{Y}_{k}-U_{k}(0,s)\big\}$.}
\Comment{initialize largest reward lower bound}
\Loop
\For{$k\in\mathcal{I}$}
\If{$\overline{Y}_{k}+ U_{k}(\tau_{k},s) \geq\underline{Y}^{\star}$}
\Comment{eliminate arm s.t.~reward upper bound is smaller than largest reward lower bound}
\State{Set $t \gets t+1$.}
\State{Select arm $\widetilde{\pi}_{t}\gets k$ and receive reward $Y^{Q,(k)}$.}
\State{Set $\tau_{k}\gets\tau_{k} + 1$.}
\Comment{update pull count}
\State{Set $\overline{Y}_{k}\gets\frac{1}{n_{k}^{P}+\tau_{k}}\big(Y^{Q,(k)}+(n_{k}^{P}+\tau_{k}-1)\overline{Y}_{k}\big)$.}
\Comment{update estimated reward}
\State{Set $\underline{Y}^{\star}\gets\max_{k\in\mathcal{I}}\big\{\overline{Y}_{k}-U_{k}(\tau_{k},s)\big\}$.}
\Comment{update largest reward lower bound}
\Else \State{Eliminate arm $k$ from active arm set: $\mathcal{I} \gets\mathcal{I}\setminus\{k\}$.}
\EndIf
\EndFor
\EndLoop
\State{\textbf{Output:} policy $\{\widetilde{\pi}_{t}\}_{t\geq1}$.}
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2211.12612" | "2211.12612.tar.gz" | "2024-01-24" | {
"title": "transfer learning for contextual multi-armed bandits",
"id": "2211.12612",
"abstract": "motivated by a range of applications, we study in this paper the problem of transfer learning for nonparametric contextual multi-armed bandits under the covariate shift model, where we have data collected on source bandits before the start of the target bandit learning. the minimax rate of convergence for the cumulative regret is established and a novel transfer learning algorithm that attains the minimax regret is proposed. the results quantify the contribution of the data from the source domains for learning in the target domain in the context of nonparametric contextual multi-armed bandits. in view of the general impossibility of adaptation to unknown smoothness, we develop a data-driven algorithm that achieves near-optimal statistical guarantees (up to a logarithmic factor) while automatically adapting to the unknown parameters over a large collection of parameter spaces under an additional self-similarity assumption. a simulation study is carried out to illustrate the benefits of utilizing the data from the auxiliary source domains for learning in the target domain.",
"categories": "stat.ml cs.lg math.st stat.th",
"doi": "",
"created": "2022-11-22",
"updated": "2024-01-24",
"authors": [
"changxiao cai",
"t. tony cai",
"hongzhe li"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2211.12612"
} | "2024-03-15T08:57:26.780784" | {
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}
} | {
"num_done": {
"figure": 0,
"algorithm": 3
}
} | {
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} | [] | "algorithm" | "0406aca3-ff97-47f7-be18-cff47d084689" | 1704 | hard |
|
\begin{algorithmic}
\State \textbf{Part 1 (Initialization)}:
$\mathcal{L}_0:=
\{\mathcal{F}_y^z \cup \mathcal{M}^{\tau}_{zU}\}$;
\ $\mathcal{B} = \{\eqref{VI5}\};$ \ $\mathcal{L'}_0:= \mathcal{L}_0 \cup \mathcal{B}$;
\ $\mathcal{U}_0:= \{\eqref{VI3};\eqref{VI4} \}$;
\ $\mathcal{A}_0:= C \setminus \mathcal{L}_0$; $\mathcal{V}^L_0 = \emptyset$;
\ $\mathcal{V}^U_0 = \emptyset$.
\State \textbf{Part 2 (Iterative Procedure): At node $k$}
\State \quad \textbf{Step 1: Solution of nodal relaxation problem:}
$ \mathbf{OA-MILP}_k: \; \min \eqref{obj_lin} \quad \text{s.to} \quad (x,y,\gamma,z,U,\mu,\tau,\omega) \in \mathcal{A}_k \ . $
\State \quad \textbf{Step 2: Set Update:} \\
\begin{itemize}
\item \textbf{If the objective value corresponding to $X^*_k$ is not better than that of the incumbent}, the node is pruned.
\item \textbf{If the objective value corresponding to $X^*_k$ is better than that of the incumbent}, then:
\begin{itemize}
\item \textbf{If $X^*_k$ is fractional}, apply user callback:
\begin{itemize}
\item If $X_k^{*}$ violates any constraint in $\mathcal{U}_o$:
\begin{itemize}
\item Move violated constraints to $\mathcal{V}_k^{U}$ and discard $X_k^{*}$.
\item Update sets of user cuts and active constraints for each open node $o \in \mathcal {O}$
\[
\mathcal{U}_o \leftarrow \mathcal{U}_o \setminus \mathcal{V}^U_k \quad \text{and} \quad
\mathcal{A}_o \leftarrow \mathcal{A}_o \cup \mathcal{V}^U_k.
\]
\end{itemize}
\item If no valid inequality in $\mathcal{U}_o$ is violated by $X^*_k$, then branching constraints are entered to cut off $X^*_k$ and the next open node is processed.
\end{itemize}
\item \textbf{If $X^*_k$ is integer-valued},
check for possible violation of lazy constraints:
\begin{itemize}
\item If $X^*_k$ violates any constraint in $\mathcal{L}^{'}_o$:
\begin{itemize}
\item Move violated lazy constraints to $\mathcal{V}^L_k$ and discard $X^*_k$.
\item Update sets of lazy and active constraints for each open node $o \in \mathcal {O}$:
\[
\mathcal{L}^{'}_o \leftarrow \mathcal{L}^{'}_o \setminus \mathcal{V}^L_k
\qquad \text{and} \qquad
\mathcal{A}_o \leftarrow \mathcal{A}_o \cup \mathcal{V}^L_k.
\]
\end{itemize}
\item If $X^*_k$ does not violate any constraint in $\mathcal{L}^{'}_o$, $X^*_k$ becomes the incumbent and node $k$ is pruned.
\end{itemize}
\end{itemize}
\end{itemize}
\State \textbf{Part 3 (Termination):} The algorithm stops when $\mathcal{O} = \emptyset$.
\end{algorithmic}
| \begin{algorithmic}
\State \textbf{Part 1 (Initialization)}:
$\mathcal{L}_0:=
\{\mathcal{F}_y^z \cup \mathcal{M}^{\tau}_{zU}\}$;
\ $\mathcal{B} = \{\eqref{VI5}\};$ \ $\mathcal{L'}_0:= \mathcal{L}_0 \cup \mathcal{B}$;
\ $\mathcal{U}_0:= \{\eqref{VI3};\eqref{VI4} \}$;
\ $\mathcal{A}_0:= C \setminus \mathcal{L}_0$; $\mathcal{V}^L_0 = \emptyset$;
\ $\mathcal{V}^U_0 = \emptyset$.
\State \textbf{Part 2 (Iterative Procedure): At node $k$}
\State \quad \textbf{Step 1: Solution of nodal relaxation problem:}
$ \mathbf{OA-MILP}_k: \; \min \eqref{obj_lin} \quad \text{s.to} \quad (x,y,\gamma,z,U,\mu,\tau,\omega) \in \mathcal{A}_k \ . $
\State \quad \textbf{Step 2: Set Update:} \\
\begin{itemize}
\item \textbf{If the objective value corresponding to $X^*_k$ is not better than that of the incumbent}, the node is pruned.
\item \textbf{If the objective value corresponding to $X^*_k$ is better than that of the incumbent}, then:
\begin{itemize}
\item \textbf{If $X^*_k$ is fractional}, apply user callback:
\begin{itemize}
\item If $X_k^{*}$ violates any constraint in $\mathcal{U}_o$:
\begin{itemize}
\item Move violated constraints to $\mathcal{V}_k^{U}$ and discard $X_k^{*}$.
\item Update sets of user cuts and active constraints for each open node $o \in \mathcal {O}$
\[
\mathcal{U}_o \leftarrow \mathcal{U}_o \setminus \mathcal{V}^U_k \quad \text{and} \quad
\mathcal{A}_o \leftarrow \mathcal{A}_o \cup \mathcal{V}^U_k.
\]
\end{itemize}
\item If no valid inequality in $\mathcal{U}_o$ is violated by $X^*_k$, then branching constraints are entered to cut off $X^*_k$ and the next open node is processed.
\end{itemize}
\item \textbf{If $X^*_k$ is integer-valued},
check for possible violation of lazy constraints:
\begin{itemize}
\item If $X^*_k$ violates any constraint in $\mathcal{L}^{'}_o$:
\begin{itemize}
\item Move violated lazy constraints to $\mathcal{V}^L_k$ and discard $X^*_k$.
\item Update sets of lazy and active constraints for each open node $o \in \mathcal {O}$:
\[
\mathcal{L}^{'}_o \leftarrow \mathcal{L}^{'}_o \setminus \mathcal{V}^L_k
\qquad \text{and} \qquad
\mathcal{A}_o \leftarrow \mathcal{A}_o \cup \mathcal{V}^L_k.
\]
\end{itemize}
\item If $X^*_k$ does not violate any constraint in $\mathcal{L}^{'}_o$, $X^*_k$ becomes the incumbent and node $k$ is pruned.
\end{itemize}
\end{itemize}
\end{itemize}
\State \textbf{Part 3 (Termination):} The algorithm stops when $\mathcal{O} = \emptyset$.
\end{algorithmic} | "https://arxiv.org/src/2206.14340" | "2206.14340.tar.gz" | "2024-01-25" | {
"title": "drone-delivery network for opioid overdose -- nonlinear integer queueing-optimization models and methods",
"id": "2206.14340",
"abstract": "we propose a new stochastic emergency network design model that uses a fleet of drones to quickly deliver naxolone in response to opioid overdoses. the network is represented as a collection of m/g/k queuing systems in which the capacity k of each system is a decision variable and the service time is modelled as a decision-dependent random variable. the model is an optimization-based queuing problem which locates fixed (drone bases) and mobile (drones) servers and determines the drone dispatching decisions, and takes the form of a nonlinear integer problem, which is intractable in its original form. we develop an efficient reformulation and algorithmic framework. our approach reformulates the multiple nonlinearities (fractional, polynomial, exponential, factorial terms) to give a mixed-integer linear programming (milp) formulation. we demonstrate its generalizablity and show that the problem of minimizing the average response time of a network of m/g/k queuing systems with unknown capacity k is always milp-representable. we design two algorithms and demonstrate that the outer approximation branch-and-cut method is the most efficient and scales well. the analysis based on real-life overdose data reveals that drones can in virginia beach: 1) decrease the response time by 78%, 2) increase the survival chance by 432%, 3) save up to 34 additional lives per year, and 4) provide annually up to 287 additional quality-adjusted life years.",
"categories": "math.oc",
"doi": "",
"created": "2022-06-28",
"updated": "2024-01-25",
"authors": [
"miguel lejeune",
"wenbo ma"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2206.14340"
} | "2024-03-15T05:17:26.927464" | {
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} | [] | "algorithm" | "88852102-934c-4f4d-b173-49a9de868b6b" | 2436 | hard |
|
\begin{algorithmic}[1]
\Require data matrix $X \in \mathbb{R}^{d \times n}_+$, number of features $k_{\text{max}}$, $\Gamma$, $\beta_{\text{max}}$, $c_j$ [for the $\ell_0$-forced version]
\State \textbf{Initialization} $\beta_{init}$%\leftarrow\frac{1}{2\lambda_{\text{max}}C_{x}}$
, $k\leftarrow1$, $w_1\leftarrow\sum_{x}xp(x)$, $\lambda_1\leftarrow1$, if $W$-orthogonal $X \leftarrow X^{\intercal}$
\State \textbf{Normalization} $x_j \leftarrow \frac{x_i}{||x_i||_2} \;$ for $i=1...n$
\Loop \, {until $\beta=\beta_{\text{max}}$}
\Repeat
\State update $p_{j|i}$, $w_j$ and $\alpha_j$ by (\ref{Gibbs}) and (\ref{alpha}) [or (\ref{optsol}) for optimally-weighted]
\Until convergence
\State $\beta \leftarrow \Gamma \beta$
\If{$k<k_{\text{max}}$}
\For {all $w_j$}
\State check the phase transition condition
\If{satisfied for $w_t$}
\State add another feature $w_{k+1}=w_t+\delta$
\State $\lambda_{w_{k+1}}\leftarrow0.5\lambda_{w_t}$, $\lambda_{w_t} \leftarrow 0.5\lambda_{w_t}$
\EndIf
\EndFor
\EndIf
\EndLoop
\State do post-processing (\ref{postpro}) on $H$
\State $W_{:j}\leftarrow w_j$ and $H_{ij}\leftarrow p_{j|i}$ $\forall i,j$
\State if {$W$-orthogonal}: $W\leftarrow H^{\intercal}$, $H\leftarrow W^{\intercal}$\\
\Return $W$, $H$
\end{algorithmic}
| \begin{algorithmic}
[1]
\Require data matrix $X \in \mathbb{R}^{d \times n}_+$, number of features $k_{\text{max}}$, $\Gamma$, $\beta_{\text{max}}$, $c_j$ [for the $\ell_0$-forced version]
\State \textbf{Initialization} $\beta_{init}$%\leftarrow\frac{1}{2\lambda_{\text{max}}C_{x}}$
, $k\leftarrow1$, $w_1\leftarrow\sum_{x}xp(x)$, $\lambda_1\leftarrow1$, if $W$-orthogonal $X \leftarrow X^{\intercal}$
\State \textbf{Normalization} $x_j \leftarrow \frac{x_i}{||x_i||_2} \;$ for $i=1...n$
\Loop \, {until $\beta=\beta_{\text{max}}$}
\Repeat
\State update $p_{j|i}$, $w_j$ and $\alpha_j$ by (\ref{Gibbs}) and (\ref{alpha}) [or (\ref{optsol}) for optimally-weighted]
\Until convergence
\State $\beta \leftarrow \Gamma \beta$
\If{$k<k_{\text{max}}$}
\For {all $w_j$}
\State check the phase transition condition
\If{satisfied for $w_t$}
\State add another feature $w_{k+1}=w_t+\delta$
\State $\lambda_{w_{k+1}}\leftarrow0.5\lambda_{w_t}$, $\lambda_{w_t} \leftarrow 0.5\lambda_{w_t}$
\EndIf
\EndFor
\EndIf
\EndLoop
\State do post-processing (\ref{postpro}) on $H$
\State $W_{:j}\leftarrow w_j$ and $H_{ij}\leftarrow p_{j|i}$ $\forall i,j$
\State if {$W$-orthogonal}: $W\leftarrow H^{\intercal}$, $H\leftarrow W^{\intercal}$\\
\Return $W$, $H$
\end{algorithmic} | "https://arxiv.org/src/2210.02672" | "2210.02672.tar.gz" | "2024-01-18" | {
"title": "a novel maximum-entropy-driven technique for low-rank orthogonal nonnegative matrix factorization with $\\ell_0$-norm sparsity constraint",
"id": "2210.02672",
"abstract": "in data-driven control and machine learning, a common requirement involves breaking down large matrices into smaller, low-rank factors that possess specific levels of sparsity. this paper introduces an innovative solution to the orthogonal nonnegative matrix factorization (onmf) problem. the objective is to approximate input data by using two low-rank nonnegative matrices, adhering to both orthogonality and $\\ell_0$-norm sparsity constraints. the proposed maximum-entropy-principle based framework ensures orthogonality and sparsity of features or the mixing matrix, while maintaining nonnegativity in both. additionally, the methodology offers a quantitative determination of the ``true'' number of underlying features, a crucial hyperparameter for onmf. experimental evaluation on synthetic and a standard datasets highlights the method's superiority in terms of sparsity, orthogonality, and computational speed compared to existing approaches. notably, the proposed method achieves comparable or improved reconstruction errors in line with the literature.",
"categories": "cs.ds cs.it cs.lg math.it math.pr",
"doi": "",
"created": "2022-10-06",
"updated": "2024-01-18",
"authors": [
"salar basiri",
"srinivasa salapaka"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2210.02672"
} | "2024-03-15T05:57:43.061097" | {
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} | [] | "algorithm" | "2abf6474-22b6-4d90-a71b-5bb411e82410" | 1254 | hard |
|
\begin{algorithmic}[1]
\State Initialize the teacher model $f_T(\cdot)$
\State $s \gets 0$ \Comment{Training steps for OD}
\While{$s < s_T$}
\State Sample a batch $\mathcal{B}$ from $\{(x_i, y_i)\}$
\State Train $f_T(\cdot)$ with cross-entropy loss on $\mathcal{B}$
\EndWhile
\State $s \gets 0$ \Comment{Training steps for Denoising}
\State $\mathcal{D}^+ \gets \{(x_i, y_i)\} \cup \{(x_i', y_i')\}$ \Comment{Mix $\mathcal{D}$ \& $\mathcal{D}'$}
\While{$s < s_S$}
\State Sample a batch $\mathcal{B}'$ from $\mathcal{D}^+$
\State Train $f(\cdot)$ with loss in Eq.~(\ref{eq:overall_loss}) on $\mathcal{B}'$ with Organic Distillation and Self-Regularization to do deonising
\EndWhile
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Initialize the teacher model $f_T(\cdot)$
\State $s \gets 0$ \Comment{Training steps for OD}
\While{$s < s_T$}
\State Sample a batch $\mathcal{B}$ from $\{(x_i, y_i)\}$
\State Train $f_T(\cdot)$ with cross-entropy loss on $\mathcal{B}$
\EndWhile
\State $s \gets 0$ \Comment{Training steps for Denoising}
\State $\mathcal{D}^+ \gets \{(x_i, y_i)\} \cup \{(x_i', y_i')\}$ \Comment{Mix $\mathcal{D}$ \& $\mathcal{D}'$}
\While{$s < s_S$}
\State Sample a batch $\mathcal{B}'$ from $\mathcal{D}^+$
\State Train $f(\cdot)$ with loss in Eq.~(\ref{eq:overall_loss}) on $\mathcal{B}'$ with Organic Distillation and Self-Regularization to do deonising
\EndWhile
\end{algorithmic} | "https://arxiv.org/src/2212.10558" | "2212.10558.tar.gz" | "2024-01-31" | {
"title": "on-the-fly denoising for data augmentation in natural language understanding",
"id": "2212.10558",
"abstract": "data augmentation (da) is frequently used to provide additional training data without extra human annotation automatically. however, data augmentation may introduce noisy data that impairs training. to guarantee the quality of augmented data, existing methods either assume no noise exists in the augmented data and adopt consistency training or use simple heuristics such as training loss and diversity constraints to filter out \"noisy\" data. however, those filtered examples may still contain useful information, and dropping them completely causes a loss of supervision signals. in this paper, based on the assumption that the original dataset is cleaner than the augmented data, we propose an on-the-fly denoising technique for data augmentation that learns from soft augmented labels provided by an organic teacher model trained on the cleaner original data. to further prevent overfitting on noisy labels, a simple self-regularization module is applied to force the model prediction to be consistent across two distinct dropouts. our method can be applied to general augmentation techniques and consistently improve the performance on both text classification and question-answering tasks.",
"categories": "cs.cl cs.ai",
"doi": "",
"created": "2022-12-20",
"updated": "2024-01-31",
"authors": [
"tianqing fang",
"wenxuan zhou",
"fangyu liu",
"hongming zhang",
"yangqiu song",
"muhao chen"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2212.10558"
} | "2024-03-15T08:24:23.744468" | {
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} | [] | "algorithm" | "21d6797e-732e-458a-9764-e96bd0d834c9" | 699 | easy |
|
\begin{algorithm}[!h]
\caption{Bounding sequence $c_{m, \delta}$} \label{alg_1}
\begin{algorithmic}[1]
\Statex {\bf Input:} $N$ sets of $p$-values generated by the joint null distribution of $\{z_1, \ldots z_m\}$
\Statex {\bf Output:} bounding sequences $c_{m, 0.5}$ and $c_{m, 1}$
\State {\bf for} $a=1, 2\ldots, N$ {\bf do}
\Statex Rank the $a$-th set of p-values such that $p_{a,(1)} < p_{a,(2)} < \ldots < p_{a,(m)}$
\Statex Compute
\[
V_{a, 0.5} = \max_{1 < j < m} {|j / m - p_{a, (j)} | \over \sqrt{p_{a,(j)}}} \qquad \text{and} \qquad V_{a, 1} = \max_{1 < j < m} {|j / m - p_{a, (j)} | \over p_{a,(j)}}
\]
\State {\bf end for}
\State Compute $c_{m, 0.5}$ as the $(1-1/\sqrt{\log m})$-th quantile of the empirical distribution of $V_{a, 0.5}, a = 1, \ldots N$ and compute $c_{m, 1}$ as the $(1-1/\sqrt{\log m})$-th quantile of the empirical distribution of $V_{a, 1}, a = 1, \ldots N$.
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[!h]
\caption{Bounding sequence $c_{m, \delta}$} \begin{algorithmic}
[1]
\Statex {\bf Input:} $N$ sets of $p$-values generated by the joint null distribution of $\{z_1, \ldots z_m\}$
\Statex {\bf Output:} bounding sequences $c_{m, 0.5}$ and $c_{m, 1}$
\State {\bf for} $a=1, 2\ldots, N$ {\bf do}
\Statex Rank the $a$-th set of p-values such that $p_{a,(1)} < p_{a,(2)} < \ldots < p_{a,(m)}$
\Statex Compute
\[
V_{a, 0.5} = \max_{1 < j < m} {|j / m - p_{a, (j)} | \over \sqrt{p_{a,(j)}}} \qquad \text{and} \qquad V_{a, 1} = \max_{1 < j < m} {|j / m - p_{a, (j)} | \over p_{a,(j)}}
\]
\State {\bf end for}
\State Compute $c_{m, 0.5}$ as the $(1-1/\sqrt{\log m})$-th quantile of the empirical distribution of $V_{a, 0.5}, a = 1, \ldots N$ and compute $c_{m, 1}$ as the $(1-1/\sqrt{\log m})$-th quantile of the empirical distribution of $V_{a, 1}, a = 1, \ldots N$.
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2212.13574" | "2212.13574.tar.gz" | "2024-02-02" | {
"title": "weak signal inclusion under dependence and applications in genome-wide association study",
"id": "2212.13574",
"abstract": "motivated by the inquiries of weak signals in underpowered genome-wide association studies (gwass), we consider the problem of retaining true signals that are not strong enough to be individually separable from a large amount of noise. we address the challenge from the perspective of false negative control and present false negative control (fnc) screening, a data-driven method to efficiently regulate false negative proportion at a user-specified level. fnc screening is developed in a realistic setting with arbitrary covariance dependence between variables. we calibrate the overall dependence through a parameter whose scale is compatible with the existing phase diagram in high-dimensional sparse inference. utilizing the new calibration, we asymptotically explicate the joint effect of covariance dependence, signal sparsity, and signal intensity on the proposed method. we interpret the results using a new phase diagram, which shows that fnc screening can efficiently select a set of candidate variables to retain a high proportion of signals even when the signals are not individually separable from noise. finite sample performance of fnc screening is compared to those of several existing methods in simulation studies. the proposed method outperforms the others in adapting to a user-specified false negative control level. we implement fnc screening to empower a two-stage gwas procedure, which demonstrates substantial power gain when working with limited sample sizes in real applications.",
"categories": "stat.me",
"doi": "",
"created": "2022-12-27",
"updated": "2024-02-02",
"authors": [
"x. jessie jeng",
"yifei hu",
"quan sun",
"yun li"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2212.13574"
} | "2024-03-15T07:22:29.819002" | {
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} | [] | "algorithm" | "4388b530-2258-4782-adf6-3ab730dc68c6" | 914 | medium |
|
\begin{algorithm}[H]
\caption{Dynamic Taylor}
\label{alg:dynamictaylor}
\begin{algorithmic}
\State Input:\begin{enumerate}
\item[1] Data input for Algorithm~\ref{alg:expansionrange}, e.g. system $\Sigma$.
\item[2] Output of Algorithm~\ref{alg:expansionrange}.
\item[3] Set number of terms, i.e., the highest degree of Taylor polynomial, $N$.
\item[4] Expansion point $\alpha_j\in R_{G_j}$ for each $j$.
\item[5] Time measured data $\bar{y}(t_0),\cdots,\bar{y}(t_s)$.
\end{enumerate}
\State Output: System of polynomial equations $\Sigma'$ with parameters approximately equal to those of $\Sigma$.
\Procedure{$\Sigma$ to power series $\Sigma^*$}{} Suppose there are $K$ transcendental functions in $\Sigma$.
\For{$j=1\to K$}
\State $\tau_j:=\tilde{G}_j$
\State $G_j\to T_{G_j}:=\sum_{k=0}^\infty G_j^{(k)}(\alpha_j)(\tau_j-\alpha_j)^k$, where differentiation is with respect to $\tau_j$.
\State For every equation $e_i=G_{i_1}+\cdots+G_{i_r}+A_i$ in $\Sigma$, $e_i^*=T_{G_{i_1}}+\cdots+T_{G_{i_r}}+A_i$ is in $\Sigma^*$, \phantom{---------}where $A_i$ is algebraic.
\EndFor
\EndProcedure
\Procedure{$\Sigma^*$ to algebraic $\Sigma'$}{}
\For{$j=1\to K$}
\State $\hat{T}_{G_j}:=\sum_{k=0}^N G_j^{(k)}(\alpha_j)(\tau-\alpha_j)^k$
\State $\tau_j\mapsto \tilde{G}_j$
\State For every equation $e_i^*=T_{G_{i_1}}+\cdots+T_{G_{i_r}}+A_i$ in $\Sigma^*$, $e_i'=\hat{T}_{G_{i_1}}(\tilde{G}_{i_1})+\cdots+\hat{T}_{G_{i_r}}(\tilde{G}_{i_r})+A_i$ \phantom{---------}is in $\Sigma'$, where $A_i$ is algebraic.
\EndFor
\State Substitute $\bar{y}(t_0),\cdots,\bar{y}(t_s)$ throughout $\Sigma'$ as they appear, if known.
\EndProcedure
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[H]
\caption{Dynamic Taylor}
\begin{algorithmic}
\State Input:\begin{enumerate}
\item[1] Data input for Algorithm~\ref{alg:expansionrange}, e.g. system $\Sigma$.
\item[2] Output of Algorithm~\ref{alg:expansionrange}.
\item[3] Set number of terms, i.e., the highest degree of Taylor polynomial, $N$.
\item[4] Expansion point $\alpha_j\in R_{G_j}$ for each $j$.
\item[5] Time measured data $\bar{y}(t_0),\cdots,\bar{y}(t_s)$.
\end{enumerate}
\State Output: System of polynomial equations $\Sigma'$ with parameters approximately equal to those of $\Sigma$.
\Procedure{$\Sigma$ to power series $\Sigma^*$}{} Suppose there are $K$ transcendental functions in $\Sigma$.
\For{$j=1\to K$}
\State $\tau_j:=\tilde{G}_j$
\State $G_j\to T_{G_j}:=\sum_{k=0}^\infty G_j^{(k)}(\alpha_j)(\tau_j-\alpha_j)^k$, where differentiation is with respect to $\tau_j$.
\State For every equation $e_i=G_{i_1}+\cdots+G_{i_r}+A_i$ in $\Sigma$, $e_i^*=T_{G_{i_1}}+\cdots+T_{G_{i_r}}+A_i$ is in $\Sigma^*$, \phantom{---------}where $A_i$ is algebraic.
\EndFor
\EndProcedure
\Procedure{$\Sigma^*$ to algebraic $\Sigma'$}{}
\For{$j=1\to K$}
\State $\hat{T}_{G_j}:=\sum_{k=0}^N G_j^{(k)}(\alpha_j)(\tau-\alpha_j)^k$
\State $\tau_j\mapsto \tilde{G}_j$
\State For every equation $e_i^*=T_{G_{i_1}}+\cdots+T_{G_{i_r}}+A_i$ in $\Sigma^*$, $e_i'=\hat{T}_{G_{i_1}}(\tilde{G}_{i_1})+\cdots+\hat{T}_{G_{i_r}}(\tilde{G}_{i_r})+A_i$ \phantom{---------}is in $\Sigma'$, where $A_i$ is algebraic.
\EndFor
\State Substitute $\bar{y}(t_0),\cdots,\bar{y}(t_s)$ throughout $\Sigma'$ as they appear, if known.
\EndProcedure
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2401.16220" | "2401.16220.tar.gz" | "2024-01-29" | {
"title": "symbolic-numeric algorithm for parameter estimation in discrete-time models with $\\exp$",
"id": "2401.16220",
"abstract": "determining unknown parameter values in dynamic models is crucial for accurate analysis of the dynamics across the different scientific disciplines. discrete-time dynamic models are widely used to model biological processes, but it is often difficult to determine these parameters. in this paper, we propose a robust symbolic-numeric approach for parameter estimation in discrete-time models that involve non-algebraic functions such as exp. we illustrate the performance (precision) of our approach by applying our approach to the flour beetle (lpa) model, an archetypal discrete-time model in biology. unlike optimization-based methods, our algorithm guarantees to find all solutions of the parameter values given time-series data for the measured variables.",
"categories": "q-bio.qm cs.sc cs.sy eess.sy math.ac math.ds",
"doi": "",
"created": "2024-01-29",
"updated": "",
"authors": [
"yosef berman",
"joshua forrest",
"matthew grote",
"alexey ovchinnikov",
"sonia rueda"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.16220"
} | "2024-03-15T06:24:53.153570" | {
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} | [] | "algorithm" | "50a133f5-3124-403f-b949-3e678220271d" | 1625 | hard |
|
\begin{algorithm}
\caption{Nesterov's Accelerated Gradient Method as specified in \cite[\S 4.2]{li2023convex} }
\label{alg:NAG}
\begin{algorithmic}[1]
\Require $\theta_0 \in \mathbb{R}^n, m \in (0, \infty)$
\State $z_0 = \theta_0, B_0 = 0, A_0 = 1/m$
\For{$t = 0,...$}
\State $B_{t+1} = B_t + .5(1+\sqrt{4B_t+1})$
\State $A_{t+1} = B_{t+1} + \frac{1}{m}$
\State $y_t = \theta_t + (1-\frac{A_t}{A_{t+1}})(z_t-\theta_t)$
\State $\theta_{t+1} = y_t - m\dot{F}(y_t)$
\State $z_{t+1} = z_t - m(A_{t+1}-A_t)\dot{F}(y_t)$
\EndFor
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Nesterov's Accelerated Gradient Method as specified in \cite[\S 4.2]{li2023convex} }
\begin{algorithmic}
[1]
\Require $\theta_0 \in \mathbb{R}^n, m \in (0, \infty)$
\State $z_0 = \theta_0, B_0 = 0, A_0 = 1/m$
\For{$t = 0,...$}
\State $B_{t+1} = B_t + .5(1+\sqrt{4B_t+1})$
\State $A_{t+1} = B_{t+1} + \frac{1}{m}$
\State $y_t = \theta_t + (1-\frac{A_t}{A_{t+1}})(z_t-\theta_t)$
\State $\theta_{t+1} = y_t - m\dot{F}(y_t)$
\State $z_{t+1} = z_t - m(A_{t+1}-A_t)\dot{F}(y_t)$
\EndFor
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2309.10894" | "2309.10894.tar.gz" | "2024-02-15" | {
"title": "a novel gradient methodology with economical objective function evaluations for data science applications",
"id": "2309.10894",
"abstract": "gradient methods are experiencing a growth in methodological and theoretical developments owing to the challenges of optimization problems arising in data science. focusing on data science applications with expensive objective function evaluations yet inexpensive gradient function evaluations, gradient methods that never make objective function evaluations are either being rejuvenated or actively developed. however, as we show, such gradient methods are all susceptible to catastrophic divergence under realistic conditions for data science applications. in light of this, gradient methods which make use of objective function evaluations become more appealing, yet, as we show, can result in an exponential increase in objective evaluations between accepted iterates. as a result, existing gradient methods are poorly suited to the needs of optimization problems arising from data science. in this work, we address this gap by developing a generic methodology that economically uses objective function evaluations in a problem-driven manner to prevent catastrophic divergence and avoid an explosion in objective evaluations between accepted iterates. our methodology allows for specific procedures that can make use of specific step size selection methodologies or search direction strategies, and we develop a novel step size selection methodology that is well-suited to data science applications. we show that a procedure resulting from our methodology is highly competitive with standard optimization methods on cutest test problems. we then show a procedure resulting from our methodology is highly favorable relative to standard optimization methods on optimization problems arising in our target data science applications. thus, we provide a novel gradient methodology that is better suited to optimization problems arising in data science.",
"categories": "math.oc stat.co",
"doi": "",
"created": "2023-09-19",
"updated": "2024-02-15",
"authors": [
"christian varner",
"vivak patel"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2309.10894"
} | "2024-03-15T05:06:27.333458" | {
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} | {
"num_done": {
"figure": 0,
"algorithm": 3,
"plot": 1
}
} | {
"NonTrivialRenderingFilter": {
"white_pixels_ratio": 98.56671985827441,
"hash": "3fbdb9bbb3af8880",
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} | [] | "algorithm" | "2a277df0-9d4b-446c-a77e-edcb68b845e5" | 541 | easy |
|
\begin{algorithm}
\caption{Variable Selection (line 8 in Algorithm~\ref{alg:VSBO})}
\begin{algorithmic}[1]
\State \textbf{Input}: $\mathcal{D}=\{(\mathbf{x}^{i},y^{i})\}_{i=1}^{t}$
\State \textbf{Output}: Set of important variables $\mathbf{x}_{ipt}$
\State Fit a GP to $\mathcal{D}$ and calculate important scores of variables $IS$ where $IS[i]$ is the important score of the i-th variable
\State Sort variables according to their important scores, $[\mathbf{x}_{s(1)},\dots, \mathbf{x}_{s(D)}]$, from the most important to the least
\For{$m=1,2,\ldots D$} \Comment{Stepwise forward selection}
\State Fit a GP to $\mathcal{D}_{m}:=\{(\mathbf{x}_{s(1):s(m)}^{i},y^{i})\}_{i=1}^{t-1}$ where $\mathbf{x}_{s(1):s(m)}^{i}$ is the $i$-th input with only the first $m$ important variables, let $L_m$ to be the value of final negative marginal log likelihood
\If{$m<3$}
\State \textbf{continue}
\ElsIf {$L_{m-1}-L_{m}\leq 0$ or $L_{m-1}-L_{m}<\frac{L_{m-2}-L_{m-1}}{10}$}
\State \textbf{break}
\EndIf
\EndFor
\State\Return
$\mathbf{x}_{ipt}=\{\mathbf{x}_{s(1)},\dots, \mathbf{x}_{s(m-1)}\}$
\end{algorithmic}
\label{alg:VS_detail}
\end{algorithm}
| \begin{algorithm}
\caption{Variable Selection (line 8 in Algorithm~\ref{alg:VSBO})}
\begin{algorithmic}
[1]
\State \textbf{Input}: $\mathcal{D}=\{(\mathbf{x}^{i},y^{i})\}_{i=1}^{t}$
\State \textbf{Output}: Set of important variables $\mathbf{x}_{ipt}$
\State Fit a GP to $\mathcal{D}$ and calculate important scores of variables $IS$ where $IS[i]$ is the important score of the i-th variable
\State Sort variables according to their important scores, $[\mathbf{x}_{s(1)},\dots, \mathbf{x}_{s(D)}]$, from the most important to the least
\For{$m=1,2,\ldots D$} \Comment{Stepwise forward selection}
\State Fit a GP to $\mathcal{D}_{m}:=\{(\mathbf{x}_{s(1):s(m)}^{i},y^{i})\}_{i=1}^{t-1}$ where $\mathbf{x}_{s(1):s(m)}^{i}$ is the $i$-th input with only the first $m$ important variables, let $L_m$ to be the value of final negative marginal log likelihood
\If{$m<3$}
\State \textbf{continue}
\ElsIf {$L_{m-1}-L_{m}\leq 0$ or $L_{m-1}-L_{m}<\frac{L_{m-2}-L_{m-1}}{10}$}
\State \textbf{break}
\EndIf
\EndFor
\State\Return
$\mathbf{x}_{ipt}=\{\mathbf{x}_{s(1)},\dots, \mathbf{x}_{s(m-1)}\}$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2109.09264" | "2109.09264.tar.gz" | "2024-02-12" | {
"title": "computationally efficient high-dimensional bayesian optimization via variable selection",
"id": "2109.09264",
"abstract": "bayesian optimization (bo) is a method for globally optimizing black-box functions. while bo has been successfully applied to many scenarios, developing effective bo algorithms that scale to functions with high-dimensional domains is still a challenge. optimizing such functions by vanilla bo is extremely time-consuming. alternative strategies for high-dimensional bo that are based on the idea of embedding the high-dimensional space to the one with low dimension are sensitive to the choice of the embedding dimension, which needs to be pre-specified. we develop a new computationally efficient high-dimensional bo method that exploits variable selection. our method is able to automatically learn axis-aligned sub-spaces, i.e. spaces containing selected variables, without the demand of any pre-specified hyperparameters. we theoretically analyze the computational complexity of our algorithm and derive the regret bound. we empirically show the efficacy of our method on several synthetic and real problems.",
"categories": "cs.lg stat.ml",
"doi": "",
"created": "2021-09-19",
"updated": "2024-02-12",
"authors": [
"yihang shen",
"carl kingsford"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2109.09264"
} | "2024-03-15T06:19:42.461951" | {
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} | [] | "algorithm" | "17a45837-f966-4a93-8b42-c4f77ed5743b" | 1118 | medium |
|
\begin{algorithm}[h]
\caption{Delta Particle Filter}
\label{alg:dpf}
\begin{enumerate}
\item{Input: data $y_{1:T}$, level $l\in\mathbb{N}$, particle number $N\in\mathbb{N}$ and parameter $\theta\in\Theta$.}
\item{Initialize: For $i\in\{1,\dots,N\}$, independently generate $\overline{W}_{\Delta_l:1}^{i,l}$ from $\mathcal{N}(0,\Delta_l)$. For $(i,k)\in\{1,\dots,N\}\times\{1,\dots,\Delta_{l-1}^{-1}\}$ set
$
\overline{W}_{k\Delta_{l-1}}^{i,l-1} = \overline{W}_{2k\Delta_{l}}^{i,l} + \overline{W}_{(2k-1)\Delta_{l}}^{i,l}.
$
Set $t=1$, $\hat{\tilde{p}}^N(y_{1:0})=1$ for convention and go to step 3.}
\item{Iterate: For $i\in\{1,\dots,N\}$ compute
$$
\tilde{u}_t^i = \frac{\max\{\kappa_{t,l}(\overline{w}_{\Delta_l:t}^{i,l}),\kappa_{t,l-1}(\overline{w}_{\Delta_{l-1}:t}^{i,l-1})\}}{\sum_{j=1}^N\max\{\kappa_{t,l}(\overline{w}_{\Delta_l:t}^{j,l}),\kappa_{t,l-1}(\overline{w}_{\Delta_{l-1}:t}^{j,l-1})\}}.
$$
Set $\hat{p}^N(y_{1:t})={\hat{p}^N(y_{1:t-1})}\tfrac{1}{N}\sum_{i=1}^N\max\{\kappa_{t,l}(\overline{w}_{\Delta_l:t}^{i,l}),\kappa_{t,l-1}(\overline{w}_{\Delta_{l-1}:t}^{i,l-1})\}$.
Then sample $(\overline{w}_{\Delta_l:t}^{1:N,l},\overline{w}_{\Delta_{l-1}:t}^{1:N,l-1})$ with replacement from
$(\overline{w}_{\Delta_l:t}^{1:N,l},\overline{w}_{\Delta_{l-1}:t}^{1:N,l-1})$
using probabilities
$\tilde{u}_t^{1:N}$. For $i\in\{1,\dots,N\}$, independently generate $\overline{W}_{t+\Delta_l:t+1}^i$ from $\mathcal{N}(0,\Delta_l)$. For $(i,k)\in\{1,\dots,N\}\times\{1,\dots,\Delta_{l-1}^{-1}\}$ set
$
\overline{W}_{t+k\Delta_{l-1}}^{i,l-1} = \overline{W}_{t+2k\Delta_{l}}^{i,l} + \overline{W}_{t+(2k-1)\Delta_{l}}^{i,l}.
$
Set $t=t+1$ and if $t=T$ go to step 4, otherwise restart step 3.}
\item{Grand Selection: For $i\in\{1,\dots,N\}$ compute
$
\tilde{u}_T^i = \frac{\max\{\kappa_{T,l}(\overline{w}_{\Delta_l:T}^{i,l}),\kappa_{T,l-1}(\overline{w}_{\Delta_{l-1}:T}^{i,l-1})\}}{\sum_{j=1}^N\max\{\kappa_{T,l}(\overline{w}_{\Delta_l:T}^{j,l}),\kappa_{T,l-1}(\overline{w}_{\Delta_{l-1}:T}^{j,l-1})\}}.
$
Set $\hat{p}^N(y_{1:T})=\hat{p}^N(y_{1:T-1})\tfrac{1}{N}\sum_{i=1}^N
\max\{\kappa_{T,l}(\overline{w}_{\Delta_l:T}^{i,l}),\kappa_{T,l-1}(\overline{w}_{\Delta_{l-1}:T}^{i,l-1})\}$.
Sample one $(\overline{w}_{\Delta_l:T}^l, \overline{w}_{\Delta_{l-1}:T}^{l-1})$ from $(\overline{w}_{\Delta_l:T}^{1:N,l},\overline{w}_{\Delta_{l-1}:T}^{1:N,l-1})$ using $\tilde{u}_T^{1:N}$ and go to step 5.}
\item{Output: trajectories $(\overline{w}_{\Delta_l:T}^l,\overline{w}_{\Delta_{l-1}:T}^{l-1})$ and normalizing constant estimate $\hat{\tilde{p}}^N(y_{1:T})$.}
\end{enumerate}
\end{algorithm}
| \begin{algorithm}
[h]
\caption{Delta Particle Filter}
\begin{enumerate}
\item{Input: data $y_{1:T}$, level $l\in\mathbb{N}$, particle number $N\in\mathbb{N}$ and parameter $\theta\in\Theta$.}
\item{Initialize: For $i\in\{1,\dots,N\}$, independently generate $\overline{W}_{\Delta_l:1}^{i,l}$ from $\mathcal{N}(0,\Delta_l)$. For $(i,k)\in\{1,\dots,N\}\times\{1,\dots,\Delta_{l-1}^{-1}\}$ set
$
\overline{W}_{k\Delta_{l-1}}^{i,l-1} = \overline{W}_{2k\Delta_{l}}^{i,l} + \overline{W}_{(2k-1)\Delta_{l}}^{i,l}.
$
Set $t=1$, $\hat{\tilde{p}}^N(y_{1:0})=1$ for convention and go to step 3.}
\item{Iterate: For $i\in\{1,\dots,N\}$ compute
$$
\tilde{u}_t^i = \frac{\max\{\kappa_{t,l}(\overline{w}_{\Delta_l:t}^{i,l}),\kappa_{t,l-1}(\overline{w}_{\Delta_{l-1}:t}^{i,l-1})\}}{\sum_{j=1}^N\max\{\kappa_{t,l}(\overline{w}_{\Delta_l:t}^{j,l}),\kappa_{t,l-1}(\overline{w}_{\Delta_{l-1}:t}^{j,l-1})\}}.
$$
Set $\hat{p}^N(y_{1:t})={\hat{p}^N(y_{1:t-1})}\tfrac{1}{N}\sum_{i=1}^N\max\{\kappa_{t,l}(\overline{w}_{\Delta_l:t}^{i,l}),\kappa_{t,l-1}(\overline{w}_{\Delta_{l-1}:t}^{i,l-1})\}$.
Then sample $(\overline{w}_{\Delta_l:t}^{1:N,l},\overline{w}_{\Delta_{l-1}:t}^{1:N,l-1})$ with replacement from
$(\overline{w}_{\Delta_l:t}^{1:N,l},\overline{w}_{\Delta_{l-1}:t}^{1:N,l-1})$
using probabilities
$\tilde{u}_t^{1:N}$. For $i\in\{1,\dots,N\}$, independently generate $\overline{W}_{t+\Delta_l:t+1}^i$ from $\mathcal{N}(0,\Delta_l)$. For $(i,k)\in\{1,\dots,N\}\times\{1,\dots,\Delta_{l-1}^{-1}\}$ set
$
\overline{W}_{t+k\Delta_{l-1}}^{i,l-1} = \overline{W}_{t+2k\Delta_{l}}^{i,l} + \overline{W}_{t+(2k-1)\Delta_{l}}^{i,l}.
$
Set $t=t+1$ and if $t=T$ go to step 4, otherwise restart step 3.}
\item{Grand Selection: For $i\in\{1,\dots,N\}$ compute
$
\tilde{u}_T^i = \frac{\max\{\kappa_{T,l}(\overline{w}_{\Delta_l:T}^{i,l}),\kappa_{T,l-1}(\overline{w}_{\Delta_{l-1}:T}^{i,l-1})\}}{\sum_{j=1}^N\max\{\kappa_{T,l}(\overline{w}_{\Delta_l:T}^{j,l}),\kappa_{T,l-1}(\overline{w}_{\Delta_{l-1}:T}^{j,l-1})\}}.
$
Set $\hat{p}^N(y_{1:T})=\hat{p}^N(y_{1:T-1})\tfrac{1}{N}\sum_{i=1}^N
\max\{\kappa_{T,l}(\overline{w}_{\Delta_l:T}^{i,l}),\kappa_{T,l-1}(\overline{w}_{\Delta_{l-1}:T}^{i,l-1})\}$.
Sample one $(\overline{w}_{\Delta_l:T}^l, \overline{w}_{\Delta_{l-1}:T}^{l-1})$ from $(\overline{w}_{\Delta_l:T}^{1:N,l},\overline{w}_{\Delta_{l-1}:T}^{1:N,l-1})$ using $\tilde{u}_T^{1:N}$ and go to step 5.}
\item{Output: trajectories $(\overline{w}_{\Delta_l:T}^l,\overline{w}_{\Delta_{l-1}:T}^{l-1})$ and normalizing constant estimate $\hat{\tilde{p}}^N(y_{1:T})$.}
\end{enumerate}
\end{algorithm} | "https://arxiv.org/src/2310.03114" | "2310.03114.tar.gz" | "2024-02-19" | {
"title": "bayesian parameter inference for partially observed stochastic volterra equations",
"id": "2310.03114",
"abstract": "in this article we consider bayesian parameter inference for a type of partially observed stochastic volterra equation (sve). sves are found in many areas such as physics and mathematical finance. in the latter field they can be used to represent long memory in unobserved volatility processes. in many cases of practical interest, sves must be time-discretized and then parameter inference is based upon the posterior associated to this time-discretized process. based upon recent studies on time-discretization of sves (e.g. richard et al. 2021), we use euler-maruyama methods for the afore-mentioned discretization. we then show how multilevel markov chain monte carlo (mcmc) methods (jasra et al. 2018) can be applied in this context. in the examples we study, we give a proof that shows that the cost to achieve a mean square error (mse) of $\\mathcal{o}(\\epsilon^2)$, $\\epsilon>0$, is {$\\mathcal{o}(\\epsilon^{-\\tfrac{4}{2h+1}})$, where $h$ is the hurst parameter. if one uses a single level mcmc method then the cost is $\\mathcal{o}(\\epsilon^{-\\tfrac{2(2h+3)}{2h+1}})$} to achieve the same mse. we illustrate these results in the context of state-space and stochastic volatility models, with the latter applied to real data.",
"categories": "stat.co stat.me",
"doi": "",
"created": "2023-10-04",
"updated": "2024-02-19",
"authors": [
"ajay jasra",
"hamza ruzayqat",
"amin wu"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2310.03114"
} | "2024-03-15T05:09:03.161347" | {
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} | [] | "algorithm" | "17852f5e-7351-4d19-9943-a69ce6cc989f" | 2563 | hard |
|
\begin{algorithm}
\caption{\texttt{IBB} (Independent Block Bootstrap)}
\label{alg:ibb}
\begin{algorithmic}[1]
\Require $(X_1, \ldots, X_n)$, $(Y_1, \ldots, Y_n)$, $d$
\State $N \gets \lfloor n/d \rfloor$
\For{$k = 1, \ldots, N$}
\State $B_{X,k} \gets (X_{(k-1)d + 1}, \ldots, X_{kd})$
\State $B_{Y,k} \gets (Y_{(k-1)d + 1}, \ldots, Y_{kd})$
\EndFor
\For{$k = 1, \ldots, N$}
\State $B_{X,k}^* \gets$ random element from $\{B_{X,1}, \ldots, B_{X,N}\}$ drawn with replacement
\State $B_{Y,k}^* \gets$ random element from $\{B_{Y,1}, \ldots, B_{Y,N}\}$ drawn with replacement
\EndFor
\State $\left(X_1^*, \ldots, X_{Nd}^*\right) \gets \left(B_{X,1}^*, \ldots, B_{X,N}^*\right)$
\State $\left(Y_1^*, \ldots, Y_{Nd}^*\right) \gets \left(B_{Y,1}^*, \ldots, B_{Y,N}^*\right)$
\Ensure $\left(X_1^*, \ldots, X_{Nd}^*\right)$, $\left(Y_1^*, \ldots, Y_{Nd}^*\right)$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{\texttt{IBB} (Independent Block Bootstrap)}
\begin{algorithmic}
[1]
\Require $(X_1, \ldots, X_n)$, $(Y_1, \ldots, Y_n)$, $d$
\State $N \gets \lfloor n/d \rfloor$
\For{$k = 1, \ldots, N$}
\State $B_{X,k} \gets (X_{(k-1)d + 1}, \ldots, X_{kd})$
\State $B_{Y,k} \gets (Y_{(k-1)d + 1}, \ldots, Y_{kd})$
\EndFor
\For{$k = 1, \ldots, N$}
\State $B_{X,k}^* \gets$ random element from $\{B_{X,1}, \ldots, B_{X,N}\}$ drawn with replacement
\State $B_{Y,k}^* \gets$ random element from $\{B_{Y,1}, \ldots, B_{Y,N}\}$ drawn with replacement
\EndFor
\State $\left(X_1^*, \ldots, X_{Nd}^*\right) \gets \left(B_{X,1}^*, \ldots, B_{X,N}^*\right)$
\State $\left(Y_1^*, \ldots, Y_{Nd}^*\right) \gets \left(B_{Y,1}^*, \ldots, B_{Y,N}^*\right)$
\Ensure $\left(X_1^*, \ldots, X_{Nd}^*\right)$, $\left(Y_1^*, \ldots, Y_{Nd}^*\right)$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2112.14091" | "2112.14091.tar.gz" | "2024-02-05" | {
"title": "a bootstrap test for independence of time series based on the distance covariance",
"id": "2112.14091",
"abstract": "we present a test for independence of two strictly stationary time series based on a bootstrap procedure for the distance covariance. our test detects any kind of dependence between the two time series within an arbitrary maximum lag $l$. in simulation studies, our test outperforms alternative testing procedures. in proving the validity of the underlying bootstrap procedure, we generalise bounds for the wasserstein distance between an empirical measure and its marginal distribution under the assumption of $\\alpha$-mixing. previous results of this kind only existed for i.i.d. processes.",
"categories": "math.st stat.th",
"doi": "",
"created": "2021-12-28",
"updated": "2024-02-05",
"authors": [
"annika betken",
"herold dehling",
"marius kroll"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2112.14091"
} | "2024-03-15T07:11:00.545120" | {
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} | [] | "algorithm" | "fb8ae28c-85f5-4740-a170-b955b44525d6" | 873 | medium |
|
\begin{algorithmic}[1]
\State $x_{\emptyset} \leftarrow 0$
\For{$k = 1, \ldots, n$}
\For{each subset $N \subseteq [n]$ with $|N| = k$}
\State $x_N \leftarrow \infty$
\For{each agent $i \in N$}
\State $y \leftarrow \textsc{Mark}_i(x_{N \setminus \{i\}}, 1/n)$
\State \algorithmicif \ $y < x_N$ \algorithmicthen \ $x_N \leftarrow y$ \algorithmiccomment{this finds the ``best'' $x_N$}
\EndFor
\EndFor
\EndFor
\State \algorithmicif \ $x_{[n]} < 1$ \algorithmicthen \ \Return true \algorithmicelse \ \Return false
\end{algorithmic}
| \begin{algorithmic}
[1]
\State $x_{\emptyset} \leftarrow 0$
\For{$k = 1, \ldots, n$}
\For{each subset $N \subseteq [n]$ with $|N| = k$}
\State $x_N \leftarrow \infty$
\For{each agent $i \in N$}
\State $y \leftarrow \textsc{Mark}_i(x_{N \setminus \{i\}}, 1/n)$
\State \algorithmicif \ $y < x_N$ \algorithmicthen \ $x_N \leftarrow y$ \algorithmiccomment{this finds the ``best'' $x_N$}
\EndFor
\EndFor
\EndFor
\State \algorithmicif \ $x_{[n]} < 1$ \algorithmicthen \ \Return true \algorithmicelse \ \Return false
\end{algorithmic} | "https://arxiv.org/src/2312.15326" | "2312.15326.tar.gz" | "2024-02-13" | {
"title": "on connected strongly-proportional cake-cutting",
"id": "2312.15326",
"abstract": "we investigate the problem of fairly dividing a divisible heterogeneous resource, also known as a cake, among a set of agents. we characterize the existence of an allocation in which every agent receives a contiguous piece worth strictly more than their proportional share, also known as a *strongly-proportional allocation*. the characterization is supplemented with an algorithm that determines the existence of a connected strongly-proportional allocation using at most $n \\cdot 2^{n-1}$ queries. we provide a simpler characterization for agents with strictly positive valuations, and show that the number of queries required to determine the existence of a connected strongly-proportional allocation is in $\\theta(n^2)$. our proofs are constructive and yield a connected strongly-proportional allocation, when it exists, using a similar number of queries.",
"categories": "math.co cs.gt econ.th",
"doi": "",
"created": "2023-12-23",
"updated": "2024-02-13",
"authors": [
"zsuzsanna jank\u00f3",
"attila jo\u00f3",
"erel segal-halevi",
"sheung man yuen"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2312.15326"
} | "2024-03-15T04:11:23.042663" | {
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} | [] | "algorithm" | "ea33ced4-5e0f-460e-9fab-72ff75af8966" | 527 | easy |
|
\begin{algorithm}[!ht]\caption{Dynamic KDE, query part, informal version of Algorithm~\ref{alg:dynamic_KDE_query}}\label{alg:dynamic_KDE_query_pseudo}
\begin{algorithmic}[1]
\State {\bf data structure} \textsc{DynamicKDE} \Comment{Theorem~\ref{thm:main_result}}
\State
\Procedure{\textsc{Query}}{$q\in \mathbb{R}^d, \epsilon \in (0,1),f_{\mathsf{KDE}} \in [0,1]$}
\For{$a=1,2,\cdots,K_1$}
\For{$r=1,2,\cdots,R$}
\State Recover near neighbours of $q$ using $\mathcal{H}_{a,r}$
\State Store them into $\mathcal{S}$
\EndFor
\For{$x_{i}\in \mathcal{S}$}
\State $w_{i}\leftarrow f(x_{i},q)$
\If{ {$x_{i}\in L_{r}$ for some $r\in[R]$}}
\State $p_i \gets \min\{\frac{1}{2^r n f_{\mathsf{KDE}}}, 1\}$
\EndIf
\EndFor
\State $T_{a}\leftarrow\sum_{x_{i}\in\mathcal{S}}\frac{w_i}{p_i}$
\EndFor
\State \Return $\mathrm{Median}_{a \in K_1} \{T_{a}\}$
\EndProcedure
\State
\State {\bf end data structure}
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}[!ht]
\caption{Dynamic KDE, query part, informal version of Algorithm~\ref{alg:dynamic_KDE_query}}\begin{algorithmic}
[1]
\State {\bf data structure} \textsc{DynamicKDE} \Comment{Theorem~\ref{thm:main_result}}
\State
\Procedure{\textsc{Query}}{$q\in \mathbb{R}^d, \epsilon \in (0,1),f_{\mathsf{KDE}} \in [0,1]$}
\For{$a=1,2,\cdots,K_1$}
\For{$r=1,2,\cdots,R$}
\State Recover near neighbours of $q$ using $\mathcal{H}_{a,r}$
\State Store them into $\mathcal{S}$
\EndFor
\For{$x_{i}\in \mathcal{S}$}
\State $w_{i}\leftarrow f(x_{i},q)$
\If{ {$x_{i}\in L_{r}$ for some $r\in[R]$}}
\State $p_i \gets \min\{\frac{1}{2^r n f_{\mathsf{KDE}}}, 1\}$
\EndIf
\EndFor
\State $T_{a}\leftarrow\sum_{x_{i}\in\mathcal{S}}\frac{w_i}{p_i}$
\EndFor
\State \Return $\mathrm{Median}_{a \in K_1} \{T_{a}\}$
\EndProcedure
\State
\State {\bf end data structure}
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2208.03915" | "2208.03915.tar.gz" | "2024-02-13" | {
"title": "dynamic maintenance of kernel density estimation data structure: from practice to theory",
"id": "2208.03915",
"abstract": "kernel density estimation (kde) stands out as a challenging task in machine learning. the problem is defined in the following way: given a kernel function $f(x,y)$ and a set of points $\\{x_1, x_2, \\cdots, x_n \\} \\subset \\mathbb{r}^d$, we would like to compute $\\frac{1}{n}\\sum_{i=1}^{n} f(x_i,y)$ for any query point $y \\in \\mathbb{r}^d$. recently, there has been a growing trend of using data structures for efficient kde. however, the proposed kde data structures focus on static settings. the robustness of kde data structures over dynamic changing data distributions is not addressed. in this work, we focus on the dynamic maintenance of kde data structures with robustness to adversarial queries. especially, we provide a theoretical framework of kde data structures. in our framework, the kde data structures only require subquadratic spaces. moreover, our data structure supports the dynamic update of the dataset in sublinear time. furthermore, we can perform adaptive queries with the potential adversary in sublinear time.",
"categories": "cs.lg stat.ml",
"doi": "",
"created": "2022-08-08",
"updated": "2024-02-13",
"authors": [
"jiehao liang",
"zhao song",
"zhaozhuo xu",
"junze yin",
"danyang zhuo"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2208.03915"
} | "2024-03-15T05:48:56.340651" | {
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} | [] | "algorithm" | "0efb6973-2e92-4be0-8f7b-42c96d7445a5" | 888 | medium |
|
\begin{algorithmic}
\Require $s_0 = 4$, $\mu_0 = 0$, $\phi_0 = 0.95$, $\sigma^{2}_{\eta,0} = 0.02$
\For{\texttt{b in} $1:B_{draws}$}
\State \text{Sample states (Kalman Filter and Smoother): } $\boldsymbol{h}_b \sim h|y^{\ast}, s_{b-1}, \phi_{b-1}, \sigma^{2}_{\eta,b-1}, \mu_{b-1}$
\State \text{Sample mixture indicators: } $s_b \sim s|y^{\ast}, \boldsymbol{h}_{b-1}$
\State \text{Sample from conjugate density $\mu$: } $\mu_b \sim \mu|y_{\ast}, s_{b-1}, \phi_{b-1}, \sigma^{2}_{\eta, b-1}, \boldsymbol{h}_{b-1}$
\State \text{Sample from conjugate density $\sigma^2_{\eta}$: } $\mu_b \sim \mu|y^{\ast}, s_{b-1}, \phi_{b-1}, \mu_{b-1}, \boldsymbol{h}_{b-1}$
\State \text{Sample via Metropolis-Hastings $\phi$: } $\phi_b \sim \phi|y^{\ast}, s_{b-1}, \mu_{b-1}, \sigma^{2}_{\eta, b-1}, \boldsymbol{h}_{b-1}$
\EndFor
\end{algorithmic}
| \begin{algorithmic}
\Require $s_0 = 4$, $\mu_0 = 0$, $\phi_0 = 0.95$, $\sigma^{2}_{\eta,0} = 0.02$
\For{\texttt{b in} $1:B_{draws}$}
\State \text{Sample states (Kalman Filter and Smoother): } $\boldsymbol{h}_b \sim h|y^{\ast}, s_{b-1}, \phi_{b-1}, \sigma^{2}_{\eta,b-1}, \mu_{b-1}$
\State \text{Sample mixture indicators: } $s_b \sim s|y^{\ast}, \boldsymbol{h}_{b-1}$
\State \text{Sample from conjugate density $\mu$: } $\mu_b \sim \mu|y_{\ast}, s_{b-1}, \phi_{b-1}, \sigma^{2}_{\eta, b-1}, \boldsymbol{h}_{b-1}$
\State \text{Sample from conjugate density $\sigma^2_{\eta}$: } $\mu_b \sim \mu|y^{\ast}, s_{b-1}, \phi_{b-1}, \mu_{b-1}, \boldsymbol{h}_{b-1}$
\State \text{Sample via Metropolis-Hastings $\phi$: } $\phi_b \sim \phi|y^{\ast}, s_{b-1}, \mu_{b-1}, \sigma^{2}_{\eta, b-1}, \boldsymbol{h}_{b-1}$
\EndFor
\end{algorithmic} | "https://arxiv.org/src/2402.12384" | "2402.12384.tar.gz" | "2024-01-27" | {
"title": "comparing mcmc algorithms in stochastic volatility models using simulation based calibration",
"id": "2402.12384",
"abstract": "simulation based calibration (sbc) is applied to analyse two commonly used, competing markov chain monte carlo algorithms for estimating the posterior distribution of a stochastic volatility model. in particular, the bespoke 'off-set mixture approximation' algorithm proposed by kim, shephard, and chib (1998) is explored together with a hamiltonian monte carlo algorithm implemented through stan. the sbc analysis involves a simulation study to assess whether each sampling algorithm has the capacity to produce valid inference for the correctly specified model, while also characterising statistical efficiency through the effective sample size. results show that stan's no-u-turn sampler, an implementation of hamiltonian monte carlo, produces a well-calibrated posterior estimate while the celebrated off-set mixture approach is less efficient and poorly calibrated, though model parameterisation also plays a role. limitations and restrictions of generality are discussed.",
"categories": "stat.ap econ.em",
"doi": "",
"created": "2024-01-27",
"updated": "",
"authors": [
"benjamin wee"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.12384"
} | "2024-03-15T03:27:09.183136" | {
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} | [] | "algorithm" | "26e708d1-288f-488f-adf7-39c41848f54f" | 830 | medium |
|
\begin{algorithmic}[1]
\State $\eta_1 = \eta$
\State $\theta_1^{in} = \theta_0$
\For{$b = 1,..., B$}
\State Run SGD with constant step size $\eta_b$ for $t_b$ steps, starting from $\theta_{b}^{in}$
\State Let the last update be $\theta_{b}^{last}$
\State $D_b = \textbf{Diagnostic}(\eta_b, w, l, q, \theta_{b}^{last})$
\State $\theta_{b+1}^{in} = \theta_{D_b}$
\If{$T_{D_b} = S$}
\State $\eta_{b+1} = \gamma\cdot\eta_b$ and $t_{b+1} = \lfloor t_b/\gamma \rfloor$
\Else
\State $\eta_{b+1} = \eta_b$ and $t_{b+1} = t_b$
\EndIf
\EndFor
\end{algorithmic}
| \begin{algorithmic}
[1]
\State $\eta_1 = \eta$
\State $\theta_1^{in} = \theta_0$
\For{$b = 1,..., B$}
\State Run SGD with constant step size $\eta_b$ for $t_b$ steps, starting from $\theta_{b}^{in}$
\State Let the last update be $\theta_{b}^{last}$
\State $D_b = \textbf{Diagnostic}(\eta_b, w, l, q, \theta_{b}^{last})$
\State $\theta_{b+1}^{in} = \theta_{D_b}$
\If{$T_{D_b} = S$}
\State $\eta_{b+1} = \gamma\cdot\eta_b$ and $t_{b+1} = \lfloor t_b/\gamma \rfloor$
\Else
\State $\eta_{b+1} = \eta_b$ and $t_{b+1} = t_b$
\EndIf
\EndFor
\end{algorithmic} | "https://arxiv.org/src/1910.08597" | "1910.08597.tar.gz" | "2024-02-16" | {
"title": "robust learning rate selection for stochastic optimization via splitting diagnostic",
"id": "1910.08597",
"abstract": "this paper proposes splitsgd, a new dynamic learning rate schedule for stochastic optimization. this method decreases the learning rate for better adaptation to the local geometry of the objective function whenever a stationary phase is detected, that is, the iterates are likely to bounce at around a vicinity of a local minimum. the detection is performed by splitting the single thread into two and using the inner product of the gradients from the two threads as a measure of stationarity. owing to this simple yet provably valid stationarity detection, splitsgd is easy-to-implement and essentially does not incur additional computational cost than standard sgd. through a series of extensive experiments, we show that this method is appropriate for both convex problems and training (non-convex) neural networks, with performance compared favorably to other stochastic optimization methods. importantly, this method is observed to be very robust with a set of default parameters for a wide range of problems and, moreover, can yield better generalization performance than other adaptive gradient methods such as adam.",
"categories": "stat.ml cs.lg math.oc stat.me",
"doi": "",
"created": "2019-10-18",
"updated": "2024-02-16",
"authors": [
"matteo sordello",
"niccol\u00f2 dalmasso",
"hangfeng he",
"weijie su"
],
"affiliation": [],
"url": "https://arxiv.org/abs/1910.08597"
} | "2024-03-15T04:35:48.772484" | {
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} | [] | "algorithm" | "2f38469c-5a96-40ca-9473-84809ef12b14" | 551 | easy |
|
\begin{algorithm}{({\bf Numerical Computation of the Projector onto ${\cal A}$})} \label{alg:projA}\
\begin{description}
\item[Step 0] ({\em Initialization}) The following are given: Current iterate $u^-$, the system and control matrices $A(t)$ and $B(t)$, the numbers of state and control variables $n$ and $m$, and the initial and terminal states $x_0$ and $x_f$, respectively.
\item[Step 1] ({\em Near-miss function}) Solve \eqref{eqn:lin_sys} with ICs in \eqref{eqn:IC}(i) to find $z(t_f,0) := x(t_f)$. \\ Set $\varphi(0) := z(t_f,0)-x_f$.
\item[Step 2] ({\em Jacobian}) For $i = 1,\ldots,n$, solve \eqref{eqn:lin_sys} with ICs in \eqref{eqn:IC}(ii), to get $z(t_f,e_i)$. \\
Set $\beta_i(t) := z(t_f,e_i) - z(t_f,0)$ and $J_\varphi(0) := \left[\beta_1(t)\ |\ \dots\ |\ \beta_n(t) \right]$.
\item[Step 3] ({\em Missing IC}) Solve $J_{\varphi}(0)\,\lambda_0 := -\varphi(0)$ for $\lambda_0$.
\item[Step 4] ({\em Projector onto ${\cal A}$}) Solve \eqref{eqn:lin_sys} with ICs in \eqref{eqn:IC}(iii) to find $\lambda(t)$. \\
Set $P_{\cal{A}}(u^-)(t) := u^-(t)-B^T(t)\lambda(t)$.
\end{description}
\end{algorithm}
| \begin{algorithm}
{({\bf Numerical Computation of the Projector onto ${\cal A}$})} \
\begin{description}
\item[Step 0] ({\em Initialization}) The following are given: Current iterate $u^-$, the system and control matrices $A(t)$ and $B(t)$, the numbers of state and control variables $n$ and $m$, and the initial and terminal states $x_0$ and $x_f$, respectively.
\item[Step 1] ({\em Near-miss function}) Solve \eqref{eqn:lin_sys} with ICs in \eqref{eqn:IC}(i) to find $z(t_f,0) := x(t_f)$. \\ Set $\varphi(0) := z(t_f,0)-x_f$.
\item[Step 2] ({\em Jacobian}) For $i = 1,\ldots,n$, solve \eqref{eqn:lin_sys} with ICs in \eqref{eqn:IC}(ii), to get $z(t_f,e_i)$. \\
Set $\beta_i(t) := z(t_f,e_i) - z(t_f,0)$ and $J_\varphi(0) := \left[\beta_1(t)\ |\ \dots\ |\ \beta_n(t) \right]$.
\item[Step 3] ({\em Missing IC}) Solve $J_{\varphi}(0)\,\lambda_0 := -\varphi(0)$ for $\lambda_0$.
\item[Step 4] ({\em Projector onto ${\cal A}$}) Solve \eqref{eqn:lin_sys} with ICs in \eqref{eqn:IC}(iii) to find $\lambda(t)$. \\
Set $P_{\cal{A}}(u^-)(t) := u^-(t)-B^T(t)\lambda(t)$.
\end{description}
\end{algorithm} | "https://arxiv.org/src/2210.17279" | "2210.17279.tar.gz" | "2024-01-11" | {
"title": "douglas--rachford algorithm for control-constrained minimum-energy control problems",
"id": "2210.17279",
"abstract": "splitting and projection-type algorithms have been applied to many optimization problems due to their simplicity and efficiency, but the application of these algorithms to optimal control is less common. in this paper we utilize the douglas--rachford (dr) algorithm to solve control-constrained minimum-energy optimal control problems. instead of the traditional approach where one discretizes the problem and solves it using large-scale finite-dimensional numerical optimization techniques we split the problem in two subproblems and use the dr algorithm to find an optimal point in the intersection of the solution sets of these two subproblems hence giving a solution to the original problem. we derive general expressions for the projections and propose a numerical approach. we obtain analytic closed-form expressions for the projectors of pure, under-, critically- and over-damped harmonic oscillators. we illustrate the working of our approach to solving not only these example problems but also a challenging machine tool manipulator problem. through numerical case studies, we explore and propose desirable ranges of values of an algorithmic parameter which yield smaller number of iterations.",
"categories": "math.oc",
"doi": "",
"created": "2022-10-31",
"updated": "2024-01-11",
"authors": [
"regina s. burachik",
"bethany i. caldwell",
"c. yal\u00e7\u0131n kaya"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2210.17279"
} | "2024-03-15T06:24:12.690702" | {
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} | [] | "algorithm" | "54fc2259-a324-4057-a8ea-94663b696837" | 1095 | medium |
|
\begin{algorithmic}[1]
\Statex \textbf{Input:} $\phi$, $\theta$, initial episodes $K_{\mathrm{init}}$, total budget of episodes $K_{\mathrm{E}}$,
\Statex \textbf{Init:} $\phi' \gets \phi$, $\theta' \gets \theta$, $\mathcal{D} \gets \emptyset$
\For{each initial episode $1,\dots,K_{\mathrm{init}}$}
\State Sample a batch $\mathcal{T}$ of $M$ sequences using pre-trained policy $\pi_\theta$
\State Score each sequence in $\mathcal{T}$
\State Add unique, valid sequences to replay memory $\mathcal{D}$
\EndFor
\For{each episode $K_{\mathrm{init}}+1,\dots,K_{\mathrm{E}}$}
\State Sample a batch $\mathcal{T}$ of $M$ sequences using current policy $\pi_\theta$
\State Score each sequence in $\mathcal{T}$
\State Add unique, valid sequences to replay memory $\mathcal{D}$
\State $\phi \gets \phi - \lambda_Q \hat{\nabla}_\phi J_Q (\phi \vert \mathcal{T})$ \Comment{On-policy update of Q-function parameters}
\State $\theta \gets \theta - \lambda_\pi \hat{\nabla}_\theta J_\pi (\theta\vert \mathcal{T})$ \Comment{On-policy update of policy parameters}
\State $\alpha \gets \alpha - \lambda_\alpha \hat{\nabla}_\alpha J_\alpha (\alpha \vert \mathcal{T})$ \Comment{On-policy update of temperature}
\State $\phi' \gets \tau \phi' + (1-\tau) \phi$ \Comment{Update target parameters}
\State $\theta' \gets \tau \theta' + (1-\tau) \theta$ \Comment{Update average policy parameters}
\For{each off-policy update}
\State $\phi \gets \phi - \lambda_Q \hat{\nabla}_\phi J_Q (\phi \vert \mathcal{D})$
\State $\theta \gets \theta - \lambda_\pi \hat{\nabla}_\theta J_\pi (\theta\vert \mathcal{D})$
\State $\alpha \gets \alpha - \lambda_\alpha \hat{\nabla}_\alpha J_a (\alpha \vert \mathcal{D})$
\State $\phi' \gets \tau \phi' + (1-\tau) \phi$
\State $\theta' \gets \tau \theta' + (1-\tau) \theta$
\EndFor
\EndFor
\end{algorithmic}
| \begin{algorithmic}
[1]
\Statex \textbf{Input:} $\phi$, $\theta$, initial episodes $K_{\mathrm{init}}$, total budget of episodes $K_{\mathrm{E}}$,
\Statex \textbf{Init:} $\phi' \gets \phi$, $\theta' \gets \theta$, $\mathcal{D} \gets \emptyset$
\For{each initial episode $1,\dots,K_{\mathrm{init}}$}
\State Sample a batch $\mathcal{T}$ of $M$ sequences using pre-trained policy $\pi_\theta$
\State Score each sequence in $\mathcal{T}$
\State Add unique, valid sequences to replay memory $\mathcal{D}$
\EndFor
\For{each episode $K_{\mathrm{init}}+1,\dots,K_{\mathrm{E}}$}
\State Sample a batch $\mathcal{T}$ of $M$ sequences using current policy $\pi_\theta$
\State Score each sequence in $\mathcal{T}$
\State Add unique, valid sequences to replay memory $\mathcal{D}$
\State $\phi \gets \phi - \lambda_Q \hat{\nabla}_\phi J_Q (\phi \vert \mathcal{T})$ \Comment{On-policy update of Q-function parameters}
\State $\theta \gets \theta - \lambda_\pi \hat{\nabla}_\theta J_\pi (\theta\vert \mathcal{T})$ \Comment{On-policy update of policy parameters}
\State $\alpha \gets \alpha - \lambda_\alpha \hat{\nabla}_\alpha J_\alpha (\alpha \vert \mathcal{T})$ \Comment{On-policy update of temperature}
\State $\phi' \gets \tau \phi' + (1-\tau) \phi$ \Comment{Update target parameters}
\State $\theta' \gets \tau \theta' + (1-\tau) \theta$ \Comment{Update average policy parameters}
\For{each off-policy update}
\State $\phi \gets \phi - \lambda_Q \hat{\nabla}_\phi J_Q (\phi \vert \mathcal{D})$
\State $\theta \gets \theta - \lambda_\pi \hat{\nabla}_\theta J_\pi (\theta\vert \mathcal{D})$
\State $\alpha \gets \alpha - \lambda_\alpha \hat{\nabla}_\alpha J_a (\alpha \vert \mathcal{D})$
\State $\phi' \gets \tau \phi' + (1-\tau) \phi$
\State $\theta' \gets \tau \theta' + (1-\tau) \theta$
\EndFor
\EndFor
\end{algorithmic} | "https://arxiv.org/src/2303.17615" | "2303.17615.tar.gz" | "2024-01-30" | {
"title": "utilizing reinforcement learning for de novo drug design",
"id": "2303.17615",
"abstract": "deep learning-based approaches for generating novel drug molecules with specific properties have gained a lot of interest in the last few years. recent studies have demonstrated promising performance for string-based generation of novel molecules utilizing reinforcement learning. in this paper, we develop a unified framework for using reinforcement learning for de novo drug design, wherein we systematically study various on- and off-policy reinforcement learning algorithms and replay buffers to learn an rnn-based policy to generate novel molecules predicted to be active against the dopamine receptor drd2. our findings suggest that it is advantageous to use at least both top-scoring and low-scoring molecules for updating the policy when structural diversity is essential. using all generated molecules at an iteration seems to enhance performance stability for on-policy algorithms. in addition, when replaying high, intermediate, and low-scoring molecules, off-policy algorithms display the potential of improving the structural diversity and number of active molecules generated, but possibly at the cost of a longer exploration phase. our work provides an open-source framework enabling researchers to investigate various reinforcement learning methods for de novo drug design.",
"categories": "q-bio.bm cs.lg",
"doi": "",
"created": "2023-03-30",
"updated": "2024-01-30",
"authors": [
"hampus gummesson svensson",
"christian tyrchan",
"ola engkvist",
"morteza haghir chehreghani"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2303.17615"
} | "2024-03-15T06:00:14.855698" | {
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} | [] | "algorithm" | "2909d43e-dd04-41e9-bbc4-dd4424606c0b" | 1810 | hard |
|
\begin{algorithmic}[1]
\Require $\mathcal{G} = (V, E) $, $\mathbf{H}^{(t-1)}=\left[\mathbf{h}_1^{(t-1)},\cdots \mathbf{h}_n^{(t-1)}\right]$, $\mathbf{A}^{(0)}$;
\Ensure $\mathbf{A}^{(t)}$;
\renewcommand{\algorithmicensure}{\textbf{Hyper-paramters:}}
\Ensure: $m$, $K$, $\gamma$
\State Initialization: $J_s = \phi$
\For{$u\in V$} /* \textit{Degree-based Node Sampling} */
\State $\mathbf{d}_u \leftarrow \sum_{v}^{|V|} \mathbf{A}^{(0)}_{u,v}$
\State $p_{s}(u) \leftarrow \frac{\mathbf{d}_u}{\sum_{i=1}^{n} \mathbf{d}_{i}}$
\EndFor
\For{$1$ to $m$}
\State Take a sampling on node $u_s$ from $V$ according to $p_{s}(u_s)$
\While{$v \in \tilde{\mathbf{N}}\left (u_s \right )$}
\State Calculate $\Delta_{u_{s},v} = \| \mathbf{h}_{u_s}^{(t-1)} - \mathbf{h}_{v}^{(t-1)} \|_2 $ %
\State $p_{s}(v) \leftarrow p_{s}(v) \cdot f(\Delta_{u_{s},v}) $
\EndWhile
\State $J_s \leftarrow J_s \cup \{u_s\}$
\EndFor
\While{sample node $u_s \in J_s$} /* \textit{Graph Refinement} */
\For{$k=1$ to $K$}
\State Select $\mathcal{k}$ nearest neighbors of $\mathbf{h}^{(t-1),k}_{u_s}$ as ${\mathbf{N}'}\left (u_s \right )$
\State $ \tilde{\mathbf{A}}^{(t-1),k}_{u_s,{\mathbf{N}'}\left (u_s \right )} \leftarrow \cos (\mathbf{h}^{(t-1),k}_{u_s}, \mathbf{h}^{(t-1),k}_{{\mathbf{N}'}\left (u_s \right )})$
\EndFor
\EndWhile
\State $\tilde{\mathbf{A}}^{(t-1)} \leftarrow \textrm{maxpooling}(\tilde{\mathbf{A}}^{(t-1),1},\tilde{\mathbf{A}}^{(t-1),2}, \cdots, \tilde{\mathbf{A}}^{(t-1),K})$
\State Obtain the refined $\mathbf{A}^{(t)}$ by Eq.(\ref{refining}).
\end{algorithmic}
| \begin{algorithmic}[1]
\Require $\mathcal{G} = (V, E) $, $\mathbf{H}^{(t-1)}=\left[\mathbf{h}_1^{(t-1)},\cdots \mathbf{h}_n^{(t-1)}\right]$, $\mathbf{A}^{(0)}$;
\Ensure $\mathbf{A}^{(t)}$;
\renewcommand{\algorithmicensure}{\textbf{Hyper-paramters:}}
\Ensure: $m$, $K$, $\gamma$
\State Initialization: $J_s = \phi$
\For{$u\in V$} /* \textit{Degree-based Node Sampling} */
\State $\mathbf{d}_u \leftarrow \sum_{v}^{|V|} \mathbf{A}^{(0)}_{u,v}$
\State $p_{s}(u) \leftarrow \frac{\mathbf{d}_u}{\sum_{i=1}^{n} \mathbf{d}_{i}}$
\EndFor
\For{$1$ to $m$}
\State Take a sampling on node $u_s$ from $V$ according to $p_{s}(u_s)$
\While{$v \in \tilde{\mathbf{N}}\left (u_s \right )$}
\State Calculate $\Delta_{u_{s},v} = \| \mathbf{h}_{u_s}^{(t-1)} - \mathbf{h}_{v}^{(t-1)} \|_2 $ %
\State $p_{s}(v) \leftarrow p_{s}(v) \cdot f(\Delta_{u_{s},v}) $
\EndWhile
\State $J_s \leftarrow J_s \cup \{u_s\}$
\EndFor
\While{sample node $u_s \in J_s$} /* \textit{Graph Refinement} */
\For{$k=1$ to $K$}
\State Select $\mathcal{k}$ nearest neighbors of $\mathbf{h}^{(t-1),k}_{u_s}$ as ${\mathbf{N}'}\left (u_s \right )$
\State $ \tilde{\mathbf{A}}^{(t-1),k}_{u_s,{\mathbf{N}'}\left (u_s \right )} \leftarrow \cos (\mathbf{h}^{(t-1),k}_{u_s}, \mathbf{h}^{(t-1),k}_{{\mathbf{N}'}\left (u_s \right )})$
\EndFor
\EndWhile
\State $\tilde{\mathbf{A}}^{(t-1)} \leftarrow \textrm{maxpooling}(\tilde{\mathbf{A}}^{(t-1),1},\tilde{\mathbf{A}}^{(t-1),2}, \cdots, \tilde{\mathbf{A}}^{(t-1),K})$
\State Obtain the refined $\mathbf{A}^{(t)}$ by Eq.(\ref{refining}).
\end{algorithmic} | "https://arxiv.org/src/2103.07295" | "2103.07295.tar.gz" | "2024-01-24" | {
"title": "adversarial graph disentanglement",
"id": "2103.07295",
"abstract": "a real-world graph has a complex topological structure, which is often formed by the interaction of different latent factors. however, most existing methods lack consideration of the intrinsic differences in relations between nodes caused by factor entanglement. in this paper, we propose an \\underline{\\textbf{a}}dversarial \\underline{\\textbf{d}}isentangled \\underline{\\textbf{g}}raph \\underline{\\textbf{c}}onvolutional \\underline{\\textbf{n}}etwork (adgcn) for disentangled graph representation learning. to begin with, we point out two aspects of graph disentanglement that need to be considered, i.e., micro-disentanglement and macro-disentanglement. for them, a component-specific aggregation approach is proposed to achieve micro-disentanglement by inferring latent components that cause the links between nodes. on the basis of micro-disentanglement, we further propose a macro-disentanglement adversarial regularizer to improve the separability among component distributions, thus restricting the interdependence among components. additionally, to reveal the topological graph structure, a diversity-preserving node sampling approach is proposed, by which the graph structure can be progressively refined in a way of local structure awareness. the experimental results on various real-world graph data verify that our adgcn obtains more favorable performance over currently available alternatives. the source codes of adgcn are available at \\textit{\\url{https://github.com/ssgood/adgcn}}.",
"categories": "cs.lg cs.ai",
"doi": "",
"created": "2021-03-12",
"updated": "2024-01-24",
"authors": [
"shuai zheng",
"zhenfeng zhu",
"zhizhe liu",
"jian cheng",
"yao zhao"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2103.07295"
} | "2024-03-15T08:52:54.851311" | {
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} | [] | "algorithm" | "3b89d2ce-94a1-4475-bcd1-65dcab9b6817" | 1545 | hard |
|
\begin{algorithm}[!ht]
\caption{A weighted training approach for A/B tests}
\label{algo:weighted}
\begin{algorithmic}[1]
\Require{The probability of treatment assignment: $p$; a model class for the weight prediction: $\mathcal{G}=\{G_{\theta_W}: \mathbb{R}^d \rightarrow \{0,1\}, {\theta_W}\in \Theta_W\}$; the machine learning model class: $\mathcal{M}=\{M_\theta: \mathcal{X} \rightarrow \mathcal{Y} , \theta\in \Theta\}$; loss functions: $\ell(M(X),Y)$ (could be $m$-dimensional).}
\State Initialize two models, the treatment model ${M}_{\theta_T}$ and the control model ${M}_{\theta_C}$, both of which are set to the current production model.
\For{$t \gets 1$ to the end of the experiment }
\For{$i \gets 1$ to $n_t$ }
\State User $i$ arrives. The platform randomly assigns user $i$ to the treatment group with probability $p$.
\State When a user is assigned to the treatment group, the platform recommends an item based on the treatment algorithm and model, and vice versa.
\State Collect data $(X_{i,t},Y_{i,t},Z_{i,t})$.
\EndFor
\State Compute weights:
$$W_{T,i,t}=\frac{G_{\theta_W}(X_{i,t})}{p} \text{ and } W_{C,i,t}=\frac{1-G_{\theta_W}(X_{i,t})}{1-p} \text{ , for } i=1,2,\ldots,n_t. $$
\State Update the treatment model ${M}_{\theta_T}$ by minimizing the weighted loss
$$\frac{1}{n_t}\sum_{i=1}^{n_t}W_{T,i,t}\ell({M}_{\theta_T}(X_{i,t}),Y_{i,t}).$$
\State Update the control model ${M}_{\theta_C}$ by minimizing the weighted loss
$$\frac{1}{n_t}\sum_{i=1}^{n_t}W_{C,i,t}\ell({M}_{\theta_C}(X_{i,t}),Y_{i,t}).$$
\State Update the model $G_{\theta_W}$ using data $\{(X_{i,t},Z_{i,t}),i=1,\ldots,n_t\}$.
\EndFor
\Return the estimator (\ref{naive_estimator}).
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[!ht]
\caption{A weighted training approach for A/B tests}
\begin{algorithmic}
[1]
\Require{The probability of treatment assignment: $p$; a model class for the weight prediction: $\mathcal{G}=\{G_{\theta_W}: \mathbb{R}^d \rightarrow \{0,1\}, {\theta_W}\in \Theta_W\}$; the machine learning model class: $\mathcal{M}=\{M_\theta: \mathcal{X} \rightarrow \mathcal{Y} , \theta\in \Theta\}$; loss functions: $\ell(M(X),Y)$ (could be $m$-dimensional).}
\State Initialize two models, the treatment model ${M}_{\theta_T}$ and the control model ${M}_{\theta_C}$, both of which are set to the current production model.
\For{$t \gets 1$ to the end of the experiment }
\For{$i \gets 1$ to $n_t$ }
\State User $i$ arrives. The platform randomly assigns user $i$ to the treatment group with probability $p$.
\State When a user is assigned to the treatment group, the platform recommends an item based on the treatment algorithm and model, and vice versa.
\State Collect data $(X_{i,t},Y_{i,t},Z_{i,t})$.
\EndFor
\State Compute weights:
$$W_{T,i,t}=\frac{G_{\theta_W}(X_{i,t})}{p} \text{ and } W_{C,i,t}=\frac{1-G_{\theta_W}(X_{i,t})}{1-p} \text{ , for } i=1,2,\ldots,n_t. $$
\State Update the treatment model ${M}_{\theta_T}$ by minimizing the weighted loss
$$\frac{1}{n_t}\sum_{i=1}^{n_t}W_{T,i,t}\ell({M}_{\theta_T}(X_{i,t}),Y_{i,t}).$$
\State Update the control model ${M}_{\theta_C}$ by minimizing the weighted loss
$$\frac{1}{n_t}\sum_{i=1}^{n_t}W_{C,i,t}\ell({M}_{\theta_C}(X_{i,t}),Y_{i,t}).$$
\State Update the model $G_{\theta_W}$ using data $\{(X_{i,t},Z_{i,t}),i=1,\ldots,n_t\}$.
\EndFor
\Return the estimator (\ref{naive_estimator}).
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2310.17496" | "2310.17496.tar.gz" | "2024-02-03" | {
"title": "tackling interference induced by data training loops in a/b tests: a weighted training approach",
"id": "2310.17496",
"abstract": "in modern recommendation systems, the standard pipeline involves training machine learning models on historical data to predict user behaviors and improve recommendations continuously. however, these data training loops can introduce interference in a/b tests, where data generated by control and treatment algorithms, potentially with different distributions, are combined. to address these challenges, we introduce a novel approach called weighted training. this approach entails training a model to predict the probability of each data point appearing in either the treatment or control data and subsequently applying weighted losses during model training. we demonstrate that this approach achieves the least variance among all estimators that do not cause shifts in the training distributions. through simulation studies, we demonstrate the lower bias and variance of our approach compared to other methods.",
"categories": "stat.me cs.lg econ.em",
"doi": "",
"created": "2023-10-26",
"updated": "2024-02-03",
"authors": [
"nian si"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2310.17496"
} | "2024-03-15T04:57:23.023908" | {
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} | [] | "algorithm" | "c64b9dc5-8108-4824-8172-022fd9a4541c" | 1683 | hard |
|
\begin{algorithmic}
\Require $a_i, B_i, \theta_i$
\\
\State Sort the values $a_i, \theta_i$ according to $\frac{a_{ij}}{\theta_{ij}}$ in a descending order.
If there are goods with $\theta_{ij} = 0$, sort them separately according to $a_{ij}$ and place them as a prefix (lower indices) before the other sorted goods. Equal values are sorted in a lexicographical order.
\\
\State Set: $a \gets 0,\quad \theta \gets 0,\quad c_s\gets 0,\quad c^* \gets 0$
\For{$j = 1, \dots, m$}
\State $a \gets a + a_{ij},\ \theta \gets \theta + \theta_{ij}$
\State $c_s \gets \frac{a}{\theta + B_i}$
\State $c^* \gets \max\{c^*, c_s\}$
\EndFor
\State \Return $c^*$
\end{algorithmic}
| \begin{algorithmic}
\Require $a_i, B_i, \theta_i$
\\
\State Sort the values $a_i, \theta_i$ according to $\frac{a_{ij}}{\theta_{ij}}$ in a descending order.
If there are goods with $\theta_{ij} = 0$, sort them separately according to $a_{ij}$ and place them as a prefix (lower indices) before the other sorted goods. Equal values are sorted in a lexicographical order.
\\
\State Set: $a \gets 0,\quad \theta \gets 0,\quad c_s\gets 0,\quad c^* \gets 0$
\For{$j = 1, \dots, m$}
\State $a \gets a + a_{ij},\ \theta \gets \theta + \theta_{ij}$
\State $c_s \gets \frac{a}{\theta + B_i}$
\State $c^* \gets \max\{c^*, c_s\}$
\EndFor
\State \Return $c^*$
\end{algorithmic} | "https://arxiv.org/src/2307.04108" | "2307.04108.tar.gz" | "2024-01-15" | {
"title": "asynchronous proportional response dynamics in markets with adversarial scheduling",
"id": "2307.04108",
"abstract": "we study proportional response dynamics (prd) in linear fisher markets where participants act asynchronously. we model this scenario as a sequential process in which in every step, an adversary selects a subset of the players that will update their bids, subject to liveness constraints. we show that if every bidder individually uses the prd update rule whenever they are included in the group of bidders selected by the adversary, then (in the generic case) the entire dynamic converges to a competitive equilibrium of the market. our proof technique uncovers further properties of linear fisher markets, such as the uniqueness of the equilibrium for generic parameters and the convergence of associated best-response dynamics and no-swap regret dynamics under certain conditions.",
"categories": "cs.gt cs.ma econ.th math.ds",
"doi": "",
"created": "2023-07-09",
"updated": "2024-01-15",
"authors": [
"yoav kolumbus",
"menahem levy",
"noam nisan"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2307.04108"
} | "2024-03-15T06:09:48.864469" | {
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} | [] | "algorithm" | "d65b5b49-084b-4b17-931b-f38be4063e2c" | 664 | easy |
|
\begin{algorithmic}[1]
\State $D_{train} \gets$ Initialize training set
\While {$C(fake)>threshold$} \Comment{The critic can be optimized until $C(fake)$ is near $0$. }
\State Randomly select a discrete variable $c$ with equal probability
\State Compute the probability mass function (PMF) of $c$
\State Randomly select a state $i^*$ inherent to $c$ according its PMF
\State Create the conditional vector $cond$ so that $\sum_i cond(i) = 1$ and $cond(i^*)=1$
\For {$batch \in \{1,\dots,N_{batches}\}$} \Comment{Gradient descent with mini-batch}
\State $real \gets d(c_{i^*}=1)\sim D_{train}$ \Comment{Sample batch of real examples respecting the constraint}
\State $z \sim \mathcal{N}(0,1)$ \Comment{Sample noise}
\State $fake \gets \tilde{d} \sim G(z)$ \Comment{Sample fake examples}
\State $real \gets [real]\times 10$ \Comment{Stack input 10 times for Pac configuration}
\State $fake \gets [fake] \times 10$
\State $L^j \gets \big( C(fake_j) - C(real_j)\big) + CE(\tilde{c}, cond)$
\State $L^{batch} \gets L^{batch} + \lambda(||\nabla L^{batch} ||_{2} - 1)^2$ \Comment{Apply gradient penalty}
\State $w_{crit} \gets w_{crit} + Adam(\nabla_{w_{crit}}\frac{1}{m}\sum_i^m L^{batch}(i))$ \Comment{Updating $C$ with Adam}
\If {$batch \bmod k = 0$} \Comment{Synchronicity, depends on $k$}
\State $w_{gen} \gets w_{gen} + Adam(\nabla_{w_{gen}}\frac{1}{m}\sum_i^m -C(G(z)))$ \Comment{Updating $G$ with Adam}
\EndIf
\EndFor
\EndWhile
\end{algorithmic}
| \begin{algorithmic}
[1]
\State $D_{train} \gets$ Initialize training set
\While {$C(fake)>threshold$} \Comment{The critic can be optimized until $C(fake)$ is near $0$. }
\State Randomly select a discrete variable $c$ with equal probability
\State Compute the probability mass function (PMF) of $c$
\State Randomly select a state $i^*$ inherent to $c$ according its PMF
\State Create the conditional vector $cond$ so that $\sum_i cond(i) = 1$ and $cond(i^*)=1$
\For {$batch \in \{1,\dots,N_{batches}\}$} \Comment{Gradient descent with mini-batch}
\State $real \gets d(c_{i^*}=1)\sim D_{train}$ \Comment{Sample batch of real examples respecting the constraint}
\State $z \sim \mathcal{N}(0,1)$ \Comment{Sample noise}
\State $fake \gets \tilde{d} \sim G(z)$ \Comment{Sample fake examples}
\State $real \gets [real]\times 10$ \Comment{Stack input 10 times for Pac configuration}
\State $fake \gets [fake] \times 10$
\State $L^j \gets \big( C(fake_j) - C(real_j)\big) + CE(\tilde{c}, cond)$
\State $L^{batch} \gets L^{batch} + \lambda(||\nabla L^{batch} ||_{2} - 1)^2$ \Comment{Apply gradient penalty}
\State $w_{crit} \gets w_{crit} + Adam(\nabla_{w_{crit}}\frac{1}{m}\sum_i^m L^{batch}(i))$ \Comment{Updating $C$ with Adam}
\If {$batch \bmod k = 0$} \Comment{Synchronicity, depends on $k$}
\State $w_{gen} \gets w_{gen} + Adam(\nabla_{w_{gen}}\frac{1}{m}\sum_i^m -C(G(z)))$ \Comment{Updating $G$ with Adam}
\EndIf
\EndFor
\EndWhile
\end{algorithmic} | "https://arxiv.org/src/2207.12255" | "2207.12255.tar.gz" | "2024-02-15" | {
"title": "implementing a hierarchical deep learning approach for simulating multi-level auction data",
"id": "2207.12255",
"abstract": "we present a deep learning solution to address the challenges of simulating realistic synthetic first-price sealed-bid auction data. the complexities encountered in this type of auction data include high-cardinality discrete feature spaces and a multilevel structure arising from multiple bids associated with a single auction instance. our methodology combines deep generative modeling (dgm) with an artificial learner that predicts the conditional bid distribution based on auction characteristics, contributing to advancements in simulation-based research. this approach lays the groundwork for creating realistic auction environments suitable for agent-based learning and modeling applications. our contribution is twofold: we introduce a comprehensive methodology for simulating multilevel discrete auction data, and we underscore the potential of dgm as a powerful instrument for refining simulation techniques and fostering the development of economic models grounded in generative ai.",
"categories": "econ.gn q-fin.ec",
"doi": "",
"created": "2022-07-25",
"updated": "2024-02-15",
"authors": [
"igor sadoune",
"andrea lodi",
"marcelin joanis"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2207.12255"
} | "2024-03-15T03:57:59.120702" | {
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} | [] | "algorithm" | "72d87570-5113-4a95-bec3-f8f6162007db" | 1446 | hard |
|
\begin{algorithm}
\caption{Algorithm to solve the optimisation problem \ref{met:merge}}\label{alg:cap}
\begin{algorithmic}
\Require Dataset $\mathbf{Y}$ and hyperparameter $\beta$
\State $\mathbf{w}= \mathbf{1}$
\For{$i \in$ $\{1,...,I\}$}
\State Solve the regression problem equation \ref{met:reg2}
\State $\mathbf{h} = \mathbf{Y} \mathbf{w} $
\State $\mathbf{z}=\mathbf{h}$
\State $z_t=0$ for $t \in \{1,...,T_d\}$ if $z_t>0$
\State $z_t=1$ for $t \in \{T_f,...,T\}$ if $z_t<1$
\State Perform isotonic projection on $\mathbf{z}$ using the PAVA algorithm \cite{wang2021remaining}
\EndFor
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Algorithm to solve the optimisation problem \ref{met:merge}}\begin{algorithmic}
\Require Dataset $\mathbf{Y}$ and hyperparameter $\beta$
\State $\mathbf{w}= \mathbf{1}$
\For{$i \in$ $\{1,...,I\}$}
\State Solve the regression problem equation \ref{met:reg2}
\State $\mathbf{h} = \mathbf{Y} \mathbf{w} $
\State $\mathbf{z}=\mathbf{h}$
\State $z_t=0$ for $t \in \{1,...,T_d\}$ if $z_t>0$
\State $z_t=1$ for $t \in \{T_f,...,T\}$ if $z_t<1$
\State Perform isotonic projection on $\mathbf{z}$ using the PAVA algorithm \cite{wang2021remaining}
\EndFor
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2312.02867" | "2312.02867.tar.gz" | "2024-02-16" | {
"title": "semi-supervised health index monitoring with feature generation and fusion",
"id": "2312.02867",
"abstract": "the health index (hi) is crucial for evaluating system health, aiding tasks like anomaly detection and predicting remaining useful life for systems demanding high safety and reliability. tight monitoring is crucial for achieving high precision at a lower cost. obtaining hi labels in real-world applications is often cost-prohibitive, requiring continuous, precise health measurements. therefore, it is more convenient to leverage run-to failure datasets that may provide potential indications of machine wear condition, making it necessary to apply semi-supervised tools for hi construction. in this study, we adapt the deep semi-supervised anomaly detection (deepsad) method for hi construction. we use the deepsad embedding as a condition indicators to address interpretability challenges and sensitivity to system-specific factors. then, we introduce a diversity loss to enrich condition indicators. we employ an alternating projection algorithm with isotonic constraints to transform the deepsad embedding into a normalized hi with an increasing trend. validation on the phme 2010 milling dataset, a recognized benchmark with ground truth his demonstrates meaningful his estimations. our contributions create opportunities for more accessible and reliable hi estimation, particularly in cases where obtaining ground truth hi labels is unfeasible.",
"categories": "cs.lg stat.me",
"doi": "",
"created": "2023-12-05",
"updated": "2024-02-16",
"authors": [
"ga\u00ebtan frusque",
"ismail nejjar",
"majid nabavi",
"olga fink"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2312.02867"
} | "2024-03-15T05:16:16.260093" | {
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} | [] | "algorithm" | "36aa95b3-dcde-4a29-af77-c90cd4c08e0d" | 606 | easy |
|
\begin{algorithm}[ht]
\caption{Existence of a connected strongly-proportional allocation for $n$ hungry agents.}
\label{alg:hungry}
\begin{algorithmic}[1]
\For{$t = 1, \ldots, n-1$}
\State $z \leftarrow \textsc{Mark}_1(0, t/n)$ \algorithmiccomment{agent $1$'s $t/n$-mark}
\For{$i = 2, \ldots, n$}
\State \algorithmicif \ $\textsc{Mark}_i(0, t/n) \neq z$ \algorithmicthen \ \Return true \algorithmiccomment{agent $1$'s and $i$'s $t/n$-marks do not coincide}
\EndFor
\EndFor
\State \Return false
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[ht]
\caption{Existence of a connected strongly-proportional allocation for $n$ hungry agents.}
\begin{algorithmic}
[1]
\For{$t = 1, \ldots, n-1$}
\State $z \leftarrow \textsc{Mark}_1(0, t/n)$ \algorithmiccomment{agent $1$'s $t/n$-mark}
\For{$i = 2, \ldots, n$}
\State \algorithmicif \ $\textsc{Mark}_i(0, t/n) \neq z$ \algorithmicthen \ \Return true \algorithmiccomment{agent $1$'s and $i$'s $t/n$-marks do not coincide}
\EndFor
\EndFor
\State \Return false
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2312.15326" | "2312.15326.tar.gz" | "2024-02-13" | {
"title": "on connected strongly-proportional cake-cutting",
"id": "2312.15326",
"abstract": "we investigate the problem of fairly dividing a divisible heterogeneous resource, also known as a cake, among a set of agents. we characterize the existence of an allocation in which every agent receives a contiguous piece worth strictly more than their proportional share, also known as a *strongly-proportional allocation*. the characterization is supplemented with an algorithm that determines the existence of a connected strongly-proportional allocation using at most $n \\cdot 2^{n-1}$ queries. we provide a simpler characterization for agents with strictly positive valuations, and show that the number of queries required to determine the existence of a connected strongly-proportional allocation is in $\\theta(n^2)$. our proofs are constructive and yield a connected strongly-proportional allocation, when it exists, using a similar number of queries.",
"categories": "math.co cs.gt econ.th",
"doi": "",
"created": "2023-12-23",
"updated": "2024-02-13",
"authors": [
"zsuzsanna jank\u00f3",
"attila jo\u00f3",
"erel segal-halevi",
"sheung man yuen"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2312.15326"
} | "2024-03-15T04:18:36.086397" | {
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} | [] | "algorithm" | "5aa6a9d2-695a-437b-95df-88078efc2922" | 510 | easy |
|
\begin{algorithm}[t!]
\begin{algorithmic}
\caption{Pseudo Python Code for $\texttt{TracInAD}$}\label{alg:tracinad}
\Require{$
\mathcal{D}_{train}, \mathcal{D}_{val}, \{\theta_{t_1},\dots,\theta_{t_n}\},
\{\eta_{t_1},\dots,\eta_{t_n}\},$ \newline
\hspace*{3em} $\ell(\theta,.), m$}
\State $\texttt{TracInAD} \gets dict()$
\State $B \gets$ random sample of size $m$ from $\mathcal{D}_{train}$
\For{$t \in \{t_1,\dots,t_n\}$}
\State $\theta \gets \theta_{t}$
\State $\eta \gets \eta_{t}$
\For{$x \in \mathcal{D}_{val}$}
\State $\texttt{TracInAD}[x] \mathrel{{+}{=}} \frac{1}{m} \sum_{x' \in B} \eta \nabla \ell(\theta,x') \cdot \nabla\ell(\theta,x)$
\EndFor
\EndFor
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[t!]
\begin{algorithmic}
\caption{Pseudo Python Code for $\texttt{TracInAD}$} \Require{$
\mathcal{D}_{train}, \mathcal{D}_{val}, \{\theta_{t_1},\dots,\theta_{t_n}\},
\{\eta_{t_1},\dots,\eta_{t_n}\},$ \newline
\hspace*{3em} $\ell(\theta,.), m$}
\State $\texttt{TracInAD} \gets dict()$
\State $B \gets$ random sample of size $m$ from $\mathcal{D}_{train}$
\For{$t \in \{t_1,\dots,t_n\}$}
\State $\theta \gets \theta_{t}$
\State $\eta \gets \eta_{t}$
\For{$x \in \mathcal{D}_{val}$}
\State $\texttt{TracInAD}[x] \mathrel{{+}{=}} \frac{1}{m} \sum_{x' \in B} \eta \nabla \ell(\theta,x') \cdot \nabla\ell(\theta,x)$
\EndFor
\EndFor
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2205.01362" | "2205.01362.tar.gz" | "2024-01-30" | {
"title": "tracinad: measuring influence for anomaly detection",
"id": "2205.01362",
"abstract": "as with many other tasks, neural networks prove very effective for anomaly detection purposes. however, very few deep-learning models are suited for detecting anomalies on tabular datasets. this paper proposes a novel methodology to flag anomalies based on tracin, an influence measure initially introduced for explicability purposes. the proposed methods can serve to augment any unsupervised deep anomaly detection method. we test our approach using variational autoencoders and show that the average influence of a subsample of training points on a test point can serve as a proxy for abnormality. our model proves to be competitive in comparison with state-of-the-art approaches: it achieves comparable or better performance in terms of detection accuracy on medical and cyber-security tabular benchmark data.",
"categories": "cs.lg",
"doi": "10.1109/ijcnn55064.2022.9892058",
"created": "2022-05-03",
"updated": "2024-01-30",
"authors": [
"hugo thimonier",
"fabrice popineau",
"arpad rimmel",
"bich-li\u00ean doan",
"fabrice daniel"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2205.01362"
} | "2024-03-15T08:20:53.958646" | {
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} | [] | "algorithm" | "8a702937-20e8-40f0-9099-a6c05cd1b23a" | 677 | easy |
|
\begin{algorithmic}[1]
\For{$k=0,1,2,\ldots$}
\Statex \textcolor{blue}{\textbf{Local updates}} for all clients: \State $v^k_{x_m} = \alpha x_m^k + (1 - \alpha) u_{x_m}^k$, \ \ \ \ $v^k_{y_m} = \alpha y_m^k + (1 - \alpha) u_{y_m}^k$ \label{alg1:line2}
\Statex
All clients \textcolor{red}{\textbf{communicate}} to locally compute
\State $\bar v_{x_m}^{k+1} = \sum_{i=1}^M w_{m,i} v^k_{x_i}$, \ \ \ \ $\bar v_{y_m}^{k+1} = \sum_{i=1}^M w_{m,i} v^k_{y_i}$ \label{alg1:line:comm}
\State and use \textcolor{blue}{\textbf{local}} method $\mathcal{M}$ to find a solution $(\hat x_m^{k+1}, \hat y_m^{k+1})$ of: \label{alg1_line:subproblem}
\begin{equation}\label{alg1:subproblem}
\min_{x_m} \max_{y_m} \left\{A_m^k(x_m, y_m) = \lambda\langle \bar v_{x_m}^{k+1},x_m \rangle + \tfrac{1}{2\eta} \|x_m- x_m^k \|^2 + f_m(x_m,y_m) - \lambda\langle \bar v_{y_m}^{k+1},y_m \rangle
- \tfrac{1}{2\eta} \|y_m - y_m^k \|^2\right\},
\end{equation}
\Statex such that $\| \nabla A_m^k (\hat x_m^{k+1}, \hat y_m^{k+1})\|^2 \leq \frac{1}{6\eta^2}\left(\|\hat x_m^{k+1} - x^k\|^2 + \|\hat y_m^{k+1} - y^k\|^2\right)$.
\Statex \textcolor{blue}{\textbf{Local updates}} for all clients: \State \label{alg1_line:update}$x_m^{k+1} = x_m^k - \eta(\lambda \bar v_m^{k+1} + \nabla_{x} f_m(\hat x_m^{k+1}, \hat y_m^{k+1}))$ \State $y_m^{k+1} = y_m^k - \eta(\lambda \bar v_m^{k+1} - \nabla_{y} f_m(\hat x_m^{k+1}, \hat y_m^{k+1}))$
\State\label{alg1_line:acc} $u_{x_m}^{k+1} = v^k_{x_m} + \alpha(\hat x_m^{k+1} - x_m^k), \ \ u_{y_m}^{k+1} = v^k_{y_m} + \alpha(\hat y_m^{k+1} - y_m^k)$
\EndFor
\end{algorithmic}
| \begin{algorithmic}
[1]
\For{$k=0,1,2,\ldots$}
\Statex \textcolor{blue}{\textbf{Local updates}} for all clients: \State $v^k_{x_m} = \alpha x_m^k + (1 - \alpha) u_{x_m}^k$, \ \ \ \ $v^k_{y_m} = \alpha y_m^k + (1 - \alpha) u_{y_m}^k$ \Statex
All clients \textcolor{red}{\textbf{communicate}} to locally compute
\State $\bar v_{x_m}^{k+1} = \sum_{i=1}^M w_{m,i} v^k_{x_i}$, \ \ \ \ $\bar v_{y_m}^{k+1} = \sum_{i=1}^M w_{m,i} v^k_{y_i}$ \State and use \textcolor{blue}{\textbf{local}} method $\mathcal{M}$ to find a solution $(\hat x_m^{k+1}, \hat y_m^{k+1})$ of: \begin{equation*}
\min_{x_m} \max_{y_m} \left\{A_m^k(x_m, y_m) = \lambda\langle \bar v_{x_m}^{k+1},x_m \rangle + \tfrac{1}{2\eta} \|x_m- x_m^k \|^2 + f_m(x_m,y_m) - \lambda\langle \bar v_{y_m}^{k+1},y_m \rangle
- \tfrac{1}{2\eta} \|y_m - y_m^k \|^2\right\},
\end{equation*}
\Statex such that $\| \nabla A_m^k (\hat x_m^{k+1}, \hat y_m^{k+1})\|^2 \leq \frac{1}{6\eta^2}\left(\|\hat x_m^{k+1} - x^k\|^2 + \|\hat y_m^{k+1} - y^k\|^2\right)$.
\Statex \textcolor{blue}{\textbf{Local updates}} for all clients: \State $x_m^{k+1} = x_m^k - \eta(\lambda \bar v_m^{k+1} + \nabla_{x} f_m(\hat x_m^{k+1}, \hat y_m^{k+1}))$ \State $y_m^{k+1} = y_m^k - \eta(\lambda \bar v_m^{k+1} - \nabla_{y} f_m(\hat x_m^{k+1}, \hat y_m^{k+1}))$
\State$u_{x_m}^{k+1} = v^k_{x_m} + \alpha(\hat x_m^{k+1} - x_m^k), \ \ u_{y_m}^{k+1} = v^k_{y_m} + \alpha(\hat y_m^{k+1} - y_m^k)$
\EndFor
\end{algorithmic} | "https://arxiv.org/src/2106.07289" | "2106.07289.tar.gz" | "2024-01-24" | {
"title": "decentralized personalized federated learning for min-max problems",
"id": "2106.07289",
"abstract": "personalized federated learning (pfl) has witnessed remarkable advancements, enabling the development of innovative machine learning applications that preserve the privacy of training data. however, existing theoretical research in this field has primarily focused on distributed optimization for minimization problems. this paper is the first to study pfl for saddle point problems encompassing a broader range of optimization problems, that require more than just solving minimization problems. in this work, we consider a recently proposed pfl setting with the mixing objective function, an approach combining the learning of a global model together with locally distributed learners. unlike most previous work, which considered only the centralized setting, we work in a more general and decentralized setup that allows us to design and analyze more practical and federated ways to connect devices to the network. we proposed new algorithms to address this problem and provide a theoretical analysis of the smooth (strongly) convex-(strongly) concave saddle point problems in stochastic and deterministic cases. numerical experiments for bilinear problems and neural networks with adversarial noise demonstrate the effectiveness of the proposed methods.",
"categories": "cs.lg cs.dc math.oc",
"doi": "",
"created": "2021-06-14",
"updated": "2024-01-24",
"authors": [
"ekaterina borodich",
"aleksandr beznosikov",
"abdurakhmon sadiev",
"vadim sushko",
"nikolay savelyev",
"martin tak\u00e1\u010d",
"alexander gasnikov"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2106.07289"
} | "2024-03-15T08:58:57.459725" | {
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} | [] | "algorithm" | "f9c36080-24d7-4be2-811f-215eea97a00d" | 1440 | hard |
|
\begin{algorithm}[h!]
\caption{Motifs mining}
\label{alg:1}
\textbf{Input:}
Training set samples $\textbf{T}$ with labeled binary classes C = [0, 1]\\
\textbf{Output:}
Extracted motifs for each class
\begin{algorithmic}[1]
\State Motifs = $\emptyset$
\State N = length($\textbf{T}$[0])
\Comment{Number of time series samples}
\State m = length($\textbf{T}$[0][0])
\Comment{Length of time series}
\For{$\textbf{T}_i$ $\leftarrow$ $\textbf{T}_1$ to $\textbf{T}_N$}
\State Motifs $\gets$ $\emptyset$
\For{l in [0.3m, 0.5m, 0.7m]}
\State $W_{i,l}$ $\gets$ generateCandidates($\textbf{T}_i$, l)
\For{all subsequences S in $W_{i,l}$}
\State $D_S$ $\gets$ findDistances(S, $W_{i,l}$)
\State quality $\gets$ assessCandidate(S, $D_S$)
\State Motifs.add(i,start\_idx, end\_idx, S, quality)
\Comment{The index of time series, the start idx and end idx of motifs will be stored}
\EndFor
\EndFor
\State sortByQuality(Motifs)
\EndFor
\State \Return $[[i\_0, start\_idx\_0, start\_idx\_0] , [i\_1, start\_idx\_1, start\_idx\_1]]$
\Comment{return the index information for motifs of different classes }
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[h!]
\caption{Motifs mining}
\textbf{Input:}
Training set samples $\textbf{T}$ with labeled binary classes C = [0, 1]\\
\textbf{Output:}
Extracted motifs for each class
\begin{algorithmic}
[1]
\State Motifs = $\emptyset$
\State N = length($\textbf{T}$[0])
\Comment{Number of time series samples}
\State m = length($\textbf{T}$[0][0])
\Comment{Length of time series}
\For{$\textbf{T}_i$ $\leftarrow$ $\textbf{T}_1$ to $\textbf{T}_N$}
\State Motifs $\gets$ $\emptyset$
\For{l in [0.3m, 0.5m, 0.7m]}
\State $W_{i,l}$ $\gets$ generateCandidates($\textbf{T}_i$, l)
\For{all subsequences S in $W_{i,l}$}
\State $D_S$ $\gets$ findDistances(S, $W_{i,l}$)
\State quality $\gets$ assessCandidate(S, $D_S$)
\State Motifs.add(i,start\_idx, end\_idx, S, quality)
\Comment{The index of time series, the start idx and end idx of motifs will be stored}
\EndFor
\EndFor
\State sortByQuality(Motifs)
\EndFor
\State \Return $[[i\_0, start\_idx\_0, start\_idx\_0] , [i\_1, start\_idx\_1, start\_idx\_1]]$
\Comment{return the index information for motifs of different classes }
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2211.04411" | "2211.04411.tar.gz" | "2024-02-01" | {
"title": "motif-guided time series counterfactual explanations",
"id": "2211.04411",
"abstract": "with the rising need of interpretable machine learning methods, there is a necessity for a rise in human effort to provide diverse explanations of the influencing factors of the model decisions. to improve the trust and transparency of ai-based systems, the explainable artificial intelligence (xai) field has emerged. the xai paradigm is bifurcated into two main categories: feature attribution and counterfactual explanation methods. while feature attribution methods are based on explaining the reason behind a model decision, counterfactual explanation methods discover the smallest input changes that will result in a different decision. in this paper, we aim at building trust and transparency in time series models by using motifs to generate counterfactual explanations. we propose motif-guided counterfactual explanation (mg-cf), a novel model that generates intuitive post-hoc counterfactual explanations that make full use of important motifs to provide interpretive information in decision-making processes. to the best of our knowledge, this is the first effort that leverages motifs to guide the counterfactual explanation generation. we validated our model using five real-world time-series datasets from the ucr repository. our experimental results show the superiority of mg-cf in balancing all the desirable counterfactual explanations properties in comparison with other competing state-of-the-art baselines.",
"categories": "cs.lg",
"doi": "",
"created": "2022-11-08",
"updated": "2024-02-01",
"authors": [
"peiyu li",
"soukaina filali boubrahimi",
"shah muhammad hamdi"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2211.04411"
} | "2024-03-15T08:04:45.521940" | {
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} | [] | "algorithm" | "df0aeb78-e184-4489-8ac7-f74592b0da58" | 1108 | medium |
|
\begin{algorithmic}
\State Initialize $O\gets \emptyset$.\footnote{This can be replaced with any other menu of public goods with no change to the analysis below.}
\While{$O$ is not $(t,u)$-stable}
\If{$O$ is not $t$-feasible}
\State By definition there exists $j\in O$ such that $|j \succ O \setminus \{ j \} | <t$.
\State Let $j$ be a minimal\newcounter{minimalfootnote}\setcounter{minimalfootnote}{\thefootnote}\footnote{This can be replaced with any other consistent tie-breaking with no change to the analysis below.} such $j$, and update $O\gets O\setminus\{j\}$.
\ElsIf{$O$ is not $u$-uncontestable\footnote{This item can be consistently swapped with the preceding one with no change to the analysis below.}}
\State By definition there exists $j\in G\setminus O$ such that $|j\succ O|\ge u$.
\State Let $j$ be a minimal\newcounter{savedcurrentfootnote}\setcounter{savedcurrentfootnote}{\thefootnote}\setcounter{footnote}{\theminimalfootnote}\footnotemark\setcounter{footnote}{\thesavedcurrentfootnote} such $j$, and update $O\gets O\cup\{j\}$.
\EndIf
\EndWhile
\end{algorithmic}
| \begin{algorithmic}
\State Initialize $O\gets \emptyset$.\footnote{This can be replaced with any other menu of public goods with no change to the analysis below.}
\While{$O$ is not $(t,u)$-stable}
\If{$O$ is not $t$-feasible}
\State By definition there exists $j\in O$ such that $|j \succ O \setminus \{ j \} | <t$.
\State Let $j$ be a minimal\newcounter{minimalfootnote}\setcounter{minimalfootnote}{\thefootnote}\footnote{This can be replaced with any other consistent tie-breaking with no change to the analysis below.} such $j$, and update $O\gets O\setminus\{j\}$.
\ElsIf{$O$ is not $u$-uncontestable\footnote{This item can be consistently swapped with the preceding one with no change to the analysis below.}}
\State By definition there exists $j\in G\setminus O$ such that $|j\succ O|\ge u$.
\State Let $j$ be a minimal\newcounter{savedcurrentfootnote}\setcounter{savedcurrentfootnote}{\thefootnote}\setcounter{footnote}{\theminimalfootnote}\footnotemark\setcounter{footnote}{\thesavedcurrentfootnote} such $j$, and update $O\gets O\cup\{j\}$.
\EndIf
\EndWhile
\end{algorithmic} | "https://arxiv.org/src/2402.11370" | "2402.11370.tar.gz" | "2024-02-17" | {
"title": "stable menus of public goods: a matching problem",
"id": "2402.11370",
"abstract": "we study a matching problem between agents and public goods, in settings without monetary transfers. since goods are public, they have no capacity constraints. there is no exogenously defined budget of goods to be provided. rather, each provided good must justify its cost, leading to strong complementarities in the \"preferences\" of goods. furthermore, goods that are in high demand given other already-provided goods must also be provided. the question of the existence of a stable solution (a menu of public goods to be provided) exhibits a rich combinatorial structure. we uncover sufficient conditions and necessary conditions for guaranteeing the existence of a stable solution, and derive both positive and negative results for strategyproof stable matching.",
"categories": "cs.gt econ.th math.co",
"doi": "",
"created": "2024-02-17",
"updated": "",
"authors": [
"sara fish",
"yannai a. gonczarowski",
"sergiu hart"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.11370"
} | "2024-03-15T03:42:28.124433" | {
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} | [] | "algorithm" | "889ab22e-62aa-4dae-b920-32e61e523162" | 1084 | medium |
|
\begin{algorithmic}[1]
\State Solve \eqref{intrphi} for first-order correctors $\phi_i$.
\State Determine the homogenized coefficients $a_h$ via \eqref{intrhomcoeff}.
\State Solve \eqref{intruhtilde} for $\tilde{u}_h$ on $\partial Q_L$ by $\tilde{u}_h = \int G_h*(\nabla\cdot g)$.
\State Solve \eqref{eqn:intrsig} for first-order flux correctors $\sigma_{ijk}$ and \eqref{eqn:2ndcordef} for second-order correctors $\psi_{ij}$.
\State Obtain $u_h$ via \eqref{eqn:effectivequadp}.
\State Solve \eqref{eqn:coruhat} for $\hat{u}$, which is the approximation we desire.
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Solve \eqref{intrphi} for first-order correctors $\phi_i$.
\State Determine the homogenized coefficients $a_h$ via \eqref{intrhomcoeff}.
\State Solve \eqref{intruhtilde} for $\tilde{u}_h$ on $\partial Q_L$ by $\tilde{u}_h = \int G_h*(\nabla\cdot g)$.
\State Solve \eqref{eqn:intrsig} for first-order flux correctors $\sigma_{ijk}$ and \eqref{eqn:2ndcordef} for second-order correctors $\psi_{ij}$.
\State Obtain $u_h$ via \eqref{eqn:effectivequadp}.
\State Solve \eqref{eqn:coruhat} for $\hat{u}$, which is the approximation we desire.
\end{algorithmic} | "https://arxiv.org/src/2109.01616" | "2109.01616.tar.gz" | "2024-01-11" | {
"title": "optimal artificial boundary conditions based on second-order correctors for three dimensional random elliptic media",
"id": "2109.01616",
"abstract": "we are interested in numerical algorithms for computing the electrical field generated by a charge distribution localized on scale $\\ell$ in an infinite heterogeneous medium, in a situation where the medium is only known in a box of diameter $l\\gg\\ell$ around the support of the charge. we propose a boundary condition that with overwhelming probability is (near) optimal with respect to scaling in terms of $\\ell$ and $l$, in the setting where the medium is a sample from a stationary ensemble with a finite range of dependence (set to be unity and with the assumption that $\\ell \\gg 1$). the boundary condition is motivated by quantitative stochastic homogenization that allows for a multipole expansion [bgo20]. this work extends [lo21], the algorithm in which is optimal in two dimension, and thus we need to take quadrupoles, next to dipoles, into account. this in turn relies on stochastic estimates of second-order, next to first-order, correctors. these estimates are provided for finite range ensembles under consideration, based on an extension of the semi-group approach of [go15].",
"categories": "math.ap cs.na math.na math.pr",
"doi": "",
"created": "2021-09-03",
"updated": "2024-01-11",
"authors": [
"jianfeng lu",
"felix otto",
"lihan wang"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2109.01616"
} | "2024-03-15T06:22:17.156672" | {
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} | [] | "algorithm" | "06cf420c-4958-4598-b8dc-76acfcd98366" | 584 | easy |
|
\begin{algorithmic}
\State Draw $X_b, Y_b, [Z_{k-1,b} \cdots Z_{0,b}]$ \Comment{Draw training batch and corresponding features from prior models}
\State $Z_{k,b} \gets f^l_k(X_b)$
\State $N, D \gets shape(Z_{k,b})$
\State $\hat{Y_b} \gets f_k(X_b)$
\State $\mathcal{L} \gets \mathcal{L}_{ce}(\hat{Y_b}, Y_b)$
\State $i \gets 0$
\While{$i \leq k-1$}
\State $Z_1, Z_2 \gets Z_{k,b}, Z_{i,b}$
\If {$t \sim Uniform[0,1] < 0.5$}
$Z_1, Z_2 \gets Z_2, Z_1$
\EndIf
\State $R \sim N(0,1/\sqrt{D}) \in \mathbb{R}^{D+1 \times r}$
\State $Z_1 \gets [Z_1, \mathbf{1}]R$
\State $\mathcal{L} \gets \mathcal{L} + \frac{\lambda}{k} \mathcal{L}_R(Z_1, Z_2)$ \Comment{Apply decorrelation loss from Equation \ref{eqn:LR}}
\State $i \gets i+1$
\EndWhile
\State $\theta_k \gets \theta_k - \eta \nabla_{\mathcal{L}} \theta_k$
\end{algorithmic}
| \begin{algorithmic}
\State Draw $X_b, Y_b, [Z_{k-1,b} \cdots Z_{0,b}]$ \Comment{Draw training batch and corresponding features from prior models}
\State $Z_{k,b} \gets f^l_k(X_b)$
\State $N, D \gets shape(Z_{k,b})$
\State $\hat{Y_b} \gets f_k(X_b)$
\State $\mathcal{L} \gets \mathcal{L}_{ce}(\hat{Y_b}, Y_b)$
\State $i \gets 0$
\While{$i \leq k-1$}
\State $Z_1, Z_2 \gets Z_{k,b}, Z_{i,b}$
\If {$t \sim Uniform[0,1] < 0.5$}
$Z_1, Z_2 \gets Z_2, Z_1$
\EndIf
\State $R \sim N(0,1/\sqrt{D}) \in \mathbb{R}^{D+1 \times r}$
\State $Z_1 \gets [Z_1, \mathbf{1}]R$
\State $\mathcal{L} \gets \mathcal{L} + \frac{\lambda}{k} \mathcal{L}_R(Z_1, Z_2)$ \Comment{Apply decorrelation loss from Equation \ref{eqn:LR}}
\State $i \gets i+1$
\EndWhile
\State $\theta_k \gets \theta_k - \eta \nabla_{\mathcal{L}} \theta_k$
\end{algorithmic} | "https://arxiv.org/src/2207.09031" | "2207.09031.tar.gz" | "2024-02-16" | {
"title": "decorrelative network architecture for robust electrocardiogram classification",
"id": "2207.09031",
"abstract": "artificial intelligence has made great progress in medical data analysis, but the lack of robustness and trustworthiness has kept these methods from being widely deployed. as it is not possible to train networks that are accurate in all scenarios, models must recognize situations where they cannot operate confidently. bayesian deep learning methods sample the model parameter space to estimate uncertainty, but these parameters are often subject to the same vulnerabilities, which can be exploited by adversarial attacks. we propose a novel ensemble approach based on feature decorrelation and fourier partitioning for teaching networks diverse complementary features, reducing the chance of perturbation-based fooling. we test our approach on single and multi-channel electrocardiogram classification, and adapt adversarial training and dverge into the bayesian ensemble framework for comparison. our results indicate that the combination of decorrelation and fourier partitioning generally maintains performance on unperturbed data while demonstrating superior robustness and uncertainty estimation on projected gradient descent and smooth adversarial attacks of various magnitudes. furthermore, our approach does not require expensive optimization with adversarial samples, adding much less compute to the training process than adversarial training or dverge. these methods can be applied to other tasks for more robust and trustworthy models.",
"categories": "cs.lg cs.ai",
"doi": "",
"created": "2022-07-18",
"updated": "2024-02-16",
"authors": [
"christopher wiedeman",
"ge wang"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2207.09031"
} | "2024-03-15T04:53:44.109126" | {
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} | [] | "algorithm" | "b8eb4c1a-b47e-4a8c-8972-f01cba2327ce" | 820 | medium |
|
\begin{algorithmic}[1]
\State Input:\begin{itemize}
\item Algebraic system of difference equations named $\Sigma'$
\item Time measured data allowing prolongation of the system.
\item For $\bar{\mu}=\mu_1,\ldots,\mu_n$ the finite set of parameters, the data $R_{\mu_i}$ of permissible intervals for each parameter value.
\end{itemize}
\State Output: Parameter values of $\Sigma'$.
\Procedure{Detect solvability}{}
\State Define $\Sigma prolong$ as an indefinite time prolongation of $\Sigma'$.
\State Redefine $\Sigma':=[]$, an `empty system' of no equations.
\State Denote $e_1,\ldots$ the equations of $\Sigma prolong$.
\State Define $J(t)=\left[\dfrac{\partial e_i}{\partial\mu_j}\right]$ where $e_i\in \Sigma',i=1,\ldots,r$, or 0 if $\Sigma'$ is empty.
\State $i:=1$
\For{$rank(J(t)):=s<n$ i.e. is not of full rank, }
\Procedure{Move equation}{}
\State $\Sigma':=\Sigma'\cup\{e_i\}$
\State $\Sigma prolong:=\Sigma prolong\backslash\{e_i\}$
\State Compute $rank(J(t))$ (note $\Sigma'$ has updated)
\If{$rank(J(t))<s+1$} $\Sigma':=\Sigma'\backslash\{e_i\}$
\EndIf
\State $i=i+1$
\If{$rank(J(t)<n$} repeat procedure Move Equation.
\EndIf
\EndProcedure
\EndFor
\Procedure{Blackbox solver and filter}{} Note Detect Solvability runs until $J(t)$ \phantom{---------}has full rank and outputs a polynomial system $\Sigma'$ that has solutions. Run any \phantom{---------}algebraic solver.
\State Filter solutions by intersecting solution set with $R_{\mu_i}$.
\EndProcedure
\EndProcedure
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Input:\begin{itemize}
\item Algebraic system of difference equations named $\Sigma'$
\item Time measured data allowing prolongation of the system.
\item For $\bar{\mu}=\mu_1,\ldots,\mu_n$ the finite set of parameters, the data $R_{\mu_i}$ of permissible intervals for each parameter value.
\end{itemize}
\State Output: Parameter values of $\Sigma'$.
\Procedure{Detect solvability}{}
\State Define $\Sigma prolong$ as an indefinite time prolongation of $\Sigma'$.
\State Redefine $\Sigma':=[]$, an `empty system' of no equations.
\State Denote $e_1,\ldots$ the equations of $\Sigma prolong$.
\State Define $J(t)=\left[\dfrac{\partial e_i}{\partial\mu_j}\right]$ where $e_i\in \Sigma',i=1,\ldots,r$, or 0 if $\Sigma'$ is empty.
\State $i:=1$
\For{$rank(J(t)):=s<n$ i.e. is not of full rank, }
\Procedure{Move equation}{}
\State $\Sigma':=\Sigma'\cup\{e_i\}$
\State $\Sigma prolong:=\Sigma prolong\backslash\{e_i\}$
\State Compute $rank(J(t))$ (note $\Sigma'$ has updated)
\If{$rank(J(t))<s+1$} $\Sigma':=\Sigma'\backslash\{e_i\}$
\EndIf
\State $i=i+1$
\If{$rank(J(t)<n$} repeat procedure Move Equation.
\EndIf
\EndProcedure
\EndFor
\Procedure{Blackbox solver and filter}{} Note Detect Solvability runs until $J(t)$ \phantom{---------}has full rank and outputs a polynomial system $\Sigma'$ that has solutions. Run any \phantom{---------}algebraic solver.
\State Filter solutions by intersecting solution set with $R_{\mu_i}$.
\EndProcedure
\EndProcedure
\end{algorithmic} | "https://arxiv.org/src/2401.16220" | "2401.16220.tar.gz" | "2024-01-29" | {
"title": "symbolic-numeric algorithm for parameter estimation in discrete-time models with $\\exp$",
"id": "2401.16220",
"abstract": "determining unknown parameter values in dynamic models is crucial for accurate analysis of the dynamics across the different scientific disciplines. discrete-time dynamic models are widely used to model biological processes, but it is often difficult to determine these parameters. in this paper, we propose a robust symbolic-numeric approach for parameter estimation in discrete-time models that involve non-algebraic functions such as exp. we illustrate the performance (precision) of our approach by applying our approach to the flour beetle (lpa) model, an archetypal discrete-time model in biology. unlike optimization-based methods, our algorithm guarantees to find all solutions of the parameter values given time-series data for the measured variables.",
"categories": "q-bio.qm cs.sc cs.sy eess.sy math.ac math.ds",
"doi": "",
"created": "2024-01-29",
"updated": "",
"authors": [
"yosef berman",
"joshua forrest",
"matthew grote",
"alexey ovchinnikov",
"sonia rueda"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.16220"
} | "2024-03-15T06:24:53.153570" | {
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} | [] | "algorithm" | "39bf72af-e57a-41d1-aab2-3034eaaea5b1" | 1500 | hard |
|
\begin{algorithm}\caption{Greedy}\label{alg:bffg}
\begin{algorithmic}[1]
\State Initialize: $A_0\gets \Phi$
\For {$i \in [m]$}
\State Let $u_i$ be the element $u\in P_i$ maximizing $f(u~|~A_{i-1}) := f(A_{i-1}\cup \{u\}) - f(A_{i-1})$.
\State $A_i\gets A_{i-1}\cup \{u_i\}$
\EndFor
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Greedy}\begin{algorithmic}
[1]
\State Initialize: $A_0\gets \Phi$
\For {$i \in [m]$}
\State Let $u_i$ be the element $u\in P_i$ maximizing $f(u~|~A_{i-1}) := f(A_{i-1}\cup \{u\}) - f(A_{i-1})$.
\State $A_i\gets A_{i-1}\cup \{u_i\}$
\EndFor
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2208.03367" | "2208.03367.tar.gz" | "2024-02-12" | {
"title": "sublinear time algorithm for online weighted bipartite matching",
"id": "2208.03367",
"abstract": "online bipartite matching is a fundamental problem in online algorithms. the goal is to match two sets of vertices to maximize the sum of the edge weights, where for one set of vertices, each vertex and its corresponding edge weights appear in a sequence. currently, in the practical recommendation system or search engine, the weights are decided by the inner product between the deep representation of a user and the deep representation of an item. the standard online matching needs to pay $nd$ time to linear scan all the $n$ items, computing weight (assuming each representation vector has length $d$), and then deciding the matching based on the weights. however, in reality, the $n$ could be very large, e.g. in online e-commerce platforms. thus, improving the time of computing weights is a problem of practical significance. in this work, we provide the theoretical foundation for computing the weights approximately. we show that, with our proposed randomized data structures, the weights can be computed in sublinear time while still preserving the competitive ratio of the matching algorithm.",
"categories": "cs.ds cs.lg",
"doi": "",
"created": "2022-08-05",
"updated": "2024-02-12",
"authors": [
"hang hu",
"zhao song",
"runzhou tao",
"zhaozhuo xu",
"junze yin",
"danyang zhuo"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2208.03367"
} | "2024-03-15T06:18:53.303533" | {
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} | [] | "algorithm" | "297c8742-3dd4-4758-8cc8-94d9e5e6b061" | 300 | easy |
|
\begin{algorithmic}[1]
\State Set $\lambda^{(0)},\rho^{(0)}$. Choose $\epsilon_1^{(0)},\epsilon_2^{(0)}$.
\State Obtain initial HS optical flow $\textbf{u}^{(0)}$
\For{$n = 1,2,\dots$ until convergence \textbf{do}}
\State update $\textbf{u}^{(n)}, d^{(n)}$
\If $\|B\textbf{u}^{(n)}-c\|_{\mathcal{H}}\le \max\{\epsilon_1^{(n)},2\delta_{\text{HS}}\}$
\If $\|fd^{(n)}\|_{\mathcal{H}}\le \epsilon_2^{(n)}$
\State break;
\Else
\State update $\lambda_1^{(n)}$ by (\ref{uzawa})
\State $\rho^{(n+1)}\gets \rho^{(n)}$
\State tighten tolerances $\epsilon_1^{(n+1)},\epsilon_2^{(n+1)}$
\EndIf
\Else
\State update $B\textbf{u}^{(n)}-c$
\State $\lambda^{(n+1)}\gets\lambda^{(n)}$
\State $\rho^{(n+1)}\gets 100\rho^{(n)}$
\State tighten tolerances $\epsilon_1^{(n+1)},\epsilon_2^{(n+1)}$
\EndIf
\EndFor
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Set $\lambda^{(0)},\rho^{(0)}$. Choose $\epsilon_1^{(0)},\epsilon_2^{(0)}$.
\State Obtain initial HS optical flow $\textbf{u}^{(0)}$
\For{$n = 1,2,\dots$ until convergence \textbf{do}}
\State update $\textbf{u}^{(n)}, d^{(n)}$
\If $\|B\textbf{u}^{(n)}-c\|_{\mathcal{H}}\le \max\{\epsilon_1^{(n)},2\delta_{\text{HS}}\}$
\If $\|fd^{(n)}\|_{\mathcal{H}}\le \epsilon_2^{(n)}$
\State break;
\Else
\State update $\lambda_1^{(n)}$ by (\ref{uzawa})
\State $\rho^{(n+1)}\gets \rho^{(n)}$
\State tighten tolerances $\epsilon_1^{(n+1)},\epsilon_2^{(n+1)}$
\EndIf
\Else
\State update $B\textbf{u}^{(n)}-c$
\State $\lambda^{(n+1)}\gets\lambda^{(n)}$
\State $\rho^{(n+1)}\gets 100\rho^{(n)}$
\State tighten tolerances $\epsilon_1^{(n+1)},\epsilon_2^{(n+1)}$
\EndIf
\EndFor
\end{algorithmic} | "https://arxiv.org/src/2011.12267" | "2011.12267.tar.gz" | "2024-02-21" | {
"title": "a framework for fluid motion estimation using a constraint-based refinement approach",
"id": "2011.12267",
"abstract": "physics-based optical flow models have been successful in capturing the deformities in fluid motion arising from digital imagery. however, a common theoretical framework analyzing several physics-based models is missing. in this regard, we formulate a general framework for fluid motion estimation using a constraint-based refinement approach. we demonstrate that for a particular choice of constraint, our results closely approximate the classical continuity equation-based method for fluid flow. this closeness is theoretically justified by augmented lagrangian method in a novel way. the convergence of uzawa iterates is shown using a modified bounded constraint algorithm. the mathematical wellposedness is studied in a hilbert space setting. further, we observe a surprising connection to the cauchy-riemann operator that diagonalizes the system leading to a diffusive phenomenon involving the divergence and the curl of the flow. several numerical experiments are performed and the results are shown on different datasets. additionally, we demonstrate that a flow-driven refinement process involving the curl of the flow outperforms the classical physics-based optical flow method without any additional assumptions on the image data.",
"categories": "cs.cv math.ap",
"doi": "",
"created": "2020-11-24",
"updated": "2024-02-21",
"authors": [
"hirak doshi",
"n. uday kiran"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2011.12267"
} | "2024-03-15T04:18:37.012979" | {
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} | [] | "algorithm" | "3976d7de-c44d-4516-a2e2-893596fb61ab" | 807 | medium |
|
\begin{algorithm}[ht]
\floatname{algorithm}{Problem}
\caption{The reinsurer's time-selection problem}
Given any initial $(t,y,z)$, the reinsurer chooses a time $p(t;c)\in[t, T]\bigcup\{\infty\}$ at which his risk exposure increases by $\bar{y}-y$ and he obtains a premium of $(\bar{y}-y)\kappa\big(p(t;c)\big)$. His objective is to minimize $K\big(t,y,z,p(t;c)\big)$ over all choices of $p(t;c)$.
\end{algorithm}
| \begin{algorithm}
[ht]
\floatname{algorithm}{Problem}
\caption{The reinsurer's time-selection problem}
Given any initial $(t,y,z)$, the reinsurer chooses a time $p(t;c)\in[t, T]\bigcup\{\infty\}$ at which his risk exposure increases by $\bar{y}-y$ and he obtains a premium of $(\bar{y}-y)\kappa\big(p(t;c)\big)$. His objective is to minimize $K\big(t,y,z,p(t;c)\big)$ over all choices of $p(t;c)$.
\end{algorithm} | "https://arxiv.org/src/2402.11580" | "2402.11580.tar.gz" | "2024-02-18" | {
"title": "stackelberg reinsurance and premium decisions with mv criterion and irreversibility",
"id": "2402.11580",
"abstract": "we study a reinsurance stackelberg game in which both the insurer and the reinsurer adopt the mean-variance (abbr. mv) criterion in their decision-making and the reinsurance is irreversible. we apply a unified singular control framework where irreversible reinsurance contracts can be signed in both discrete and continuous times. the results theoretically illustrate that, rather than continuous-time contracts or a bunch of discrete-time contracts, a single once-for-all reinsurance contract is preferred. moreover, the stackelberg game turns out to be centering on the signing time of the single contract. the insurer signs the contract if the premium rate is lower than a time-dependent threshold and the reinsurer designs a premium that triggers the signing of the contract at his preferred time. further, we find that reinsurance preference, discount and reversion have a decreasing dominance in the reinsurer's decision-making, which is not seen for the insurer.",
"categories": "q-fin.mf",
"doi": "",
"created": "2024-02-18",
"updated": "",
"authors": [
"zongxia liang",
"xiaodong luo"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.11580"
} | "2024-03-15T03:31:21.490355" | {
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} | [] | "algorithm" | "488a833c-7569-4972-8f3a-04b397d23278" | 413 | easy |
|
\begin{algorithm}
\caption{PITT numerical update scheme}
\label{alg:pitt_numerical_update}
\begin{algorithmic}
\Require $V_0$, $T_{h1}$, $T_{h2}$, time $t$, $L$ layers
\For{$l = 1,2,\ldots,L$}
\State $X_l \gets Dropout(LA(T_{h1}, T_{h2}, V_{l-1})$
\State $t_l \gets MLP\left(\frac{l\cdot t}{L}\right)$
\State $V_l \gets V_{l-1} + MLP(\left[X_{l}, t_{l}\right])$
\EndFor
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{PITT numerical update scheme}
\begin{algorithmic}
\Require $V_0$, $T_{h1}$, $T_{h2}$, time $t$, $L$ layers
\For{$l = 1,2,\ldots,L$}
\State $X_l \gets Dropout(LA(T_{h1}, T_{h2}, V_{l-1})$
\State $t_l \gets MLP\left(\frac{l\cdot t}{L}\right)$
\State $V_l \gets V_{l-1} + MLP(\left[X_{l}, t_{l}\right])$
\EndFor
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2305.08757" | "2305.08757.tar.gz" | "2024-02-12" | {
"title": "physics informed token transformer for solving partial differential equations",
"id": "2305.08757",
"abstract": "solving partial differential equations (pdes) is the core of many fields of science and engineering. while classical approaches are often prohibitively slow, machine learning models often fail to incorporate complete system information. over the past few years, transformers have had a significant impact on the field of artificial intelligence and have seen increased usage in pde applications. however, despite their success, transformers currently lack integration with physics and reasoning. this study aims to address this issue by introducing pitt: physics informed token transformer. the purpose of pitt is to incorporate the knowledge of physics by embedding partial differential equations (pdes) into the learning process. pitt uses an equation tokenization method to learn an analytically-driven numerical update operator. by tokenizing pdes and embedding partial derivatives, the transformer models become aware of the underlying knowledge behind physical processes. to demonstrate this, pitt is tested on challenging 1d and 2d pde neural operator prediction tasks. the results show that pitt outperforms popular neural operator models and has the ability to extract physically relevant information from governing equations.",
"categories": "cs.lg physics.comp-ph",
"doi": "",
"created": "2023-05-15",
"updated": "2024-02-12",
"authors": [
"cooper lorsung",
"zijie li",
"amir barati farimani"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2305.08757"
} | "2024-03-15T05:13:40.045735" | {
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} | [] | "algorithm" | "dda431c9-ce60-47d9-a4f8-038519606958" | 369 | easy |
|
\begin{algorithm}[H]
\caption{Square system method}
\label{alg:squresystem}
\begin{algorithmic}[1]
\State Input:\begin{itemize}
\item Algebraic system of difference equations named $\Sigma'$
\item Time measured data allowing prolongation of the system.
\item For $\bar{\mu}=\mu_1,\ldots,\mu_n$ the finite set of parameters, the data $R_{\mu_i}$ of permissible intervals for each parameter value.
\end{itemize}
\State Output: Parameter values of $\Sigma'$.
\Procedure{Detect solvability}{}
\State Define $\Sigma prolong$ as an indefinite time prolongation of $\Sigma'$.
\State Redefine $\Sigma':=[]$, an `empty system' of no equations.
\State Denote $e_1,\ldots$ the equations of $\Sigma prolong$.
\State Define $J(t)=\left[\dfrac{\partial e_i}{\partial\mu_j}\right]$ where $e_i\in \Sigma',i=1,\ldots,r$, or 0 if $\Sigma'$ is empty.
\State $i:=1$
\For{$rank(J(t)):=s<n$ i.e. is not of full rank, }
\Procedure{Move equation}{}
\State $\Sigma':=\Sigma'\cup\{e_i\}$
\State $\Sigma prolong:=\Sigma prolong\backslash\{e_i\}$
\State Compute $rank(J(t))$ (note $\Sigma'$ has updated)
\If{$rank(J(t))<s+1$} $\Sigma':=\Sigma'\backslash\{e_i\}$
\EndIf
\State $i=i+1$
\If{$rank(J(t)<n$} repeat procedure Move Equation.
\EndIf
\EndProcedure
\EndFor
\Procedure{Blackbox solver and filter}{} Note Detect Solvability runs until $J(t)$ \phantom{---------}has full rank and outputs a polynomial system $\Sigma'$ that has solutions. Run any \phantom{---------}algebraic solver.
\State Filter solutions by intersecting solution set with $R_{\mu_i}$.
\EndProcedure
\EndProcedure
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[H]
\caption{Square system method}
\begin{algorithmic}
[1]
\State Input:\begin{itemize}
\item Algebraic system of difference equations named $\Sigma'$
\item Time measured data allowing prolongation of the system.
\item For $\bar{\mu}=\mu_1,\ldots,\mu_n$ the finite set of parameters, the data $R_{\mu_i}$ of permissible intervals for each parameter value.
\end{itemize}
\State Output: Parameter values of $\Sigma'$.
\Procedure{Detect solvability}{}
\State Define $\Sigma prolong$ as an indefinite time prolongation of $\Sigma'$.
\State Redefine $\Sigma':=[]$, an `empty system' of no equations.
\State Denote $e_1,\ldots$ the equations of $\Sigma prolong$.
\State Define $J(t)=\left[\dfrac{\partial e_i}{\partial\mu_j}\right]$ where $e_i\in \Sigma',i=1,\ldots,r$, or 0 if $\Sigma'$ is empty.
\State $i:=1$
\For{$rank(J(t)):=s<n$ i.e. is not of full rank, }
\Procedure{Move equation}{}
\State $\Sigma':=\Sigma'\cup\{e_i\}$
\State $\Sigma prolong:=\Sigma prolong\backslash\{e_i\}$
\State Compute $rank(J(t))$ (note $\Sigma'$ has updated)
\If{$rank(J(t))<s+1$} $\Sigma':=\Sigma'\backslash\{e_i\}$
\EndIf
\State $i=i+1$
\If{$rank(J(t)<n$} repeat procedure Move Equation.
\EndIf
\EndProcedure
\EndFor
\Procedure{Blackbox solver and filter}{} Note Detect Solvability runs until $J(t)$ \phantom{---------}has full rank and outputs a polynomial system $\Sigma'$ that has solutions. Run any \phantom{---------}algebraic solver.
\State Filter solutions by intersecting solution set with $R_{\mu_i}$.
\EndProcedure
\EndProcedure
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2401.16220" | "2401.16220.tar.gz" | "2024-01-29" | {
"title": "symbolic-numeric algorithm for parameter estimation in discrete-time models with $\\exp$",
"id": "2401.16220",
"abstract": "determining unknown parameter values in dynamic models is crucial for accurate analysis of the dynamics across the different scientific disciplines. discrete-time dynamic models are widely used to model biological processes, but it is often difficult to determine these parameters. in this paper, we propose a robust symbolic-numeric approach for parameter estimation in discrete-time models that involve non-algebraic functions such as exp. we illustrate the performance (precision) of our approach by applying our approach to the flour beetle (lpa) model, an archetypal discrete-time model in biology. unlike optimization-based methods, our algorithm guarantees to find all solutions of the parameter values given time-series data for the measured variables.",
"categories": "q-bio.qm cs.sc cs.sy eess.sy math.ac math.ds",
"doi": "",
"created": "2024-01-29",
"updated": "",
"authors": [
"yosef berman",
"joshua forrest",
"matthew grote",
"alexey ovchinnikov",
"sonia rueda"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.16220"
} | "2024-03-15T06:24:53.153570" | {
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} | [] | "algorithm" | "31237cdf-ff3a-45c1-a76b-89b571059859" | 1569 | hard |
|
\begin{algorithm}[]
\caption{Outer Approximation Branch-and-Cut Algorithm (OA-B\&C)} \label{algo_oa-bc}
{\small
\begin{algorithmic}
\State \textbf{Part 1 (Initialization)}:
$\mathcal{L}_0:=
\{\mathcal{F}_y^z \cup \mathcal{M}^{\tau}_{zU}\}$;
\ $\mathcal{B} = \{\eqref{VI5}\};$ \ $\mathcal{L'}_0:= \mathcal{L}_0 \cup \mathcal{B}$;
\ $\mathcal{U}_0:= \{\eqref{VI3};\eqref{VI4} \}$;
\ $\mathcal{A}_0:= C \setminus \mathcal{L}_0$; $\mathcal{V}^L_0 = \emptyset$;
\ $\mathcal{V}^U_0 = \emptyset$.
\State \textbf{Part 2 (Iterative Procedure): At node $k$}
\State \quad \textbf{Step 1: Solution of nodal relaxation problem:}
$ \mathbf{OA-MILP}_k: \; \min \eqref{obj_lin} \quad \text{s.to} \quad (x,y,\gamma,z,U,\mu,\tau,\omega) \in \mathcal{A}_k \ . $
\State \quad \textbf{Step 2: Set Update:} \\
\begin{itemize}
\item \textbf{If the objective value corresponding to $X^*_k$ is not better than that of the incumbent}, the node is pruned.
\item \textbf{If the objective value corresponding to $X^*_k$ is better than that of the incumbent}, then:
\begin{itemize}
\item \textbf{If $X^*_k$ is fractional}, apply user callback:
\begin{itemize}
\item If $X_k^{*}$ violates any constraint in $\mathcal{U}_o$:
\begin{itemize}
\item Move violated constraints to $\mathcal{V}_k^{U}$ and discard $X_k^{*}$.
\item Update sets of user cuts and active constraints for each open node $o \in \mathcal {O}$
\[
\mathcal{U}_o \leftarrow \mathcal{U}_o \setminus \mathcal{V}^U_k \quad \text{and} \quad
\mathcal{A}_o \leftarrow \mathcal{A}_o \cup \mathcal{V}^U_k.
\]
\end{itemize}
\item If no valid inequality in $\mathcal{U}_o$ is violated by $X^*_k$, then branching constraints are entered to cut off $X^*_k$ and the next open node is processed.
\end{itemize}
\item \textbf{If $X^*_k$ is integer-valued},
check for possible violation of lazy constraints:
\begin{itemize}
\item If $X^*_k$ violates any constraint in $\mathcal{L}^{'}_o$:
\begin{itemize}
\item Move violated lazy constraints to $\mathcal{V}^L_k$ and discard $X^*_k$.
\item Update sets of lazy and active constraints for each open node $o \in \mathcal {O}$:
\[
\mathcal{L}^{'}_o \leftarrow \mathcal{L}^{'}_o \setminus \mathcal{V}^L_k
\qquad \text{and} \qquad
\mathcal{A}_o \leftarrow \mathcal{A}_o \cup \mathcal{V}^L_k.
\]
\end{itemize}
\item If $X^*_k$ does not violate any constraint in $\mathcal{L}^{'}_o$, $X^*_k$ becomes the incumbent and node $k$ is pruned.
\end{itemize}
\end{itemize}
\end{itemize}
\State \textbf{Part 3 (Termination):} The algorithm stops when $\mathcal{O} = \emptyset$.
\end{algorithmic}
}
\end{algorithm}
| \begin{algorithm}[]
\caption{Outer Approximation Branch-and-Cut Algorithm (OA-B\&C)} {\small
\begin{algorithmic}
\State \textbf{Part 1 (Initialization)}:
$\mathcal{L}_0:=
\{\mathcal{F}_y^z \cup \mathcal{M}^{\tau}_{zU}\}$;
\ $\mathcal{B} = \{\eqref{VI5}\};$ \ $\mathcal{L'}_0:= \mathcal{L}_0 \cup \mathcal{B}$;
\ $\mathcal{U}_0:= \{\eqref{VI3};\eqref{VI4} \}$;
\ $\mathcal{A}_0:= C \setminus \mathcal{L}_0$; $\mathcal{V}^L_0 = \emptyset$;
\ $\mathcal{V}^U_0 = \emptyset$.
\State \textbf{Part 2 (Iterative Procedure): At node $k$}
\State \quad \textbf{Step 1: Solution of nodal relaxation problem:}
$ \mathbf{OA-MILP}_k: \; \min \eqref{obj_lin} \quad \text{s.to} \quad (x,y,\gamma,z,U,\mu,\tau,\omega) \in \mathcal{A}_k \ . $
\State \quad \textbf{Step 2: Set Update:} \\
\begin{itemize}
\item \textbf{If the objective value corresponding to $X^*_k$ is not better than that of the incumbent}, the node is pruned.
\item \textbf{If the objective value corresponding to $X^*_k$ is better than that of the incumbent}, then:
\begin{itemize}
\item \textbf{If $X^*_k$ is fractional}, apply user callback:
\begin{itemize}
\item If $X_k^{*}$ violates any constraint in $\mathcal{U}_o$:
\begin{itemize}
\item Move violated constraints to $\mathcal{V}_k^{U}$ and discard $X_k^{*}$.
\item Update sets of user cuts and active constraints for each open node $o \in \mathcal {O}$
\[
\mathcal{U}_o \leftarrow \mathcal{U}_o \setminus \mathcal{V}^U_k \quad \text{and} \quad
\mathcal{A}_o \leftarrow \mathcal{A}_o \cup \mathcal{V}^U_k.
\]
\end{itemize}
\item If no valid inequality in $\mathcal{U}_o$ is violated by $X^*_k$, then branching constraints are entered to cut off $X^*_k$ and the next open node is processed.
\end{itemize}
\item \textbf{If $X^*_k$ is integer-valued},
check for possible violation of lazy constraints:
\begin{itemize}
\item If $X^*_k$ violates any constraint in $\mathcal{L}^{'}_o$:
\begin{itemize}
\item Move violated lazy constraints to $\mathcal{V}^L_k$ and discard $X^*_k$.
\item Update sets of lazy and active constraints for each open node $o \in \mathcal {O}$:
\[
\mathcal{L}^{'}_o \leftarrow \mathcal{L}^{'}_o \setminus \mathcal{V}^L_k
\qquad \text{and} \qquad
\mathcal{A}_o \leftarrow \mathcal{A}_o \cup \mathcal{V}^L_k.
\]
\end{itemize}
\item If $X^*_k$ does not violate any constraint in $\mathcal{L}^{'}_o$, $X^*_k$ becomes the incumbent and node $k$ is pruned.
\end{itemize}
\end{itemize}
\end{itemize}
\State \textbf{Part 3 (Termination):} The algorithm stops when $\mathcal{O} = \emptyset$.
\end{algorithmic}
}
\end{algorithm} | "https://arxiv.org/src/2206.14340" | "2206.14340.tar.gz" | "2024-01-25" | {
"title": "drone-delivery network for opioid overdose -- nonlinear integer queueing-optimization models and methods",
"id": "2206.14340",
"abstract": "we propose a new stochastic emergency network design model that uses a fleet of drones to quickly deliver naxolone in response to opioid overdoses. the network is represented as a collection of m/g/k queuing systems in which the capacity k of each system is a decision variable and the service time is modelled as a decision-dependent random variable. the model is an optimization-based queuing problem which locates fixed (drone bases) and mobile (drones) servers and determines the drone dispatching decisions, and takes the form of a nonlinear integer problem, which is intractable in its original form. we develop an efficient reformulation and algorithmic framework. our approach reformulates the multiple nonlinearities (fractional, polynomial, exponential, factorial terms) to give a mixed-integer linear programming (milp) formulation. we demonstrate its generalizablity and show that the problem of minimizing the average response time of a network of m/g/k queuing systems with unknown capacity k is always milp-representable. we design two algorithms and demonstrate that the outer approximation branch-and-cut method is the most efficient and scales well. the analysis based on real-life overdose data reveals that drones can in virginia beach: 1) decrease the response time by 78%, 2) increase the survival chance by 432%, 3) save up to 34 additional lives per year, and 4) provide annually up to 287 additional quality-adjusted life years.",
"categories": "math.oc",
"doi": "",
"created": "2022-06-28",
"updated": "2024-01-25",
"authors": [
"miguel lejeune",
"wenbo ma"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2206.14340"
} | "2024-03-15T05:17:26.927464" | {
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} | [] | "algorithm" | "8d03fd35-cfba-42a6-9a5a-003641134809" | 2548 | hard |
|
\begin{algorithmic}[1]
\Statex \textbf{Inputs:} $s,i,d,a,r,e,v,h$, daily vaccinations
\Statex \textbf{Output:}
{$\vec{\beta}_{uu}, \vec{\beta}_{vu}, \vec{\beta}_{vv}$, $\vec{\beta}_{uv}$}
\Statex \textbf{Initialization:} $n=7$ or $n= 14$
\For{each time step $j$}
\State Select window $z_{j}=\{j-n+1,...,j\}$
\State Initialize parameters $\beta_{uu}$, $\beta_{vu}$, $\beta_{vv}$, $\beta_{uv}$
\State Calculate the initial cost $C_{j}(n,i,d,\hat{i}_{j},\hat{d}_{j})$
\State $flag=0$
\While{$flag=0$}
\State Create the trial parameters set $P_{k}$
\State Calculate a cost using every parameter from $P_{k}$ set
\State Find the minimum of all costs $C_{j}'(n,i,d,\hat{i}_{j},\hat{d}_{j})$ \If{$C_{j}'(n,i,d,\hat{i}_{j},\hat{d}_{j}) < C_{j}(n,i,d,\hat{i}_{j},\hat{d}_{j})$}
\State $C_{j}(n,i,d,\hat{i}_{j},\hat{d}_{j}) = C_{j}'(n,i,d,\hat{i}_{j},\hat{d}_{j})$
\State Keep the modified infection rate and create new set of trial parameters $P_{k}'$
\Else
\State $flag=1$
\State {$\vec{\beta}_{uu}(j)=\beta_{uu}$}
\State{$\vec{\beta}_{vu}(j) =\beta_{vu}$}
\State{$\vec{\beta}_{vv}(j)=\beta_{vv}$}
\State{$\vec{\beta}_{uv}(j)=\beta_{uv}$}
\EndIf
\EndWhile
\EndFor
\end{algorithmic}
| \begin{algorithmic}
[1]
\Statex \textbf{Inputs:} $s,i,d,a,r,e,v,h$, daily vaccinations
\Statex \textbf{Output:}
{$\vec{\beta}_{uu}, \vec{\beta}_{vu}, \vec{\beta}_{vv}$, $\vec{\beta}_{uv}$}
\Statex \textbf{Initialization:} $n=7$ or $n= 14$
\For{each time step $j$}
\State Select window $z_{j}=\{j-n+1,...,j\}$
\State Initialize parameters $\beta_{uu}$, $\beta_{vu}$, $\beta_{vv}$, $\beta_{uv}$
\State Calculate the initial cost $C_{j}(n,i,d,\hat{i}_{j},\hat{d}_{j})$
\State $flag=0$
\While{$flag=0$}
\State Create the trial parameters set $P_{k}$
\State Calculate a cost using every parameter from $P_{k}$ set
\State Find the minimum of all costs $C_{j}'(n,i,d,\hat{i}_{j},\hat{d}_{j})$ \If{$C_{j}'(n,i,d,\hat{i}_{j},\hat{d}_{j}) < C_{j}(n,i,d,\hat{i}_{j},\hat{d}_{j})$}
\State $C_{j}(n,i,d,\hat{i}_{j},\hat{d}_{j}) = C_{j}'(n,i,d,\hat{i}_{j},\hat{d}_{j})$
\State Keep the modified infection rate and create new set of trial parameters $P_{k}'$
\Else
\State $flag=1$
\State {$\vec{\beta}_{uu}(j)=\beta_{uu}$}
\State{$\vec{\beta}_{vu}(j) =\beta_{vu}$}
\State{$\vec{\beta}_{vv}(j)=\beta_{vv}$}
\State{$\vec{\beta}_{uv}(j)=\beta_{uv}$}
\EndIf
\EndWhile
\EndFor
\end{algorithmic} | "https://arxiv.org/src/2401.06629" | "2401.06629.tar.gz" | "2024-01-12" | {
"title": "pandemic infection forecasting through compartmental model and learning-based approaches",
"id": "2401.06629",
"abstract": "the emergence and spread of deadly pandemics has repeatedly occurred throughout history, causing widespread infections and loss of life. the rapid spread of pandemics have made governments across the world adopt a range of actions, including non-pharmaceutical measures to contain its impact. however, the dynamic nature of pandemics makes selecting intervention strategies challenging. hence, the development of suitable monitoring and forecasting tools for tracking infected cases is crucial for designing and implementing effective measures. motivated by this, we present a hybrid pandemic infection forecasting methodology that integrates compartmental model and learning-based approaches. in particular, we develop a compartmental model that includes time-varying infection rates, which are the key parameters that determine the pandemic's evolution. to identify the time-dependent infection rates, we establish a hybrid methodology that combines the developed compartmental model and tools from optimization and neural networks. specifically, the proposed methodology estimates the infection rates by fitting the model to available data, regarding the covid-19 pandemic in cyprus, and then predicting their future values through either a) extrapolation, or b) feeding them to neural networks. the developed approach exhibits strong accuracy in predicting infections seven days in advance, achieving low average percentage errors both using the extrapolation (9.90%) and neural network (5.04%) approaches.",
"categories": "q-bio.pe math.oc q-bio.qm",
"doi": "",
"created": "2024-01-12",
"updated": "",
"authors": [
"marianna karapitta",
"andreas kasis",
"charithea stylianides",
"kleanthis malialis",
"panayiotis kolios"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.06629"
} | "2024-03-15T07:35:55.770135" | {
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} | [] | "algorithm" | "9ae7b949-ca00-44a3-8ca5-f5e9a4f79d28" | 1174 | hard |
|
\begin{algorithmic}[1]
\State \textbf{Input:} matrix $M \in \mathbb{R}^{n\times m}$ with orthonormal columns
\State \textbf{Output:} index set $I$ if cardinality $m$
\State $I = \{\mathsf{argmax}\ |M(:,1)|\}$
\For $k = 2,\dots,m$
\State $c = M(I,1:k-1)^{-1} M(I,k)$
\State $r = M(:,k) - M(:,1:k-1)c$
\State $I = I \cup \{\mathsf{argmax}\ |r|\}$
\EndFor
\end{algorithmic}
| \begin{algorithmic}
[1]
\State \textbf{Input:} matrix $M \in \mathbb{R}^{n\times m}$ with orthonormal columns
\State \textbf{Output:} index set $I$ if cardinality $m$
\State $I = \{\mathsf{argmax}\ |M(:,1)|\}$
\For $k = 2,\dots,m$
\State $c = M(I,1:k-1)^{-1} M(I,k)$
\State $r = M(:,k) - M(:,1:k-1)c$
\State $I = I \cup \{\mathsf{argmax}\ |r|\}$
\EndFor
\end{algorithmic} | "https://arxiv.org/src/2211.11338" | "2211.11338.tar.gz" | "2024-02-25" | {
"title": "approximation in the extended functional tensor train format",
"id": "2211.11338",
"abstract": "this work proposes the extended functional tensor train (eftt) format for compressing and working with multivariate functions on tensor product domains. our compression algorithm combines tensorized chebyshev interpolation with a low-rank approximation algorithm that is entirely based on function evaluations. compared to existing methods based on the functional tensor train format, the adaptivity of our approach often results in reducing the required storage, sometimes considerably, while achieving the same accuracy. in particular, we reduce the number of function evaluations required to achieve a prescribed accuracy by up to over 96% compared to the algorithm from [gorodetsky, karaman and marzouk, comput. methods appl. mech. eng., 347 (2019)].",
"categories": "math.na cs.na",
"doi": "",
"created": "2022-11-21",
"updated": "2024-02-25",
"authors": [
"christoph str\u00f6ssner",
"bonan sun",
"daniel kressner"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2211.11338"
} | "2024-03-15T03:21:44.181934" | {
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} | [] | "algorithm" | "6af1a0d0-3663-4af3-a5c2-abd7fb6c009f" | 371 | easy |
|
\begin{algorithm}
\caption{General strategy for permutation testing by betting} \label{alg:general}
\hspace*{\algorithmicindent} \textbf{Input:} Sequence of test statistics $Y_0,Y_1, Y_2, \ldots$.\\
\textbf{Optional Input:} Stopping rule $\mathcal S$, potentially data-dependent and decided on the fly.\\
\hspace*{\algorithmicindent} \textbf{Output:} E-process $(W_t)_{t \geq 1}$, and p-process $(1/\sup_{s \leq t} W_s)_{t \geq 1}$.\\
\textbf{Optional output:} Stopping time $\tau$, e-value $W_{\tau}$, p-value $1/\sup_{s \leq \tau} W_s$.
\begin{algorithmic}[1]
\State $W_0 = 1$
\For{$t=1,2,...$}
\State Choose betting strategy $B_t=(B_t(1),\ldots,B_t(t+1))$ with $\sum_{r=1}^{t+1} B_t(r)=t+1$
\State Reveal $R_t$
\State $W_t = W_{t-1} \cdot B_t(R_t)$
\If{$\mathcal S(R_1,\ldots,R_t)=\text{stop}$}
\State $\tau=t$
\State \Return $\tau, W_{\tau}, (\max_{s=1,\ldots,\tau} W_s)^{-1}$
\EndIf
\EndFor
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{General strategy for permutation testing by betting} \hspace*{\algorithmicindent} \textbf{Input:} Sequence of test statistics $Y_0,Y_1, Y_2, \ldots$.\\
\textbf{Optional Input:} Stopping rule $\mathcal S$, potentially data-dependent and decided on the fly.\\
\hspace*{\algorithmicindent} \textbf{Output:} E-process $(W_t)_{t \geq 1}$, and p-process $(1/\sup_{s \leq t} W_s)_{t \geq 1}$.\\
\textbf{Optional output:} Stopping time $\tau$, e-value $W_{\tau}$, p-value $1/\sup_{s \leq \tau} W_s$.
\begin{algorithmic}
[1]
\State $W_0 = 1$
\For{$t=1,2,...$}
\State Choose betting strategy $B_t=(B_t(1),\ldots,B_t(t+1))$ with $\sum_{r=1}^{t+1} B_t(r)=t+1$
\State Reveal $R_t$
\State $W_t = W_{t-1} \cdot B_t(R_t)$
\If{$\mathcal S(R_1,\ldots,R_t)=\text{stop}$}
\State $\tau=t$
\State \Return $\tau, W_{\tau}, (\max_{s=1,\ldots,\tau} W_s)^{-1}$
\EndIf
\EndFor
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2401.07365" | "2401.07365.tar.gz" | "2024-02-18" | {
"title": "sequential monte-carlo testing by betting",
"id": "2401.07365",
"abstract": "in a monte-carlo test, the observed dataset is fixed, and several resampled or permuted versions of the dataset are generated in order to test a null hypothesis that the original dataset is exchangeable with the resampled/permuted ones. sequential monte-carlo tests aim to save computational resources by generating these additional datasets sequentially one by one, and potentially stopping early. while earlier tests yield valid inference at a particular prespecified stopping rule, our work develops a new anytime-valid monte-carlo test that can be continuously monitored, yielding a p-value or e-value at any stopping time possibly not specified in advance. despite the added flexibility, it significantly outperforms the well-known method by besag and clifford, stopping earlier under both the null and the alternative without compromising power. the core technical advance is the development of new test martingales (nonnegative martingales with initial value one) for testing exchangeability against a very particular alternative. these test martingales are constructed using new and simple betting strategies that smartly bet on the relative ranks of generated test statistics. the betting strategies are guided by the derivation of a simple log-optimal betting strategy, have closed form expressions for the wealth process, provable guarantees on resampling risk, and display excellent power in practice.",
"categories": "stat.me",
"doi": "",
"created": "2024-01-14",
"updated": "2024-02-18",
"authors": [
"lasse fischer",
"aaditya ramdas"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.07365"
} | "2024-03-15T05:18:01.125945" | {
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} | [] | "algorithm" | "472eefd0-75c7-43d8-8f88-ed86e45b1a37" | 910 | medium |
|
\begin{algorithm}
\caption{Non-Accelerated Composite Stochastic Mirror-Descent (NACSMD)}
\label{Algo NACSMD}
\begin{algorithmic}
\Require Number of iterations $T \geq 0$, starting point $x_1 \in \mathcal{X}$, step-sizes $(\alpha_t,\gamma_t)_t$%, proximal function $V$
\For{$ 1 \leq t \leq T$}
\begin{equation}
x_{t+1} = \arg\min_{x\in {\cal X}} \{ \alpha_t [ \langle G(x_t,\xi_t) , x \rangle + H(x) ] + \gamma_t D^{H}(x,x_{t}) \}
\end{equation}
\EndFor
\State Output $x_{T+1}^{ag}:= \frac{\sum_{t=1}^{T} \alpha_{t} x_{t+1}}{\sum_{t=1}^{T} \alpha_{t}}$.
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Non-Accelerated Composite Stochastic Mirror-Descent (NACSMD)}
\begin{algorithmic}
\Require Number of iterations $T \geq 0$, starting point $x_1 \in \mathcal{X}$, step-sizes $(\alpha_t,\gamma_t)_t$%, proximal function $V$
\For{$ 1 \leq t \leq T$}
\begin{equation*}
x_{t+1} = \arg\min_{x\in {\cal X}} \{ \alpha_t [ \langle G(x_t,\xi_t) , x \rangle + H(x) ] + \gamma_t D^{H}(x,x_{t}) \}
\end{equation*}
\EndFor
\State Output $x_{T+1}^{ag}:= \frac{\sum_{t=1}^{T} \alpha_{t} x_{t+1}}{\sum_{t=1}^{T} \alpha_{t}}$.
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2211.01758" | "2211.01758.tar.gz" | "2024-01-23" | {
"title": "optimal algorithms for stochastic complementary composite minimization",
"id": "2211.01758",
"abstract": "inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. this problem corresponds to the minimization of the sum of a (weakly) smooth function endowed with a stochastic first-order oracle, and a structured uniformly convex (possibly nonsmooth and non-lipschitz) regularization term. despite intensive work on closely related settings, prior to our work no complexity bounds for this problem were known. we close this gap by providing novel excess risk bounds, both in expectation and with high probability. our algorithms are nearly optimal, which we prove via novel lower complexity bounds for this class of problems. we conclude by providing numerical results comparing our methods to the state of the art.",
"categories": "cs.lg math.oc",
"doi": "",
"created": "2022-11-03",
"updated": "2024-01-23",
"authors": [
"alexandre d'aspremont",
"crist\u00f3bal guzm\u00e1n",
"cl\u00e9ment lezane"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2211.01758"
} | "2024-03-15T05:49:42.262116" | {
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} | [] | "algorithm" | "b3434f1f-2c3d-4043-8650-b931b344b5c0" | 568 | easy |
|
\begin{algorithmic}[1]
\State $\beta \gets \beta^*$ \Comment{load best set of parameters for BidNet}
\State $\alpha \gets \alpha^*$ \Comment{load optimized set of parameters for synthesizer}
\State $\tilde{\mathbf{c}}\sim A_{\alpha^*}(\mathbf{z})$\Comment{sample synthetic examples from the trained synthesizer}
\State $\mathbf{c} \sim D_{test}$\Comment{sample a test-set of real instances}
\State $\hat{b} \sim B_{\beta^*}(\mathbf{c})$\Comment{sample predicted bids from the test-set of real instances using BidNet}
\State $\tilde{b} \sim B_{\beta^*}(\tilde{\mathbf{c}})$\Comment{sample fake bids with the synthetic data emanating from the synthesizer}
\State $Dist(p(b) || p(\tilde{b}))$\Comment{compute the statistical distance between the fake and real distributions of bids}
\State $Dist(p(b) || p(\hat{b}))$\Comment{compute the statistical distance between the predicted and real distributions of bids}
\State $Dist(p(\hat{b}) || p(\tilde{b}))$\Comment{compute the statistical distance between the predicted and fake distributions of bids}
\end{algorithmic}
| \begin{algorithmic}
[1]
\State $\beta \gets \beta^*$ \Comment{load best set of parameters for BidNet}
\State $\alpha \gets \alpha^*$ \Comment{load optimized set of parameters for synthesizer}
\State $\tilde{\mathbf{c}}\sim A_{\alpha^*}(\mathbf{z})$\Comment{sample synthetic examples from the trained synthesizer}
\State $\mathbf{c} \sim D_{test}$\Comment{sample a test-set of real instances}
\State $\hat{b} \sim B_{\beta^*}(\mathbf{c})$\Comment{sample predicted bids from the test-set of real instances using BidNet}
\State $\tilde{b} \sim B_{\beta^*}(\tilde{\mathbf{c}})$\Comment{sample fake bids with the synthetic data emanating from the synthesizer}
\State $Dist(p(b) || p(\tilde{b}))$\Comment{compute the statistical distance between the fake and real distributions of bids}
\State $Dist(p(b) || p(\hat{b}))$\Comment{compute the statistical distance between the predicted and real distributions of bids}
\State $Dist(p(\hat{b}) || p(\tilde{b}))$\Comment{compute the statistical distance between the predicted and fake distributions of bids}
\end{algorithmic} | "https://arxiv.org/src/2207.12255" | "2207.12255.tar.gz" | "2024-02-15" | {
"title": "implementing a hierarchical deep learning approach for simulating multi-level auction data",
"id": "2207.12255",
"abstract": "we present a deep learning solution to address the challenges of simulating realistic synthetic first-price sealed-bid auction data. the complexities encountered in this type of auction data include high-cardinality discrete feature spaces and a multilevel structure arising from multiple bids associated with a single auction instance. our methodology combines deep generative modeling (dgm) with an artificial learner that predicts the conditional bid distribution based on auction characteristics, contributing to advancements in simulation-based research. this approach lays the groundwork for creating realistic auction environments suitable for agent-based learning and modeling applications. our contribution is twofold: we introduce a comprehensive methodology for simulating multilevel discrete auction data, and we underscore the potential of dgm as a powerful instrument for refining simulation techniques and fostering the development of economic models grounded in generative ai.",
"categories": "econ.gn q-fin.ec",
"doi": "",
"created": "2022-07-25",
"updated": "2024-02-15",
"authors": [
"igor sadoune",
"andrea lodi",
"marcelin joanis"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2207.12255"
} | "2024-03-15T04:05:27.239976" | {
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} | [] | "algorithm" | "7752de0d-02c9-458d-beae-0182637b3cb3" | 1064 | medium |
|
\begin{algorithm}
\caption{Imprecise Bayesian Neural Network}\label{alg:ibnn}
\begin{algorithmic}
\item
\textbf{S1} Specify a \textit{finite} set $\mathcal{P}$ of plausible prior probabilities on the parameters $\theta$ of the neural network, and a \textit{finite} set $\mathcal{L}_{x,\theta}$ of plausible likelihoods.
\item
\textbf{S2} Compute posterior $P_D=\mathsf{post}(P,P_{x,\theta})$, for all $P\in\mathcal{P}$ and all $P_{x,\theta}\in\mathcal{L}_{x,\theta}$.
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Imprecise Bayesian Neural Network}\begin{algorithmic}
\item
\textbf{S1} Specify a \textit{finite} set $\mathcal{P}$ of plausible prior probabilities on the parameters $\theta$ of the neural network, and a \textit{finite} set $\mathcal{L}_{x,\theta}$ of plausible likelihoods.
\item
\textbf{S2} Compute posterior $P_D=\mathsf{post}(P,P_{x,\theta})$, for all $P\in\mathcal{P}$ and all $P_{x,\theta}\in\mathcal{L}_{x,\theta}$.
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2302.09656" | "2302.09656.tar.gz" | "2024-02-22" | {
"title": "credal bayesian deep learning",
"id": "2302.09656",
"abstract": "uncertainty quantification and robustness to distribution shifts are important goals in machine learning and artificial intelligence. although bayesian neural networks (bnns) allow for uncertainty in the predictions to be assessed, different sources of uncertainty are indistinguishable. we present credal bayesian deep learning (cbdl). heuristically, cbdl allows to train an (uncountably) infinite ensemble of bnns, using only finitely many elements. this is possible thanks to prior and likelihood finitely generated credal sets (fgcss), a concept from the imprecise probability literature. intuitively, convex combinations of a finite collection of prior-likelihood pairs are able to represent infinitely many such pairs. after training, cbdl outputs a set of posteriors on the parameters of the neural network. at inference time, such posterior set is used to derive a set of predictive distributions that is in turn utilized to distinguish between aleatoric and epistemic uncertainties, and to quantify them. the predictive set also produces either (i) a collection of outputs enjoying desirable probabilistic guarantees, or (ii) the single output that is deemed the best, that is, the one having the highest predictive lower probability -- another imprecise-probabilistic concept. cbdl is more robust than single bnns to prior and likelihood misspecification, and to distribution shift. we show that cbdl is better at quantifying and disentangling different types of uncertainties than single bnns, ensemble of bnns, and bayesian model averaging. in addition, we apply cbdl to two case studies to demonstrate its downstream tasks capabilities: one, for motion prediction in autonomous driving scenarios, and two, to model blood glucose and insulin dynamics for artificial pancreas control. we show that cbdl performs better when compared to an ensemble of bnns baseline.",
"categories": "cs.lg stat.ml",
"doi": "",
"created": "2023-02-19",
"updated": "2024-02-22",
"authors": [
"michele caprio",
"souradeep dutta",
"kuk jin jang",
"vivian lin",
"radoslav ivanov",
"oleg sokolsky",
"insup lee"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2302.09656"
} | "2024-03-15T04:08:18.406723" | {
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} | [] | "algorithm" | "af210405-ee4d-43d4-affe-786399b7c612" | 484 | easy |
|
\begin{algorithmic}
\Function{NewtonOptimization}{$\bold{M}$, $\boldsymbol{\beta}$, $\boldsymbol{\phi}$}\Comment{$\bold{M}$ represents moments; $\boldsymbol{\beta}$ is the initial value of parameters; $\boldsymbol{\phi}$ represents sufficient statistics. }
\State $converged \gets $False$;\ n \gets 0;\ tol \gets 1\times 10^{-8};\ maxI \gets 400$; \ $\Delta\boldsymbol{\beta}\gets \bold{0}$;
\While{$converged$ is $False$ and $n\le maxI$ }
\State $\alpha \gets \Call{BackTrackingLineSearch}{\boldsymbol{\beta}, \Delta\boldsymbol{\beta}, \bold{M}, \boldsymbol{\phi}}$ \Comment{$\alpha$ is the step size}
\State $\boldsymbol{\beta} \gets \boldsymbol{\beta} + \alpha \Delta\boldsymbol{\beta}$ \Comment{Update the parameters}
\State $H \gets \nabla^2_{\boldsymbol{\beta}} L(\boldsymbol{\beta}; \bold{M}, \boldsymbol{\phi}$);\ $G \gets \nabla_{\boldsymbol{\beta}} L(\boldsymbol{\beta}; \bold{M}, \boldsymbol{\phi})$ \Comment{Compute the Hessian and gradient of the objective $L$ \eqref{MLE optimization goal}}
\State $\lambda \gets 1\times 10^{-3}$
\State $L_H,fail \gets \Call{CholeskyDecomposition}{H}$ \Comment{Standard Cholesky Decomposition Algorithm}
\While{$fail$} \Comment{$fail$ is $True$ if Cholesky decomposition failed}
\State $L_H,fail \gets \Call{CholeskyDecomposition}{H + \lambda I}$ \Comment{Adding a multiple of the identity}
\State $\lambda \gets 10\times\lambda$
\EndWhile
\State $\bold{w} = \Call{TriangularSolve}{L_H, -G}$ \Comment{Solve $L_H \bold{w} = -G$ in which $L_H$ is lower triangular matrix}
\State $\Delta\boldsymbol{\beta} = \Call{TriangularSolve}{L_H^T, \bold{w} }$ \Comment{Compute the update direction of the Newton's method}
\State $res \gets 0.5 \times \Delta\boldsymbol{\beta} \cdot \nabla L(\boldsymbol{\beta}) $
\State $converged \gets res \le tol$ or $\alpha \le 1\times10^{-6}$ \Comment{Check Convergence}
\State $n\gets n +1$
\EndWhile
\State \textbf{return} $\boldsymbol{\beta}$
\EndFunction
\Function{BackTrackingLineSearch}{$\boldsymbol{\beta}$, $\Delta\boldsymbol{\beta}, \bold{M}, \boldsymbol{\phi}$} \Comment{Backtracking line search to determine the step size}
\State $\alpha \gets 2$; $s \gets 0$;\ $maxT \gets 25$;\ $satisfied \gets False$
\While{$satisfied$ is $False$ and $s \le maxT$}
\If{not $satisfied$}
\State $\alpha \gets 0.5 \alpha$
\EndIf
\State $satisfied \gets \Call{ArmijoCondition}{\boldsymbol{\beta},\alpha \Delta\boldsymbol{\beta}, \bold{M}, \boldsymbol{\phi}}$
\State $s\gets s + 1$
\EndWhile
\State \textbf{return} $\alpha$
\EndFunction
\Function{ArmijoCondition} {$\boldsymbol{\beta}$, $\Delta\boldsymbol{\beta}, \bold{M}, \boldsymbol{\phi}$} \Comment{The Armijo's condition as stopping criterion of line search}
\State $c\gets 5\times 10^{-4}$;\ $atol \gets 5\times 10^{-6}$;\ $rtol \gets 5\times 10^{-5}$
\State $gradD = -c \nabla_{\boldsymbol{\beta}} L(\boldsymbol{\beta}; \bold{M}, \boldsymbol{\phi})\cdot\Delta\boldsymbol{\beta}$
\State $LD = L(\boldsymbol{\beta}; \bold{M}, \boldsymbol{\phi} ) - L(\boldsymbol{\beta} + \Delta\boldsymbol{\beta};\bold{M}, \boldsymbol{\phi})$
\State \textbf{return} $(LD - gradD) \ge -( atol + rtol\times |LD| ) $ \Comment{The RHS is $0$ with floating-point error tolerance}
\EndFunction
\end{algorithmic}
| \begin{algorithmic}
\Function{NewtonOptimization}{$\bold{M}$, $\boldsymbol{\beta}$, $\boldsymbol{\phi}$}\Comment{$\bold{M}$ represents moments; $\boldsymbol{\beta}$ is the initial value of parameters; $\boldsymbol{\phi}$ represents sufficient statistics. }
\State $converged \gets $False$;\ n \gets 0;\ tol \gets 1\times 10^{-8};\ maxI \gets 400$; \ $\Delta\boldsymbol{\beta}\gets \bold{0}$;
\While{$converged$ is $False$ and $n\le maxI$ }
\State $\alpha \gets \Call{BackTrackingLineSearch}{\boldsymbol{\beta}, \Delta\boldsymbol{\beta}, \bold{M}, \boldsymbol{\phi}}$ \Comment{$\alpha$ is the step size}
\State $\boldsymbol{\beta} \gets \boldsymbol{\beta} + \alpha \Delta\boldsymbol{\beta}$ \Comment{Update the parameters}
\State $H \gets \nabla^2_{\boldsymbol{\beta}} L(\boldsymbol{\beta}; \bold{M}, \boldsymbol{\phi}$);\ $G \gets \nabla_{\boldsymbol{\beta}} L(\boldsymbol{\beta}; \bold{M}, \boldsymbol{\phi})$ \Comment{Compute the Hessian and gradient of the objective $L$ \eqref{MLE optimization goal}}
\State $\lambda \gets 1\times 10^{-3}$
\State $L_H,fail \gets \Call{CholeskyDecomposition}{H}$ \Comment{Standard Cholesky Decomposition Algorithm}
\While{$fail$} \Comment{$fail$ is $True$ if Cholesky decomposition failed}
\State $L_H,fail \gets \Call{CholeskyDecomposition}{H + \lambda I}$ \Comment{Adding a multiple of the identity}
\State $\lambda \gets 10\times\lambda$
\EndWhile
\State $\bold{w} = \Call{TriangularSolve}{L_H, -G}$ \Comment{Solve $L_H \bold{w} = -G$ in which $L_H$ is lower triangular matrix}
\State $\Delta\boldsymbol{\beta} = \Call{TriangularSolve}{L_H^T, \bold{w} }$ \Comment{Compute the update direction of the Newton's method}
\State $res \gets 0.5 \times \Delta\boldsymbol{\beta} \cdot \nabla L(\boldsymbol{\beta}) $
\State $converged \gets res \le tol$ or $\alpha \le 1\times10^{-6}$ \Comment{Check Convergence}
\State $n\gets n +1$
\EndWhile
\State \textbf{return} $\boldsymbol{\beta}$
\EndFunction
\Function{BackTrackingLineSearch}{$\boldsymbol{\beta}$, $\Delta\boldsymbol{\beta}, \bold{M}, \boldsymbol{\phi}$} \Comment{Backtracking line search to determine the step size}
\State $\alpha \gets 2$; $s \gets 0$;\ $maxT \gets 25$;\ $satisfied \gets False$
\While{$satisfied$ is $False$ and $s \le maxT$}
\If{not $satisfied$}
\State $\alpha \gets 0.5 \alpha$
\EndIf
\State $satisfied \gets \Call{ArmijoCondition}{\boldsymbol{\beta},\alpha \Delta\boldsymbol{\beta}, \bold{M}, \boldsymbol{\phi}}$
\State $s\gets s + 1$
\EndWhile
\State \textbf{return} $\alpha$
\EndFunction
\Function{ArmijoCondition} {$\boldsymbol{\beta}$, $\Delta\boldsymbol{\beta}, \bold{M}, \boldsymbol{\phi}$} \Comment{The Armijo's condition as stopping criterion of line search}
\State $c\gets 5\times 10^{-4}$;\ $atol \gets 5\times 10^{-6}$;\ $rtol \gets 5\times 10^{-5}$
\State $gradD = -c \nabla_{\boldsymbol{\beta}} L(\boldsymbol{\beta}; \bold{M}, \boldsymbol{\phi})\cdot\Delta\boldsymbol{\beta}$
\State $LD = L(\boldsymbol{\beta}; \bold{M}, \boldsymbol{\phi} ) - L(\boldsymbol{\beta} + \Delta\boldsymbol{\beta};\bold{M}, \boldsymbol{\phi})$
\State \textbf{return} $(LD - gradD) \ge -( atol + rtol\times |LD| ) $ \Comment{The RHS is $0$ with floating-point error tolerance}
\EndFunction
\end{algorithmic} | "https://arxiv.org/src/2303.02898" | "2303.02898.tar.gz" | "2024-02-19" | {
"title": "stabilizing the maximal entropy moment method for rarefied gas dynamics at single-precision",
"id": "2303.02898",
"abstract": "the maximal entropy moment method (mem) is systematic solution of the challenging problem: generating extended hydrodynamic equations valid for both dense and rarefied gases. however, simulating mem suffers from a computational expensive and ill-conditioned maximal entropy problem. it causes numerical overflow and breakdown when the numerical precision is insufficient, especially for flows like high-speed shock waves. it also prevents modern gpus from accelerating mem with their enormous single floating-point precision computation power. this paper aims to stabilize mem, making it possible to simulating very strong normal shock waves on modern gpus at single precision. we improve the condition number of the maximal entropy problem by proposing gauge transformations, which moves not only flow fields but also hydrodynamic equations into a more optimal coordinate system. we addressed numerical overflow and breakdown in the maximal entropy problem by employing the canonical form of distribution and a modified newton optimization method. moreover, we discovered a counter-intuitive phenomenon that over-refined spatial mesh beyond mean free path degrades the stability of mem. with these techniques, we accomplished single-precision gpu simulations of high speed shock wave up to mach 10 utilizing 35 moments mem, while previous methods only achieved mach 4 on double-precision.",
"categories": "physics.flu-dyn cs.lg",
"doi": "",
"created": "2023-03-06",
"updated": "2024-02-19",
"authors": [
"candi zheng",
"wang yang",
"shiyi chen"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2303.02898"
} | "2024-03-15T03:56:31.323537" | {
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} | [] | "algorithm" | "d072fad7-9556-42f5-951f-77688060ae01" | 3209 | hard |
|
\begin{algorithmic}[1]
\Require Baseline covariates $Z_1, \cdots, Z_n$
\State Estimate $\bar{\mu}_i$ by regressing baseline outcomes on covariates $Z$
\State Estimate $\bar{\sigma}^2$ the variance of the residuals from this regression
\State Consider the range of values $\bar{\psi} \in [\bar{\sigma}^2, 4 \bar{\sigma}^2]$
\If{past experiments are available}
\State Use $\bar{\phi}_n$ from previous experiments
\Else
\State Consider a range of values of plausible spillover effects
\EndIf
\end{algorithmic}
| \begin{algorithmic}
[1]
\Require Baseline covariates $Z_1, \cdots, Z_n$
\State Estimate $\bar{\mu}_i$ by regressing baseline outcomes on covariates $Z$
\State Estimate $\bar{\sigma}^2$ the variance of the residuals from this regression
\State Consider the range of values $\bar{\psi} \in [\bar{\sigma}^2, 4 \bar{\sigma}^2]$
\If{past experiments are available}
\State Use $\bar{\phi}_n$ from previous experiments
\Else
\State Consider a range of values of plausible spillover effects
\EndIf
\end{algorithmic} | "https://arxiv.org/src/2310.14983" | "2310.14983.tar.gz" | "2024-01-13" | {
"title": "causal clustering: design of cluster experiments under network interference",
"id": "2310.14983",
"abstract": "this paper studies the design of cluster experiments to estimate the global treatment effect in the presence of network spillovers. we provide a framework to choose the clustering that minimizes the worst-case mean-squared error of the estimated global effect. we show that optimal clustering solves a novel penalized min-cut optimization problem computed via off-the-shelf semi-definite programming algorithms. our analysis also characterizes simple conditions to choose between any two cluster designs, including choosing between a cluster or individual-level randomization. we illustrate the method's properties using unique network data from the universe of facebook's users and existing data from a field experiment.",
"categories": "econ.em math.st stat.me stat.th",
"doi": "",
"created": "2023-10-23",
"updated": "2024-01-13",
"authors": [
"davide viviano",
"lihua lei",
"guido imbens",
"brian karrer",
"okke schrijvers",
"liang shi"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2310.14983"
} | "2024-03-15T06:10:54.538396" | {
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} | [] | "algorithm" | "ce86669e-8b17-4c81-9cb9-f33153413764" | 507 | easy |
|
\begin{algorithmic}[1]
\State $\mathcal{F} \leftarrow \textsc{makePF}(\{\{r\} | r \in \mathcal{R}\})$
\State converged $\leftarrow \texttt{false}$
\While{\texttt{not} converged}
\State converged $\leftarrow \texttt{true}$
\State $\mathcal{F}_0 \leftarrow \textsc{SSF}(\mathcal{F}, k)$
\State $\mathcal{F}' \leftarrow \emptyset$
\For{$S \in \mathcal{F}_0$}
\For{$r \in \mathcal{R}$}
\State $S' \leftarrow S \cup \{r\}$
\State $\mathcal{F}' \leftarrow \mathcal{F}' \cup \{S'\}$
\EndFor
\EndFor
\State $\mathcal{F}' \leftarrow \textsc{makePF}(\mathcal{F}' \cup \mathcal{F})$
\State $\texttt{converged} \leftarrow \mathcal{F}' == \mathcal{F}$
\State $\mathcal{F} \leftarrow \mathcal{F}'$
\EndWhile
\Return $\mathcal{F}$
\end{algorithmic}
| \begin{algorithmic}
[1]
\State $\mathcal{F} \leftarrow \textsc{makePF}(\{\{r\} | r \in \mathcal{R}\})$
\State converged $\leftarrow \texttt{false}$
\While{\texttt{not} converged}
\State converged $\leftarrow \texttt{true}$
\State $\mathcal{F}_0 \leftarrow \textsc{SSF}(\mathcal{F}, k)$
\State $\mathcal{F}' \leftarrow \emptyset$
\For{$S \in \mathcal{F}_0$}
\For{$r \in \mathcal{R}$}
\State $S' \leftarrow S \cup \{r\}$
\State $\mathcal{F}' \leftarrow \mathcal{F}' \cup \{S'\}$
\EndFor
\EndFor
\State $\mathcal{F}' \leftarrow \textsc{makePF}(\mathcal{F}' \cup \mathcal{F})$
\State $\texttt{converged} \leftarrow \mathcal{F}' == \mathcal{F}$
\State $\mathcal{F} \leftarrow \mathcal{F}'$
\EndWhile
\Return $\mathcal{F}$
\end{algorithmic} | "https://arxiv.org/src/2311.00964" | "2311.00964.tar.gz" | "2024-01-17" | {
"title": "on finding bi-objective pareto-optimal fraud prevention rule sets for fintech applications",
"id": "2311.00964",
"abstract": "rules are widely used in fintech institutions to make fraud prevention decisions, since rules are highly interpretable thanks to their intuitive if-then structure. in practice, a two-stage framework of fraud prevention decision rule set mining is usually employed in large fintech institutions. this paper is concerned with finding high-quality rule subsets in a bi-objective space (such as precision and recall) from an initial pool of rules. to this end, we adopt the concept of pareto optimality and aim to find a set of non-dominated rule subsets, which constitutes a pareto front. we propose a heuristic-based framework called pors and we identify that the core of pors is the problem of solution selection on the front (ssf). we provide a systematic categorization of the ssf problem and a thorough empirical evaluation of various ssf methods on both public and proprietary datasets. we also introduce a novel variant of sequential covering algorithm called spectralrules to encourage the diversity of the initial rule set and we empirically find that spectralrules further improves the quality of the found pareto front. on two real application scenarios within alipay, we demonstrate the advantages of our proposed methodology compared to existing work.",
"categories": "cs.lg q-fin.st",
"doi": "",
"created": "2023-11-01",
"updated": "2024-01-17",
"authors": [
"chengyao wen",
"yin lou"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2311.00964"
} | "2024-03-15T05:59:22.584765" | {
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} | [] | "algorithm" | "56433a36-7e84-4ae9-bed2-37f1f6867574" | 734 | medium |
|
\begin{algorithmic}[1]
\Statex {\bf Input:} $p$-values of the observed test statistics and bounding sequences $c_{m, 0.5}$ and $c_{m, 1}$
\Statex {\bf Output:} a proportion estimate $\hat \pi$
\State Rank the variables by their $p$-values so that $p_{(1)} < p_{(2)} < \ldots < p_{(m)}$
\State Compute
\[
\hat{\pi}_{0.5}= \max_{1 < j < m}\frac{ j/m-p_{(j)}-c_{m,0.5} \cdot \sqrt{p_{(j)}}} {1-p_{(j)}} \qquad \mbox{and} \qquad \hat{\pi}_{1}= \max_{1 < j < m}\frac{ j/m-p_{(j)} -c_{m,1} \cdot p_{(j)}} {1-p_{(j)}}
\]
\State Obtain $\hat \pi = \max\{\hat{\pi}_{0.5}, \hat{\pi}_{1}\}$
\end{algorithmic}
| \begin{algorithmic}
[1]
\Statex {\bf Input:} $p$-values of the observed test statistics and bounding sequences $c_{m, 0.5}$ and $c_{m, 1}$
\Statex {\bf Output:} a proportion estimate $\hat \pi$
\State Rank the variables by their $p$-values so that $p_{(1)} < p_{(2)} < \ldots < p_{(m)}$
\State Compute
\[
\hat{\pi}_{0.5}= \max_{1 < j < m}\frac{ j/m-p_{(j)}-c_{m,0.5} \cdot \sqrt{p_{(j)}}} {1-p_{(j)}} \qquad \mbox{and} \qquad \hat{\pi}_{1}= \max_{1 < j < m}\frac{ j/m-p_{(j)} -c_{m,1} \cdot p_{(j)}} {1-p_{(j)}}
\]
\State Obtain $\hat \pi = \max\{\hat{\pi}_{0.5}, \hat{\pi}_{1}\}$
\end{algorithmic} | "https://arxiv.org/src/2212.13574" | "2212.13574.tar.gz" | "2024-02-02" | {
"title": "weak signal inclusion under dependence and applications in genome-wide association study",
"id": "2212.13574",
"abstract": "motivated by the inquiries of weak signals in underpowered genome-wide association studies (gwass), we consider the problem of retaining true signals that are not strong enough to be individually separable from a large amount of noise. we address the challenge from the perspective of false negative control and present false negative control (fnc) screening, a data-driven method to efficiently regulate false negative proportion at a user-specified level. fnc screening is developed in a realistic setting with arbitrary covariance dependence between variables. we calibrate the overall dependence through a parameter whose scale is compatible with the existing phase diagram in high-dimensional sparse inference. utilizing the new calibration, we asymptotically explicate the joint effect of covariance dependence, signal sparsity, and signal intensity on the proposed method. we interpret the results using a new phase diagram, which shows that fnc screening can efficiently select a set of candidate variables to retain a high proportion of signals even when the signals are not individually separable from noise. finite sample performance of fnc screening is compared to those of several existing methods in simulation studies. the proposed method outperforms the others in adapting to a user-specified false negative control level. we implement fnc screening to empower a two-stage gwas procedure, which demonstrates substantial power gain when working with limited sample sizes in real applications.",
"categories": "stat.me",
"doi": "",
"created": "2022-12-27",
"updated": "2024-02-02",
"authors": [
"x. jessie jeng",
"yifei hu",
"quan sun",
"yun li"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2212.13574"
} | "2024-03-15T07:22:29.819002" | {
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} | [] | "algorithm" | "fa3e3b7f-a246-4d6f-9354-0f8675d5fcd7" | 598 | easy |
|
\begin{algorithmic}[1]
\State \textbf{Input}: iteration index $t$, $\mathcal{D}=\{(\mathbf{x}^{i},y^{i})\}_{i=1}^{t}$, $N_{init}$, $N_{vs}$, set of important variables chosen at iteration $t-N_{vs}$, denote as $\hat{\mathbf{x}}_{ipt}$
\State \textbf{Output}: Set of important variables chosen at iteration $t$, denote as $\mathbf{x}_{ipt}$
\If{$t=N_{init}+N_{vs}$ or $\hat{\mathbf{x}}_{ipt}=\mathbf{x}$} \Comment{First time to do variable selection or $\hat{\mathbf{x}}_{ipt}$ contains all variables}
\State \Return Algorithm~\ref{alg:VS_detail}
\ElsIf{$\max_{k\in \{t-N_{vs}+1, t-N_{vs}+2, \dots, t\}}y^{k}\leq\max_{k\in \{1,\dots, t-N_{vs}\}}y^{k}$} \Comment{Inaccurate case}
\State \Return Algorithm~\ref{alg:momentum_inacc}
\Else \Comment{Accurate case}
\State \Return Algorithm~\ref{alg:momentum_acc}
\EndIf
\end{algorithmic}
| \begin{algorithmic}
[1]
\State \textbf{Input}: iteration index $t$, $\mathcal{D}=\{(\mathbf{x}^{i},y^{i})\}_{i=1}^{t}$, $N_{init}$, $N_{vs}$, set of important variables chosen at iteration $t-N_{vs}$, denote as $\hat{\mathbf{x}}_{ipt}$
\State \textbf{Output}: Set of important variables chosen at iteration $t$, denote as $\mathbf{x}_{ipt}$
\If{$t=N_{init}+N_{vs}$ or $\hat{\mathbf{x}}_{ipt}=\mathbf{x}$} \Comment{First time to do variable selection or $\hat{\mathbf{x}}_{ipt}$ contains all variables}
\State \Return Algorithm~\ref{alg:VS_detail}
\ElsIf{$\max_{k\in \{t-N_{vs}+1, t-N_{vs}+2, \dots, t\}}y^{k}\leq\max_{k\in \{1,\dots, t-N_{vs}\}}y^{k}$} \Comment{Inaccurate case}
\State \Return Algorithm~\ref{alg:momentum_inacc}
\Else \Comment{Accurate case}
\State \Return Algorithm~\ref{alg:momentum_acc}
\EndIf
\end{algorithmic} | "https://arxiv.org/src/2109.09264" | "2109.09264.tar.gz" | "2024-02-12" | {
"title": "computationally efficient high-dimensional bayesian optimization via variable selection",
"id": "2109.09264",
"abstract": "bayesian optimization (bo) is a method for globally optimizing black-box functions. while bo has been successfully applied to many scenarios, developing effective bo algorithms that scale to functions with high-dimensional domains is still a challenge. optimizing such functions by vanilla bo is extremely time-consuming. alternative strategies for high-dimensional bo that are based on the idea of embedding the high-dimensional space to the one with low dimension are sensitive to the choice of the embedding dimension, which needs to be pre-specified. we develop a new computationally efficient high-dimensional bo method that exploits variable selection. our method is able to automatically learn axis-aligned sub-spaces, i.e. spaces containing selected variables, without the demand of any pre-specified hyperparameters. we theoretically analyze the computational complexity of our algorithm and derive the regret bound. we empirically show the efficacy of our method on several synthetic and real problems.",
"categories": "cs.lg stat.ml",
"doi": "",
"created": "2021-09-19",
"updated": "2024-02-12",
"authors": [
"yihang shen",
"carl kingsford"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2109.09264"
} | "2024-03-15T06:07:56.040616" | {
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} | [] | "algorithm" | "2762af07-844b-4fc9-aafb-1ea1c5c8f367" | 831 | medium |
|
\begin{algorithmic}
\Require $n=2$, $N\in\mathbb{N}$ sufficiently large
\Require $X_{1i}$ are independent for $i=0,1,...,k-1$
\Require $X_{2i}=1+r$, $r>-1$ for $i=0,1,...,k-1$
\Require $\boldsymbol\pi_{i}=(q_i(\widehat{W}_i,A_i),1-q_i(\widehat{W}_i,A_i))$ for $i=0,1,...,k-1$
\State $l\gets 0$\Comment{initialize $l$}
\While{$l\leq N$}
\State $l\gets l+1$
\State $i\gets 0$ \Comment{initialize i}
\State $I\gets 1$ \Comment{initialize $I_i$}
\State $A\gets A_0$ \Comment{initialize $A_i$}
\State $\widehat{W}\gets P$ \Comment{initialize $\widehat{W}_i$}
\While{$i\leq k$}
\State $i\gets i+1$
\State $X$ is a realization of $X_{1,i-1}$
\State $Y\gets q_{i-1}(\overline{W},A)\cdot X+(1-q_{i-1}(\overline{W},A))\cdot (1+r)$
\State $B^j$ is a realization of $B_{i-1}^j$ for $j=1,2,...,A$
\State $I\gets I-\sum_{j=1}^IB^j$
\State $A\gets A-\sum_{j=1}^AB^j$
\State $\widehat{W}\gets Y\widehat{W}-IAw_i$ \Comment{computes $\widehat{W}_i$}
\EndWhile
\State $b_l\gets\begin{cases}1,&\widehat{W}\geq 0\\0,&\text{otherwise}\end{cases}$
\EndWhile
\State $\mathbb{P}(\widehat{W}_k\geq w)\gets\frac{1}{N}\sum_{l=1}^Nb_l$\\
\Return{$\mathbb{P}(\widehat{W}_k\geq w)$}
\end{algorithmic}
| \begin{algorithmic}
\Require $n=2$, $N\in\mathbb{N}$ sufficiently large
\Require $X_{1i}$ are independent for $i=0,1,...,k-1$
\Require $X_{2i}=1+r$, $r>-1$ for $i=0,1,...,k-1$
\Require $\boldsymbol\pi_{i}=(q_i(\widehat{W}_i,A_i),1-q_i(\widehat{W}_i,A_i))$ for $i=0,1,...,k-1$
\State $l\gets 0$\Comment{initialize $l$}
\While{$l\leq N$}
\State $l\gets l+1$
\State $i\gets 0$ \Comment{initialize i}
\State $I\gets 1$ \Comment{initialize $I_i$}
\State $A\gets A_0$ \Comment{initialize $A_i$}
\State $\widehat{W}\gets P$ \Comment{initialize $\widehat{W}_i$}
\While{$i\leq k$}
\State $i\gets i+1$
\State $X$ is a realization of $X_{1,i-1}$
\State $Y\gets q_{i-1}(\overline{W},A)\cdot X+(1-q_{i-1}(\overline{W},A))\cdot (1+r)$
\State $B^j$ is a realization of $B_{i-1}^j$ for $j=1,2,...,A$
\State $I\gets I-\sum_{j=1}^IB^j$
\State $A\gets A-\sum_{j=1}^AB^j$
\State $\widehat{W}\gets Y\widehat{W}-IAw_i$ \Comment{computes $\widehat{W}_i$}
\EndWhile
\State $b_l\gets\begin{cases}
1,&\widehat{W}\geq 0\\0,&\text{otherwise}\end{cases}$
\EndWhile
\State $\mathbb{P}(\widehat{W}_k\geq w)\gets\frac{1}{N}\sum_{l=1}^Nb_l$\\
\Return{$\mathbb{P}(\widehat{W}_k\geq w)$}
\end{algorithmic} | "https://arxiv.org/src/2402.17164" | "2402.17164.tar.gz" | "2024-02-26" | {
"title": "withdrawal success optimization in a pooled annuity fund",
"id": "2402.17164",
"abstract": "consider a closed pooled annuity fund investing in n assets with discrete-time rebalancing. at time 0, each annuitant makes an initial contribution to the fund, committing to a predetermined schedule of withdrawals. require annuitants to be homogeneous in the sense that their initial contributions and predetermined withdrawal schedules are identical, and their mortality distributions are identical and independent. under the forementioned setup, the probability for a particular annuitant to complete the prescribed withdrawals until death is maximized over progressively measurable portfolio weight functions. applications consider fund portfolios that mix two assets: the s&p composite index and an inflation-protected bond. the maximum probability is computed for annually rebalanced schedules consisting of an initial investment and then equal annual withdrawals until death. a considerable increase in the maximum probability is achieved by increasing the number of annuitants initially in the pool. for example, when the per-annuitant initial contribution and annual withdrawal amount are held constant, starting with 20 annuitants instead of just 1 can increase the maximum probability (measured on a scale from 0 to 1) by as much as .15.",
"categories": "q-fin.mf",
"doi": "",
"created": "2024-02-26",
"updated": "",
"authors": [
"hayden brown"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.17164"
} | "2024-03-15T02:40:56.763732" | {
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} | [] | "algorithm" | "da14d1df-06be-4198-a9fa-cf514273b72c" | 1170 | hard |
|
\begin{algorithm}
\caption{Discrete Soft Actor-Critic for \textit{de novo} drug design}\label{alg:sac}
\begin{algorithmic}[1]
\Statex \textbf{Input:} $\phi$, $\theta$, initial episodes $K_{\mathrm{init}}$, total budget of episodes $K_{\mathrm{E}}$,
\Statex \textbf{Init:} $\phi' \gets \phi$, $\theta' \gets \theta$, $\mathcal{D} \gets \emptyset$
\For{each initial episode $1,\dots,K_{\mathrm{init}}$}
\State Sample a batch $\mathcal{T}$ of $M$ sequences using pre-trained policy $\pi_\theta$
\State Score each sequence in $\mathcal{T}$
\State Add unique, valid sequences to replay memory $\mathcal{D}$
\EndFor
\For{each episode $K_{\mathrm{init}}+1,\dots,K_{\mathrm{E}}$}
\State Sample a batch $\mathcal{T}$ of $M$ sequences using current policy $\pi_\theta$
\State Score each sequence in $\mathcal{T}$
\State Add unique, valid sequences to replay memory $\mathcal{D}$
\State $\phi \gets \phi - \lambda_Q \hat{\nabla}_\phi J_Q (\phi \vert \mathcal{T})$ \Comment{On-policy update of Q-function parameters}
\State $\theta \gets \theta - \lambda_\pi \hat{\nabla}_\theta J_\pi (\theta\vert \mathcal{T})$ \Comment{On-policy update of policy parameters}
\State $\alpha \gets \alpha - \lambda_\alpha \hat{\nabla}_\alpha J_\alpha (\alpha \vert \mathcal{T})$ \Comment{On-policy update of temperature}
\State $\phi' \gets \tau \phi' + (1-\tau) \phi$ \Comment{Update target parameters}
\State $\theta' \gets \tau \theta' + (1-\tau) \theta$ \Comment{Update average policy parameters}
\For{each off-policy update}
\State $\phi \gets \phi - \lambda_Q \hat{\nabla}_\phi J_Q (\phi \vert \mathcal{D})$
\State $\theta \gets \theta - \lambda_\pi \hat{\nabla}_\theta J_\pi (\theta\vert \mathcal{D})$
\State $\alpha \gets \alpha - \lambda_\alpha \hat{\nabla}_\alpha J_a (\alpha \vert \mathcal{D})$
\State $\phi' \gets \tau \phi' + (1-\tau) \phi$
\State $\theta' \gets \tau \theta' + (1-\tau) \theta$
\EndFor
\EndFor
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Discrete Soft Actor-Critic for \textit{de novo} drug design}\begin{algorithmic}
[1]
\Statex \textbf{Input:} $\phi$, $\theta$, initial episodes $K_{\mathrm{init}}$, total budget of episodes $K_{\mathrm{E}}$,
\Statex \textbf{Init:} $\phi' \gets \phi$, $\theta' \gets \theta$, $\mathcal{D} \gets \emptyset$
\For{each initial episode $1,\dots,K_{\mathrm{init}}$}
\State Sample a batch $\mathcal{T}$ of $M$ sequences using pre-trained policy $\pi_\theta$
\State Score each sequence in $\mathcal{T}$
\State Add unique, valid sequences to replay memory $\mathcal{D}$
\EndFor
\For{each episode $K_{\mathrm{init}}+1,\dots,K_{\mathrm{E}}$}
\State Sample a batch $\mathcal{T}$ of $M$ sequences using current policy $\pi_\theta$
\State Score each sequence in $\mathcal{T}$
\State Add unique, valid sequences to replay memory $\mathcal{D}$
\State $\phi \gets \phi - \lambda_Q \hat{\nabla}_\phi J_Q (\phi \vert \mathcal{T})$ \Comment{On-policy update of Q-function parameters}
\State $\theta \gets \theta - \lambda_\pi \hat{\nabla}_\theta J_\pi (\theta\vert \mathcal{T})$ \Comment{On-policy update of policy parameters}
\State $\alpha \gets \alpha - \lambda_\alpha \hat{\nabla}_\alpha J_\alpha (\alpha \vert \mathcal{T})$ \Comment{On-policy update of temperature}
\State $\phi' \gets \tau \phi' + (1-\tau) \phi$ \Comment{Update target parameters}
\State $\theta' \gets \tau \theta' + (1-\tau) \theta$ \Comment{Update average policy parameters}
\For{each off-policy update}
\State $\phi \gets \phi - \lambda_Q \hat{\nabla}_\phi J_Q (\phi \vert \mathcal{D})$
\State $\theta \gets \theta - \lambda_\pi \hat{\nabla}_\theta J_\pi (\theta\vert \mathcal{D})$
\State $\alpha \gets \alpha - \lambda_\alpha \hat{\nabla}_\alpha J_a (\alpha \vert \mathcal{D})$
\State $\phi' \gets \tau \phi' + (1-\tau) \phi$
\State $\theta' \gets \tau \theta' + (1-\tau) \theta$
\EndFor
\EndFor
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2303.17615" | "2303.17615.tar.gz" | "2024-01-30" | {
"title": "utilizing reinforcement learning for de novo drug design",
"id": "2303.17615",
"abstract": "deep learning-based approaches for generating novel drug molecules with specific properties have gained a lot of interest in the last few years. recent studies have demonstrated promising performance for string-based generation of novel molecules utilizing reinforcement learning. in this paper, we develop a unified framework for using reinforcement learning for de novo drug design, wherein we systematically study various on- and off-policy reinforcement learning algorithms and replay buffers to learn an rnn-based policy to generate novel molecules predicted to be active against the dopamine receptor drd2. our findings suggest that it is advantageous to use at least both top-scoring and low-scoring molecules for updating the policy when structural diversity is essential. using all generated molecules at an iteration seems to enhance performance stability for on-policy algorithms. in addition, when replaying high, intermediate, and low-scoring molecules, off-policy algorithms display the potential of improving the structural diversity and number of active molecules generated, but possibly at the cost of a longer exploration phase. our work provides an open-source framework enabling researchers to investigate various reinforcement learning methods for de novo drug design.",
"categories": "q-bio.bm cs.lg",
"doi": "",
"created": "2023-03-30",
"updated": "2024-01-30",
"authors": [
"hampus gummesson svensson",
"christian tyrchan",
"ola engkvist",
"morteza haghir chehreghani"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2303.17615"
} | "2024-03-15T06:00:14.855698" | {
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} | [] | "algorithm" | "5bc27b20-1fab-47d0-b048-85fe081cac5c" | 1913 | hard |
|
\begin{algorithm}[h!]
\caption{Incremental learning for infection rates prediction}
\label{alg:nnmethod}
\begin{algorithmic}[1]
\Statex \textbf{Input:} ``Lookback'' window size $W$, Day ahead to predict $D$
\State Wait $W$ days to fill window.
\State Create model $f^W.init()$ \Comment $j = W$
\State Observe instance $\grave{\beta}^W = \{\beta^W, \beta^{W-1}, ..., \beta^1\}$
\State Predict $\hat{\beta}^{W+1} = f^W.predict(\grave{\beta}^W)$
\For{each day $j \in [W + 1, W + D -1)$} \Comment Only predictions these days
\State Observe ground truth $\beta^j$
\State Create instance $\grave{\beta}^j = \{\beta^j, \beta^{j-1}, .., \beta^{j-W+1}\}$
\State Predict $\hat{\beta}^{j + D} = f^W.predict(\grave{\beta}^j)$ \Comment $f^W$ hasn't been updated yet
\EndFor
\For{each day $j \in [W + D, \infty)$} \Comment Predictions and training
\State Observe ground truth $\beta^j$
\State Incremental training $f^j = f^{j-1}.train((\grave{\beta}^{j-D}, \beta^j))$ \Comment As in Eq (\ref{eq:training})
\State Create instance $\grave{\beta}^j = \{\beta^j, \beta^{j-1}, .., \beta^{j-W+1}\}$
\State Predict $\hat{\beta}^{j + D} = f^j.predict(\grave{\beta}^j)$
\EndFor
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[h!]
\caption{Incremental learning for infection rates prediction}
\begin{algorithmic}
[1]
\Statex \textbf{Input:} ``Lookback'' window size $W$, Day ahead to predict $D$
\State Wait $W$ days to fill window.
\State Create model $f^W.init()$ \Comment $j = W$
\State Observe instance $\grave{\beta}^W = \{\beta^W, \beta^{W-1}, ..., \beta^1\}$
\State Predict $\hat{\beta}^{W+1} = f^W.predict(\grave{\beta}^W)$
\For{each day $j \in [W + 1, W + D -1)$} \Comment Only predictions these days
\State Observe ground truth $\beta^j$
\State Create instance $\grave{\beta}^j = \{\beta^j, \beta^{j-1}, .., \beta^{j-W+1}\}$
\State Predict $\hat{\beta}^{j + D} = f^W.predict(\grave{\beta}^j)$ \Comment $f^W$ hasn't been updated yet
\EndFor
\For{each day $j \in [W + D, \infty)$} \Comment Predictions and training
\State Observe ground truth $\beta^j$
\State Incremental training $f^j = f^{j-1}.train((\grave{\beta}^{j-D}, \beta^j))$ \Comment As in Eq (\ref{eq:training})
\State Create instance $\grave{\beta}^j = \{\beta^j, \beta^{j-1}, .., \beta^{j-W+1}\}$
\State Predict $\hat{\beta}^{j + D} = f^j.predict(\grave{\beta}^j)$
\EndFor
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2401.06629" | "2401.06629.tar.gz" | "2024-01-12" | {
"title": "pandemic infection forecasting through compartmental model and learning-based approaches",
"id": "2401.06629",
"abstract": "the emergence and spread of deadly pandemics has repeatedly occurred throughout history, causing widespread infections and loss of life. the rapid spread of pandemics have made governments across the world adopt a range of actions, including non-pharmaceutical measures to contain its impact. however, the dynamic nature of pandemics makes selecting intervention strategies challenging. hence, the development of suitable monitoring and forecasting tools for tracking infected cases is crucial for designing and implementing effective measures. motivated by this, we present a hybrid pandemic infection forecasting methodology that integrates compartmental model and learning-based approaches. in particular, we develop a compartmental model that includes time-varying infection rates, which are the key parameters that determine the pandemic's evolution. to identify the time-dependent infection rates, we establish a hybrid methodology that combines the developed compartmental model and tools from optimization and neural networks. specifically, the proposed methodology estimates the infection rates by fitting the model to available data, regarding the covid-19 pandemic in cyprus, and then predicting their future values through either a) extrapolation, or b) feeding them to neural networks. the developed approach exhibits strong accuracy in predicting infections seven days in advance, achieving low average percentage errors both using the extrapolation (9.90%) and neural network (5.04%) approaches.",
"categories": "q-bio.pe math.oc q-bio.qm",
"doi": "",
"created": "2024-01-12",
"updated": "",
"authors": [
"marianna karapitta",
"andreas kasis",
"charithea stylianides",
"kleanthis malialis",
"panayiotis kolios"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.06629"
} | "2024-03-15T07:35:55.770135" | {
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} | [] | "algorithm" | "d94ccb53-8f69-4701-a9d6-76e2b9b651d1" | 1169 | hard |
|
\begin{algorithm}\small
\caption{Approximating $\hat\sigma^2$}
\algorithmicrequire positive integers $N_\sigma$ and $N_\sigma^\prime$
\begin{algorithmic}[1]
\For{$l$ in 1 to $N_\sigma$}
\State draw subsample $\{ \iota_1,\dots, \iota_{n - D_\sigma} \}$ of size $n - D_\sigma$ without replacement from $\{ 1, \dots, n \}$
\For{$l^\prime$ in 1 to $N_\sigma^\prime$}
\State draw subsample $\{ \iota_1^\ast,\dots, \iota_{s}^\ast \}$ of size $s$ without replacement from $\{ \iota_1,\dots, \iota_{n - D_\sigma} \}$
\State apply Algorithm 1 to $\{ \iota_1^\ast,\dots, \iota_{s}^\ast \}$ and record $\mathcal{L}^{\ast}_{(l^\prime)}$
\EndFor
\State compute $\{ \tilde{\omega}_1 (x), \dots ,\tilde{\omega}_n (x) \}$ by applying Eq.\ (\ref{eq:wei}) to $\{\mathcal{L}^{\ast}_{(1)} ,\dots, \mathcal{L}^{\ast}_{(N_\sigma^\prime)} \}$
\State $\hat{\boldsymbol{\mu}}_{(l)} \gets \text{Average}( \{ \tilde{\omega}_1 (x)\boldsymbol{\phi} (y_1) , \dots ,\tilde{\omega}_n (x) \boldsymbol{\phi} (y_n) \} )$
\EndFor
\State $\hat{\sigma}^{2\ast} \gets (n - D_\sigma) [\hat{\mathcal{T}}_x (y) \times \text{CovarianceMatrix}( \{ \hat{\boldsymbol{\mu}}_{(1)},\dots, \hat{\boldsymbol{\mu}}_{(N_\sigma)}\} ) \times \hat{\mathcal{T}}_x (y)^\tau ]/ D_\sigma$.
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\small
\caption{Approximating $\hat\sigma^2$}
\algorithmicrequire positive integers $N_\sigma$ and $N_\sigma^\prime$
\begin{algorithmic}
[1]
\For{$l$ in 1 to $N_\sigma$}
\State draw subsample $\{ \iota_1,\dots, \iota_{n - D_\sigma} \}$ of size $n - D_\sigma$ without replacement from $\{ 1, \dots, n \}$
\For{$l^\prime$ in 1 to $N_\sigma^\prime$}
\State draw subsample $\{ \iota_1^\ast,\dots, \iota_{s}^\ast \}$ of size $s$ without replacement from $\{ \iota_1,\dots, \iota_{n - D_\sigma} \}$
\State apply Algorithm 1 to $\{ \iota_1^\ast,\dots, \iota_{s}^\ast \}$ and record $\mathcal{L}^{\ast}_{(l^\prime)}$
\EndFor
\State compute $\{ \tilde{\omega}_1 (x), \dots ,\tilde{\omega}_n (x) \}$ by applying Eq.\ (\ref{eq:wei}) to $\{\mathcal{L}^{\ast}_{(1)} ,\dots, \mathcal{L}^{\ast}_{(N_\sigma^\prime)} \}$
\State $\hat{\boldsymbol{\mu}}_{(l)} \gets \text{Average}( \{ \tilde{\omega}_1 (x)\boldsymbol{\phi} (y_1) , \dots ,\tilde{\omega}_n (x) \boldsymbol{\phi} (y_n) \} )$
\EndFor
\State $\hat{\sigma}^{2\ast} \gets (n - D_\sigma) [\hat{\mathcal{T}}_x (y) \times \text{CovarianceMatrix}( \{ \hat{\boldsymbol{\mu}}_{(1)},\dots, \hat{\boldsymbol{\mu}}_{(N_\sigma)}\} ) \times \hat{\mathcal{T}}_x (y)^\tau ]/ D_\sigma$.
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2309.13251" | "2309.13251.tar.gz" | "2024-01-10" | {
"title": "nonparametric estimation of conditional densities by generalized random forests",
"id": "2309.13251",
"abstract": "considering a continuous random variable y together with a continuous random vector x, i propose a nonparametric estimator f^(.|x) for the conditional density of y given x=x. this estimator takes the form of an exponential series whose coefficients t = (t1,...,tj) are the solution of a system of nonlinear equations that depends on an estimator of the conditional expectation e[p(y)|x=x], where p(.) is a j-dimensional vector of basis functions. a key feature is that e[p(y)|x=x] is estimated by generalized random forest (athey, tibshirani, and wager, 2019), targeting the heterogeneity of t across x. i show that f^(.|x) is uniformly consistent and asymptotically normal, while allowing j to grow to infinity. i also provide a standard error formula to construct asymptotically valid confidence intervals. results from monte carlo experiments and an empirical illustration are provided.",
"categories": "econ.em",
"doi": "",
"created": "2023-09-23",
"updated": "2024-01-10",
"authors": [
"federico zincenko"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2309.13251"
} | "2024-03-15T06:26:55.263031" | {
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} | [] | "algorithm" | "736e8c64-df38-4b3c-9024-bc77f2a616e6" | 1265 | hard |
|
\begin{algorithm}
\caption{Variable Selection (VS) with Momentum}
\begin{algorithmic}[1]
\State \textbf{Input}: iteration index $t$, $\mathcal{D}=\{(\mathbf{x}^{i},y^{i})\}_{i=1}^{t}$, $N_{init}$, $N_{vs}$, set of important variables chosen at iteration $t-N_{vs}$, denote as $\hat{\mathbf{x}}_{ipt}$
\State \textbf{Output}: Set of important variables chosen at iteration $t$, denote as $\mathbf{x}_{ipt}$
\If{$t=N_{init}+N_{vs}$ or $\hat{\mathbf{x}}_{ipt}=\mathbf{x}$} \Comment{First time to do variable selection or $\hat{\mathbf{x}}_{ipt}$ contains all variables}
\State \Return Algorithm~\ref{alg:VS_detail}
\ElsIf{$\max_{k\in \{t-N_{vs}+1, t-N_{vs}+2, \dots, t\}}y^{k}\leq\max_{k\in \{1,\dots, t-N_{vs}\}}y^{k}$} \Comment{Inaccurate case}
\State \Return Algorithm~\ref{alg:momentum_inacc}
\Else \Comment{Accurate case}
\State \Return Algorithm~\ref{alg:momentum_acc}
\EndIf
\end{algorithmic}
\label{alg:VS_momentum}
\end{algorithm}
| \begin{algorithm}
\caption{Variable Selection (VS) with Momentum}
\begin{algorithmic}
[1]
\State \textbf{Input}: iteration index $t$, $\mathcal{D}=\{(\mathbf{x}^{i},y^{i})\}_{i=1}^{t}$, $N_{init}$, $N_{vs}$, set of important variables chosen at iteration $t-N_{vs}$, denote as $\hat{\mathbf{x}}_{ipt}$
\State \textbf{Output}: Set of important variables chosen at iteration $t$, denote as $\mathbf{x}_{ipt}$
\If{$t=N_{init}+N_{vs}$ or $\hat{\mathbf{x}}_{ipt}=\mathbf{x}$} \Comment{First time to do variable selection or $\hat{\mathbf{x}}_{ipt}$ contains all variables}
\State \Return Algorithm~\ref{alg:VS_detail}
\ElsIf{$\max_{k\in \{t-N_{vs}+1, t-N_{vs}+2, \dots, t\}}y^{k}\leq\max_{k\in \{1,\dots, t-N_{vs}\}}y^{k}$} \Comment{Inaccurate case}
\State \Return Algorithm~\ref{alg:momentum_inacc}
\Else \Comment{Accurate case}
\State \Return Algorithm~\ref{alg:momentum_acc}
\EndIf
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2109.09264" | "2109.09264.tar.gz" | "2024-02-12" | {
"title": "computationally efficient high-dimensional bayesian optimization via variable selection",
"id": "2109.09264",
"abstract": "bayesian optimization (bo) is a method for globally optimizing black-box functions. while bo has been successfully applied to many scenarios, developing effective bo algorithms that scale to functions with high-dimensional domains is still a challenge. optimizing such functions by vanilla bo is extremely time-consuming. alternative strategies for high-dimensional bo that are based on the idea of embedding the high-dimensional space to the one with low dimension are sensitive to the choice of the embedding dimension, which needs to be pre-specified. we develop a new computationally efficient high-dimensional bo method that exploits variable selection. our method is able to automatically learn axis-aligned sub-spaces, i.e. spaces containing selected variables, without the demand of any pre-specified hyperparameters. we theoretically analyze the computational complexity of our algorithm and derive the regret bound. we empirically show the efficacy of our method on several synthetic and real problems.",
"categories": "cs.lg stat.ml",
"doi": "",
"created": "2021-09-19",
"updated": "2024-02-12",
"authors": [
"yihang shen",
"carl kingsford"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2109.09264"
} | "2024-03-15T06:24:09.021286" | {
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} | [] | "algorithm" | "4a353026-90d1-45ab-b777-07b23417da66" | 913 | medium |
|
\begin{algorithmic}[1]
\State{$ t \gets 1; \ \textbf{m}_{1} \gets \mathbf{1}_{\bar{C}}; \ \alpha \gets 1 $ \hfill \# Step t = 1}\label{start_t1:ln}
\For{$ e \gets 1,...,E $ }
\State{FBP() \hfill \# Algorithm~\ref{FBP:alg}}
\EndFor
\State{$ \bar{\textbf{s}}_{1} \gets \text{mean of} \ \tilde{s} \ \text{across data} $ }\label{first_sample_independent_score:ln}\label{end_t1:ln}
\For{$ t \gets 2,...,T $} \hfill \# Steps $ t \geq 2 $
\State{\hfill \# Phase 1}
\State{$ \bar{\textbf{s}}_t \gets \bar{\textbf{s}}_{t-1}; \ \alpha \gets \frac{1}{2}; \ \textbf{m}_{t} \gets \textbf{m}_{t-1} $ }
\For{$ e \gets 1,...,E_{1} $}
\State{FBP()}
\EndFor
\State{$ \bar{\textbf{s}} \gets \text{mean of} \ \tilde{s} \ \text{on data} $ \hfill \# Phase 2}
\State{$ \bar{\textbf{s}}_{t} \gets \frac{1}{2}(\bar{\textbf{s}}_{t} + \bar{\textbf{s}}) $ }\label{update_sample_independent_score:ln}
\For{$ e \gets E_{1}+1,...,E_{2} $}
\State{$ \alpha \gets \max \{\alpha - \frac{1}{2(E_{2}-E_{1})},0 \} $} \label{modify_alpha:ln}
\State{FBP()}
\EndFor
\State{\# Indices that sort an array; \hfill Phase 3}
\State{$ R = \text{argsort} \{ \bar{\textbf{s}}_{t}[i] : \textbf{m}_{t}[i] = 1 \} $}\label{argsort_features:ln}
\State{$ D_{t} \gets \{R[0],...,R[C_{t-1}-C_{t}] \} $}\label{select_set:ln}
\For{$ e \gets E_{2} + 1,...,E_{3} $}
\State{$ \textbf{m}_{t} \gets \max \{\textbf{m}_{t} - \frac{\mathbb{I}[i]_{i \in D_{t}} }{E_{3} - E_{2}}, \textbf{0}_{\bar{C}} \} $}\label{modify_mask:ln}
\State{FBP()}
\EndFor
\For{$ e \gets E_{3}+1,...,E $} \hfill \# Phase 4
\State{FBP()}
\EndFor
\State{Cache $ \mathcal{T}_{t} $, $ \textbf{m}_{t},\bar{\textbf{s}}_{t} $ for equation~\ref{Outer_Loop:eq}}
\EndFor
\end{algorithmic}
| \begin{algorithmic}
[1]
\State{$ t \gets 1; \ \textbf{m}_{1} \gets \mathbf{1}_{\bar{C}}; \ \alpha \gets 1 $ \hfill \# Step t = 1}\For{$ e \gets 1,...,E $ }
\State{FBP() \hfill \# Algorithm~\ref{FBP:alg}}
\EndFor
\State{$ \bar{\textbf{s}}_{1} \gets \text{mean of} \ \tilde{s} \ \text{across data} $ }\For{$ t \gets 2,...,T $} \hfill \# Steps $ t \geq 2 $
\State{\hfill \# Phase 1}
\State{$ \bar{\textbf{s}}_t \gets \bar{\textbf{s}}_{t-1}; \ \alpha \gets \frac{1}{2}; \ \textbf{m}_{t} \gets \textbf{m}_{t-1} $ }
\For{$ e \gets 1,...,E_{1} $}
\State{FBP()}
\EndFor
\State{$ \bar{\textbf{s}} \gets \text{mean of} \ \tilde{s} \ \text{on data} $ \hfill \# Phase 2}
\State{$ \bar{\textbf{s}}_{t} \gets \frac{1}{2}(\bar{\textbf{s}}_{t} + \bar{\textbf{s}}) $ } \For{$ e \gets E_{1}+1,...,E_{2} $}
\State{$ \alpha \gets \max \{\alpha - \frac{1}{2(E_{2}-E_{1})},0 \} $} \State{FBP()}
\EndFor
\State{\# Indices that sort an array; \hfill Phase 3}
\State{$ R = \text{argsort} \{ \bar{\textbf{s}}_{t}[i] : \textbf{m}_{t}[i] = 1 \} $} \State{$ D_{t} \gets \{R[0],...,R[C_{t-1}-C_{t}] \} $} \For{$ e \gets E_{2} + 1,...,E_{3} $}
\State{$ \textbf{m}_{t} \gets \max \{\textbf{m}_{t} - \frac{\mathbb{I}[i]_{i \in D_{t}} }{E_{3} - E_{2}}, \textbf{0}_{\bar{C}} \} $} \State{FBP()}
\EndFor
\For{$ e \gets E_{3}+1,...,E $} \hfill \# Phase 4
\State{FBP()}
\EndFor
\State{Cache $ \mathcal{T}_{t} $, $ \textbf{m}_{t},\bar{\textbf{s}}_{t} $ for equation~\ref{Outer_Loop:eq}}
\EndFor
\end{algorithmic} | "https://arxiv.org/src/2210.06891" | "2210.06891.tar.gz" | "2024-02-23" | {
"title": "experimental design for multi-channel imaging via task-driven feature selection",
"id": "2210.06891",
"abstract": "this paper presents a data-driven, task-specific paradigm for experimental design, to shorten acquisition time, reduce costs, and accelerate the deployment of imaging devices. current approaches in experimental design focus on model-parameter estimation and require specification of a particular model, whereas in imaging, other tasks may drive the design. furthermore, such approaches often lead to intractable optimization problems in real-world imaging applications. here we present a new paradigm for experimental design that simultaneously optimizes the design (set of image channels) and trains a machine-learning model to execute a user-specified image-analysis task. the approach obtains data densely-sampled over the measurement space (many image channels) for a small number of acquisitions, then identifies a subset of channels of prespecified size that best supports the task. we propose a method: tadred for task-driven experimental design in imaging, to identify the most informative channel-subset whilst simultaneously training a network to execute the task given the subset. experiments demonstrate the potential of tadred in diverse imaging applications: several clinically-relevant tasks in magnetic resonance imaging; and remote sensing and physiological applications of hyperspectral imaging. results show substantial improvement over classical experimental design, two recent application-specific methods within the new paradigm, and state-of-the-art approaches in supervised feature selection. we anticipate further applications of our approach. code is available: https://github.com/sbb-gh/experimental-design-multichannel",
"categories": "cs.lg cs.ai q-bio.nc",
"doi": "",
"created": "2022-10-13",
"updated": "2024-02-23",
"authors": [
"stefano b. blumberg",
"paddy j. slator",
"daniel c. alexander"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2210.06891"
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} | [] | "algorithm" | "87804314-b74f-4ac6-ad76-024ac9b40c57" | 1473 | hard |
|
\begin{algorithm}[H]
\caption{Optimal Regress-later with Neural Networks (OPT-RLNN)}\label{alg-opt-rlnn}
\begin{algorithmic}[1]
\State Setup the target portfolio information (with strike $K$ and exercise points $\{t_0, t_1, t_2, \ldots, t_M\}$) and time-zero market data ($S_0$, $r$, $\sigma$)
\State Generate $S_{t_m}\left(\omega_j\right)$ for paths $j=1,\ldots,N, \, m = 0,\ldots,M$
\State $V_{t_M} \leftarrow h \left(S_{t_M}\right)$ evaluate option value for each path at $t_M$
\For{$m=M\ldots,1$}
\State Initialize $\beta_{t_m}$ as per the proposed parameter initialisation (i.e. static hedge portfolio weights and constituent option strikes) in Section \ref{Parameter Initialisation}
\State $\beta_{t_m} \leftarrow \underset{\beta} {\mathrm{argmin}} \left(\frac{1}{N} \sum_{j = 1}^{N} \frac{1}{2} \left(V_{t_m}(\mathbf{S}_{t_m}(\omega_j))-G^{\beta}\left(\mathbf{S}_{t_m}(\omega_j)\right)\right)^2\right) = \underset{W, \boldsymbol{b}} {\mathrm{argmin}} \ L(t_m; W, \boldsymbol{b})$; Fitting the network with the proposed optimisation technique in Section \ref{Optimisation Methodology}
\For{$j=1,\ldots,N$}
\State $Q_{t_{m-1}}\left(S_{t_{m-1}}(\omega_j)\right) \leftarrow \mathbb{E}\left[\tilde{G}^{\beta_{t_m}} (S_{t_m}) \mid S_{t_{m-1}} (\omega_j)\right]$, which is the continuation value evaluated using Black-Scholes pricing model
\If{$h(S_{t_{m-1}}(\omega_j)) > Q_{t_{m-1}}\left(S_{t_{m-1}}(\omega_j)\right)$}
\State$V_{t_{m-1}}(S_{t_{m-1}}(\omega_j)) \leftarrow h(S_{t_{m-1}}(\omega_j))$
\Else
\State $V_{t_{m-1}}(S_{t_{m-1}}(\omega_j)) \leftarrow Q_{t_{m-1}}\left(S_{t_{m-1}}(\omega_j)\right)$
\EndIf
\EndFor
\EndFor
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[H]
\caption{Optimal Regress-later with Neural Networks (OPT-RLNN)}\begin{algorithmic}
[1]
\State Setup the target portfolio information (with strike $K$ and exercise points $\{t_0, t_1, t_2, \ldots, t_M\}$) and time-zero market data ($S_0$, $r$, $\sigma$)
\State Generate $S_{t_m}\left(\omega_j\right)$ for paths $j=1,\ldots,N, \, m = 0,\ldots,M$
\State $V_{t_M} \leftarrow h \left(S_{t_M}\right)$ evaluate option value for each path at $t_M$
\For{$m=M\ldots,1$}
\State Initialize $\beta_{t_m}$ as per the proposed parameter initialisation (i.e. static hedge portfolio weights and constituent option strikes) in Section \ref{Parameter Initialisation}
\State $\beta_{t_m} \leftarrow \underset{\beta} {\mathrm{argmin}} \left(\frac{1}{N} \sum_{j = 1}^{N} \frac{1}{2} \left(V_{t_m}(\mathbf{S}_{t_m}(\omega_j))-G^{\beta}\left(\mathbf{S}_{t_m}(\omega_j)\right)\right)^2\right) = \underset{W, \boldsymbol{b}} {\mathrm{argmin}} \ L(t_m; W, \boldsymbol{b})$; Fitting the network with the proposed optimisation technique in Section \ref{Optimisation Methodology}
\For{$j=1,\ldots,N$}
\State $Q_{t_{m-1}}\left(S_{t_{m-1}}(\omega_j)\right) \leftarrow \mathbb{E}\left[\tilde{G}^{\beta_{t_m}} (S_{t_m}) \mid S_{t_{m-1}} (\omega_j)\right]$, which is the continuation value evaluated using Black-Scholes pricing model
\If{$h(S_{t_{m-1}}(\omega_j)) > Q_{t_{m-1}}\left(S_{t_{m-1}}(\omega_j)\right)$}
\State$V_{t_{m-1}}(S_{t_{m-1}}(\omega_j)) \leftarrow h(S_{t_{m-1}}(\omega_j))$
\Else
\State $V_{t_{m-1}}(S_{t_{m-1}}(\omega_j)) \leftarrow Q_{t_{m-1}}\left(S_{t_{m-1}}(\omega_j)\right)$
\EndIf
\EndFor
\EndFor
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2402.15936" | "2402.15936.tar.gz" | "2024-02-24" | {
"title": "optimizing neural networks for bermudan option pricing: convergence acceleration, future exposure evaluation and interpolation in counterparty credit risk",
"id": "2402.15936",
"abstract": "this paper presents a monte-carlo-based artificial neural network framework for pricing bermudan options, offering several notable advantages. these advantages encompass the efficient static hedging of the target bermudan option and the effective generation of exposure profiles for risk management. we also introduce a novel optimisation algorithm designed to expedite the convergence of the neural network framework proposed by lokeshwar et al. (2022) supported by a comprehensive error convergence analysis. we conduct an extensive comparative analysis of the present value (pv) distribution under markovian and no-arbitrage assumptions. we compare the proposed neural network model in conjunction with the approach initially introduced by longstaff and schwartz (2001) and benchmark it against the cos model, the pricing model pioneered by fang and oosterlee (2009), across all bermudan exercise time points. additionally, we evaluate exposure profiles, including expected exposure and potential future exposure, generated by our proposed model and the longstaff-schwartz model, comparing them against the cos model. we also derive exposure profiles at finer non-standard grid points or risk horizons using the proposed approach, juxtaposed with the longstaff schwartz method with linear interpolation and benchmark against the cos method. in addition, we explore the effectiveness of various interpolation schemes within the context of the longstaff-schwartz method for generating exposures at finer grid horizons.",
"categories": "q-fin.cp q-fin.pr q-fin.rm",
"doi": "",
"created": "2024-02-24",
"updated": "",
"authors": [
"vikranth lokeshwar dhandapani",
"shashi jain"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.15936"
} | "2024-03-15T02:36:57.519067" | {
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} | [] | "algorithm" | "bfdafd59-4b11-4acc-9e7b-2917dca5f767" | 1643 | hard |
|
\begin{algorithm}
\caption{The individual stock return fitting step in training GF-AGRU (for stock $i$).} \label{algorithm_i}
\textbf{Hyperparameters}: the same as in Algorithm \ref{algorithm_N}.\\
\textbf{Input}: training data including the features $F_{<t}$ and the label $Y_i^t$. $F_{<t}$ is constructed by concatenating historical daily market returns and historical daily stock returns (both in the form of Equation \eqref{eqn:features_Ft}), and $Y_i^t$ is the future one-month stock return. The training set collects data points on a daily frequency. \\
\textbf{Initialize}: tail parameters $\nu^M_i=\{u^M_i,v^M_i\},\nu_i=\{u_i,v_i\}$ and the Attention-GRU network parameters $\theta_{\text{AGRU}}$ (a different Attention-GRU from that in Algorithm \ref{algorithm_N} and those for other stocks).
\begin{algorithmic}[1]
\For{$b=1:N_m$}
\State (TV-AGRU)
\State Fix $\{\nu^M_i,\nu_i\}$ given by FIX-OPTIM.
\For{$j=1:N_{\text{tv}}$}
\State Compute $\Theta^t_i = \{\alpha^t_i,\beta^t_i,\gamma^t_i\} = \text{AGRU}(F_{<t};\theta_{\text{AGRU}})$.
\State Compute the quasi-NLL loss $L=\sum_{t=1}^S (-\ell_{i|M}^t)$ (with known $\tilde{Z}_M^t$ obtained from Algorithm \ref{algorithm_N}, see Equation \eqref{latentstock}) and its partial derivatives with respect to $\theta_{\text{AGRU}}$.
\State Update: $\theta_{\text{AGRU}} \gets \text{RMSProp}(\theta_{\text{AGRU}},\nabla_{\theta_{\text{AGRU}}} L,l_{\text{tv}})$.
\EndFor
\State (FIX-OPTIM)
\State Fix $\theta_{\text{AGRU}}$ given by TV-AGRU.
\State Compute $\Theta^t_i = \{\alpha^t_i,\beta^t_i,\gamma^t_i\} = \text{AGRU}(F_{<t};\theta_{\text{AGRU}})$ and fix $\Theta^t_i$.
\For{$j=1:N_{\text{fix}}$}
\State Compute the quasi-NLL loss $L=\sum_{t=1}^S (-\ell_{i|M}^t)$ (with known $\tilde{Z}_M^t$ obtained from Algorithm \ref{algorithm_N}, see Equation \eqref{latentstock}) and its partial derivatives with respect to $\{\nu^M_i,\nu_i\}$.
\State Update: $\{\nu^M_i,\nu_i\} \gets \text{RMSProp}(\{\nu^M_i,\nu_i\},\nabla_{\{\nu^M_i,\nu_i\}} L,l_{\text{fix}})$.
\EndFor
\EndFor
\end{algorithmic}
\textbf{Output}: learnable parameters $\{\nu^M_i,\nu_i\}$ and $\theta_{\text{AGRU}}$; the time-varying model parameters $\Theta^t_i$.
\end{algorithm}
| \begin{algorithm}
\caption{The individual stock return fitting step in training GF-AGRU (for stock $i$).} \textbf{Hyperparameters}: the same as in Algorithm \ref{algorithm_N}.\\
\textbf{Input}: training data including the features $F_{<t}$ and the label $Y_i^t$. $F_{<t}$ is constructed by concatenating historical daily market returns and historical daily stock returns (both in the form of Equation \eqref{eqn:features_Ft}), and $Y_i^t$ is the future one-month stock return. The training set collects data points on a daily frequency. \\
\textbf{Initialize}: tail parameters $\nu^M_i=\{u^M_i,v^M_i\},\nu_i=\{u_i,v_i\}$ and the Attention-GRU network parameters $\theta_{\text{AGRU}}$ (a different Attention-GRU from that in Algorithm \ref{algorithm_N} and those for other stocks).
\begin{algorithmic}
[1]
\For{$b=1:N_m$}
\State (TV-AGRU)
\State Fix $\{\nu^M_i,\nu_i\}$ given by FIX-OPTIM.
\For{$j=1:N_{\text{tv}}$}
\State Compute $\Theta^t_i = \{\alpha^t_i,\beta^t_i,\gamma^t_i\} = \text{AGRU}(F_{<t};\theta_{\text{AGRU}})$.
\State Compute the quasi-NLL loss $L=\sum_{t=1}^S (-\ell_{i|M}^t)$ (with known $\tilde{Z}_M^t$ obtained from Algorithm \ref{algorithm_N}, see Equation \eqref{latentstock}) and its partial derivatives with respect to $\theta_{\text{AGRU}}$.
\State Update: $\theta_{\text{AGRU}} \gets \text{RMSProp}(\theta_{\text{AGRU}},\nabla_{\theta_{\text{AGRU}}} L,l_{\text{tv}})$.
\EndFor
\State (FIX-OPTIM)
\State Fix $\theta_{\text{AGRU}}$ given by TV-AGRU.
\State Compute $\Theta^t_i = \{\alpha^t_i,\beta^t_i,\gamma^t_i\} = \text{AGRU}(F_{<t};\theta_{\text{AGRU}})$ and fix $\Theta^t_i$.
\For{$j=1:N_{\text{fix}}$}
\State Compute the quasi-NLL loss $L=\sum_{t=1}^S (-\ell_{i|M}^t)$ (with known $\tilde{Z}_M^t$ obtained from Algorithm \ref{algorithm_N}, see Equation \eqref{latentstock}) and its partial derivatives with respect to $\{\nu^M_i,\nu_i\}$.
\State Update: $\{\nu^M_i,\nu_i\} \gets \text{RMSProp}(\{\nu^M_i,\nu_i\},\nabla_{\{\nu^M_i,\nu_i\}} L,l_{\text{fix}})$.
\EndFor
\EndFor
\end{algorithmic}
\textbf{Output}: learnable parameters $\{\nu^M_i,\nu_i\}$ and $\theta_{\text{AGRU}}$; the time-varying model parameters $\Theta^t_i$.
\end{algorithm} | "https://arxiv.org/src/2301.07318" | "2301.07318.tar.gz" | "2024-01-16" | {
"title": "dynamic cvar portfolio construction with attention-powered generative factor learning",
"id": "2301.07318",
"abstract": "the dynamic portfolio construction problem requires dynamic modeling of the joint distribution of multivariate stock returns. to achieve this, we propose a dynamic generative factor model which uses random variable transformation as an implicit way of distribution modeling and relies on the attention-gru network for dynamic learning and forecasting. the proposed model captures the dynamic dependence among multivariate stock returns, especially focusing on the tail-side properties. we also propose a two-step iterative algorithm to train the model and then predict the time-varying model parameters, including the time-invariant tail parameters. at each investment date, we can easily simulate new samples from the learned generative model, and we further perform cvar portfolio optimization with the simulated samples to form a dynamic portfolio strategy. the numerical experiment on stock data shows that our model leads to wiser investments that promise higher reward-risk ratios and present lower tail risks.",
"categories": "q-fin.pm",
"doi": "",
"created": "2023-01-18",
"updated": "2024-01-16",
"authors": [
"chuting sun",
"qi wu",
"xing yan"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2301.07318"
} | "2024-03-15T06:00:53.804038" | {
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} | [] | "algorithm" | "61c70b9d-2569-4597-a145-631b9b0bd5f6" | 2171 | hard |
|
\begin{algorithmic}
\Require $L,\ell,\gamma_k$
\Ensure $\theta_k, \gamma_{k+1}$
\State Solve $L\theta_k^2+(\gamma_k-\ell)\theta_k-\gamma_k=0$ via
the quadratic formula for the positive root $\theta_k$.
\State Let $\gamma_{k+1}:=(1-\theta_k)\gamma_k+\theta_k\ell$
\end{algorithmic}
| \begin{algorithmic}
\Require $L,\ell,\gamma_k$
\Ensure $\theta_k, \gamma_{k+1}$
\State Solve $L\theta_k^2+(\gamma_k-\ell)\theta_k-\gamma_k=0$ via
the quadratic formula for the positive root $\theta_k$.
\State Let $\gamma_{k+1}:=(1-\theta_k)\gamma_k+\theta_k\ell$
\end{algorithmic} | "https://arxiv.org/src/2111.11613" | "2111.11613.tar.gz" | "2024-01-03" | {
"title": "nonlinear conjugate gradient for smooth convex functions",
"id": "2111.11613",
"abstract": "the method of nonlinear conjugate gradients (ncg) is widely used in practice for unconstrained optimization, but it satisfies weak complexity bounds at best when applied to smooth convex functions. in contrast, nesterov's accelerated gradient (ag) method is optimal up to constant factors for this class. however, when specialized to quadratic function, conjugate gradient is optimal in a strong sense among function-gradient methods. therefore, there is seemingly a gap in the menu of available algorithms: ncg, the optimal algorithm for quadratic functions that also exhibits good practical performance for general functions, has poor complexity bounds compared to ag. we propose an ncg method called c+ag (\"conjugate plus accelerated gradient\") to close this gap, that is, it is optimal for quadratic functions and still satisfies the best possible complexity bound for more general smooth convex functions. it takes conjugate gradient steps until insufficient progress is made, at which time it switches to accelerated gradient steps, and later retries conjugate gradient. the proposed method has the following theoretical properties: (i) it is identical to linear conjugate gradient (and hence terminates finitely) if the objective function is quadratic; (ii) its running-time bound is $o(\\eps^{-1/2})$ gradient evaluations for an $l$-smooth convex function, where $\\eps$ is the desired residual reduction, (iii) its running-time bound is $o(\\sqrt{l/\\ell}\\ln(1/\\eps))$ if the function is both $l$-smooth and $\\ell$-strongly convex. in computational tests, the function-gradient evaluation count for the c+ag method typically behaves as whichever is better of ag or classical ncg. in some test cases it outperforms both.",
"categories": "math.oc",
"doi": "",
"created": "2021-11-22",
"updated": "2024-01-03",
"authors": [
"sahar karimi",
"stephen vavasis"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2111.11613"
} | "2024-03-15T07:02:13.702050" | {
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} | [] | "algorithm" | "ab9e74ea-091f-49c0-b47a-a97fd4a2ad96" | 280 | easy |
|
\begin{algorithm}
\caption{MAP-EM algorithm for the computation of $\hat{\mathbf{c}}$ in \eqref{computec}}
\begin{algorithmic}[1]
\State Select an initial estimate $\hat{\mathbf{c}}^{(1)}$, a maximum number of iterations $M_{\textnormal{iter}}$, and a tolerance factor $\epsilon$
\State $j\gets 1$, $\textnormal{flag}\gets 1$
\While{$j\leq M_{\textnormal{iter}}$ and $\textnormal{flag}=1$}
\State \textbf{E-step}: Compute the expectation
\begin{equation}
\label{qfunction}
Q(\mathbf{c},\hspace{-0.02cm}\hat{\mathbf{c}}^{(j)}\hspace{-0.01cm}) \hspace{-0.04cm}= \hspace{-0.04cm}\mathbb{E}\hspace{-0.03cm}\left\{ \log \textnormal{p}(\mathbf{z}_{1:N}\hspace{-0.02cm},\hspace{-0.02cm}\mathcal{Y}_{1:N}|\mathbf{c}\hspace{-0.02cm})|\mathcal{Y}_{1:N}\hspace{-0.02cm},\hspace{-0.02cm}\hat{\mathbf{c}}^{(j)}\hspace{-0.04cm}\right\}\hspace{-0.03cm}.\hspace{-0.1cm}
\end{equation}
\State \textbf{M-step}: Solve the optimization problem
\begin{equation}
\label{mstep}
\hat{\mathbf{c}}^{(j+1)} = \underset{\mathbf{c}\in \mathbb{R}^N}{\arg \max} \left( Q(\mathbf{c},\hat{\mathbf{c}}^{(j)}) -\frac{\gamma\mathbf{c}^{\top}\mathbf{Kc}}{2} \right).
\end{equation}
\If{$\dfrac{\|\hat{\mathbf{c}}^{(j+1)}-\hat{\mathbf{c}}^{(j)}\|_2}{\|\hat{\mathbf{c}}^{(j)}\|_2}<\epsilon$} \State $\textnormal{flag} \gets 0$
\EndIf
\State $j \gets j+1$
\EndWhile
\end{algorithmic}
\label{algorithm1}
\end{algorithm}
| \begin{algorithm}
\caption{MAP-EM algorithm for the computation of $\hat{\mathbf{c}}$ in \eqref{computec}}
\begin{algorithmic}
[1]
\State Select an initial estimate $\hat{\mathbf{c}}^{(1)}$, a maximum number of iterations $M_{\textnormal{iter}}$, and a tolerance factor $\epsilon$
\State $j\gets 1$, $\textnormal{flag}\gets 1$
\While{$j\leq M_{\textnormal{iter}}$ and $\textnormal{flag}=1$}
\State \textbf{E-step}: Compute the expectation
\begin{equation*}
Q(\mathbf{c},\hspace{-0.02cm}\hat{\mathbf{c}}^{(j)}\hspace{-0.01cm}) \hspace{-0.04cm}= \hspace{-0.04cm}\mathbb{E}\hspace{-0.03cm}\left\{ \log \textnormal{p}(\mathbf{z}_{1:N}\hspace{-0.02cm},\hspace{-0.02cm}\mathcal{Y}_{1:N}|\mathbf{c}\hspace{-0.02cm})|\mathcal{Y}_{1:N}\hspace{-0.02cm},\hspace{-0.02cm}\hat{\mathbf{c}}^{(j)}\hspace{-0.04cm}\right\}\hspace{-0.03cm}.\hspace{-0.1cm}
\end{equation*}
\State \textbf{M-step}: Solve the optimization problem
\begin{equation*}
\hat{\mathbf{c}}^{(j+1)} = \underset{\mathbf{c}\in \mathbb{R}^N}{\arg \max} \left( Q(\mathbf{c},\hat{\mathbf{c}}^{(j)}) -\frac{\gamma\mathbf{c}^{\top}\mathbf{Kc}}{2} \right).
\end{equation*}
\If{$\dfrac{\|\hat{\mathbf{c}}^{(j+1)}-\hat{\mathbf{c}}^{(j)}\|_2}{\|\hat{\mathbf{c}}^{(j)}\|_2}<\epsilon$} \State $\textnormal{flag} \gets 0$
\EndIf
\State $j \gets j+1$
\EndWhile
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2303.06045" | "2303.06045.tar.gz" | "2024-02-23" | {
"title": "kernel-based identification using lebesgue-sampled data",
"id": "2303.06045",
"abstract": "sampling in control applications is increasingly done non-equidistantly in time. this includes applications in motion control, networked control, resource-aware control, and event-based control. some of these applications, like the ones where displacement is tracked using incremental encoders, are driven by signals that are only measured when their values cross fixed thresholds in the amplitude domain. this paper introduces a non-parametric estimator of the impulse response and transfer function of continuous-time systems based on such amplitude-equidistant sampling strategy, known as lebesgue sampling. to this end, kernel methods are developed to formulate an algorithm that adequately takes into account the bounded output uncertainty between the event timestamps, which ultimately leads to more accurate models and more efficient output sampling compared to the equidistantly-sampled kernel-based approach. the efficacy of our proposed method is demonstrated through a mass-spring damper example with encoder measurements and extensive monte carlo simulation studies on system benchmarks.",
"categories": "eess.sy cs.sy",
"doi": "",
"created": "2023-03-10",
"updated": "2024-02-23",
"authors": [
"rodrigo a. gonz\u00e1lez",
"koen tiels",
"tom oomen"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2303.06045"
} | "2024-03-15T03:38:24.648127" | {
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} | [] | "algorithm" | "b83c2725-73c7-4a20-aaee-e87c21eff5ce" | 1334 | hard |
|
\begin{algorithm}[H]
\caption{Approximate Minimal Sub-Cover}
\label{alg:AMSC}
\begin{algorithmic}[1]
\State Set $G_\text{now} = \vec{G}(C_i)$.
\While{$G_\text{now}$ has at least one vertex}
\State Add the vertex $v^*$ with the largest out-degree in $G_\text{now}$ and its corresponding radius to the dominating set $C_i^*$.
\State Remove $v^*$ and its neighbors from $G_\text{now}$.
\EndWhile
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[H]
\caption{Approximate Minimal Sub-Cover}
\begin{algorithmic}
[1]
\State Set $G_\text{now} = \vec{G}(C_i)$.
\While{$G_\text{now}$ has at least one vertex}
\State Add the vertex $v^*$ with the largest out-degree in $G_\text{now}$ and its corresponding radius to the dominating set $C_i^*$.
\State Remove $v^*$ and its neighbors from $G_\text{now}$.
\EndWhile
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2301.09734" | "2301.09734.tar.gz" | "2024-02-08" | {
"title": "topological learning in multi-class data sets",
"id": "2301.09734",
"abstract": "we specialize techniques from topological data analysis to the problem of characterizing the topological complexity (as defined in the body of the paper) of a multi-class data set. as a by-product, a topological classifier is defined that uses an open sub-covering of the data set. this sub-covering can be used to construct a simplicial complex whose topological features (e.g., betti numbers) provide information about the classification problem. we use these topological constructs to study the impact of topological complexity on learning in feedforward deep neural networks (dnns). we hypothesize that topological complexity is negatively correlated with the ability of a fully connected feedforward deep neural network to learn to classify data correctly. we evaluate our topological classification algorithm on multiple constructed and open source data sets. we also validate our hypothesis regarding the relationship between topological complexity and learning in dnn's on multiple data sets.",
"categories": "cs.lg physics.data-an",
"doi": "",
"created": "2023-01-23",
"updated": "2024-02-08",
"authors": [
"christopher griffin",
"trevor karn",
"benjamin apple"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2301.09734"
} | "2024-03-15T07:16:13.009881" | {
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} | [] | "algorithm" | "84df6c7b-73a3-4b5c-8522-effeda62a386" | 411 | easy |
|
\begin{algorithm}[H]
\centering
\small
\caption{SNN Index}\label{algo:index}
\begin{algorithmic}[1]
\State \textbf{Input:} Data matrix $P=[p_1,p_2,\ldots,p_n]^T \in \mathbb{R}^{n \times d}$
\State Compute $\mu := \mathrm{mean}(\{p_j\})$
\State Compute the mean-centered matrix $X$ with rows $x_i:= p_i - \mu$
\State Compute the singular value decomposition of $X=U\Sigma V^T$
\State Compute the sorting keys $\alpha_i = x_i^T v_1$ for $i=1,2,\ldots,n$
\State Sort data points $X$ such that $\alpha_1\leq \alpha_2\leq \cdots\leq \alpha_n$
\State Compute $\overline{x_i} = (x_i^T x_i)/2$ for $i=1,2,\ldots,n$
\State \textbf{Return:} $\mu$, $X$, $v_1$, $[\alpha_i]$, $[\overline{x_i}]$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[H]
\centering
\small
\caption{SNN Index} \begin{algorithmic}
[1]
\State \textbf{Input:} Data matrix $P=[p_1,p_2,\ldots,p_n]^T \in \mathbb{R}^{n \times d}$
\State Compute $\mu := \mathrm{mean}(\{p_j\})$
\State Compute the mean-centered matrix $X$ with rows $x_i:= p_i - \mu$
\State Compute the singular value decomposition of $X=U\Sigma V^T$
\State Compute the sorting keys $\alpha_i = x_i^T v_1$ for $i=1,2,\ldots,n$
\State Sort data points $X$ such that $\alpha_1\leq \alpha_2\leq \cdots\leq \alpha_n$
\State Compute $\overline{x_i} = (x_i^T x_i)/2$ for $i=1,2,\ldots,n$
\State \textbf{Return:} $\mu$, $X$, $v_1$, $[\alpha_i]$, $[\overline{x_i}]$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2212.07679" | "2212.07679.tar.gz" | "2024-01-29" | {
"title": "fast and exact fixed-radius neighbor search based on sorting",
"id": "2212.07679",
"abstract": "fixed-radius near neighbor search is a fundamental data operation that retrieves all data points within a user-specified distance to a query point. there are efficient algorithms that can provide fast approximate query responses, but they often have a very compute-intensive indexing phase and require careful parameter tuning. therefore, exact brute force and tree-based search methods are still widely used. here we propose a new fixed-radius near neighbor search method, called snn, that significantly improves over brute force and tree-based methods in terms of index and query time, provably returns exact results, and requires no parameter tuning. snn exploits a sorting of the data points by their first principal component to prune the query search space. further speedup is gained from an efficient implementation using high-level basic linear algebra subprograms (blas). we provide theoretical analysis of our method and demonstrate its practical performance when used stand-alone and when applied within the dbscan clustering algorithm.",
"categories": "cs.ir cs.ds",
"doi": "",
"created": "2022-12-15",
"updated": "2024-01-29",
"authors": [
"xinye chen",
"stefan g\u00fcttel"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2212.07679"
} | "2024-03-15T08:42:59.915070" | {
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} | [] | "algorithm" | "ffa00ef9-6d6e-4f52-8d10-7662be803134" | 700 | easy |
|
\begin{algorithmic}
\Require Data \(\{t^{(i)}, \hat{\mathbf{u}}^{(i)}\}_{i=0}^N\), untrained model \(\mathbf{U}(...; \boldsymbol{\theta})\)\\
\Return Coupling strength(\(k\)), homotopy parameter decrement ratio(\(\kappa\)), number of homotopy steps(\(s\)), epochs per homotopy step(\(n_{epoch}\)), learning rate(\(\eta\))
\State \(\hat{\mathbf{u}}(t)=CubicSmoothingSpline(\{t^{(i)}, \hat{\mathbf{u}}^{(i)}\}_{i=0}^N)\)
\Comment{Construct data interpolant}
\State \(\lambda \gets 1\)
\Comment Initialize homotopy parameter
\For{\(s\) in \(0\dots n_{step}-1\)}
\For{\(epoch\) in \(0\dots n_{epoch}-1\)}
\State \(\{\mathbf{u}^{(i)}\}_{i=0}^N = ODESolve(\dot{\mathbf{u}} = \mathbf{U}(t, \mathbf{u} ; \boldsymbol{\theta})- \lambda k \mathbf{I}_n(\mathbf{u}-\hat{\mathbf{u}}(t)))\)
\Comment{Solve coupled dynamics}
\State \(\{\tilde{\mathbf{u}}^{(i)}\}_{i=0}^N = ODESolve(\dot{\tilde{\mathbf{u}}} = \mathbf{U}(t, \tilde{\mathbf{u}}; \boldsymbol{\theta}))\)
\Comment{Also solve uncoupled dynamics}
\State \(MSE(\boldsymbol{\theta})=\frac{1}{N+1}\sum_i\left|\tilde{\mathbf{u}}^{(i)}(\boldsymbol{\theta})-\hat{\mathbf{u}}^{(i)}\right|^2\)
\If{\(MSE \leq MSE_{best}\)}
\State \(MSE_{best} \gets MSE\)
\Comment{Model performance is gauged by uncoupled dynamics error}
\State \(\boldsymbol{\theta}^* \gets \boldsymbol{\theta}\)
\Comment{Checkpoint best model parameters}
\EndIf
\State \(\mathcal{L}(\boldsymbol{\theta})=\frac{1}{N+1} \sum_i \left|\mathbf{u}^{(i)}(\boldsymbol{\theta}) - \hat{\mathbf{u}}^{(i)} \right|^2\)
\Comment{Loss function is calculated using coupled dynamics}
\State \({\boldsymbol{\theta} \gets OptimizerStep(\eta, \boldsymbol{\theta}, \nabla_{\boldsymbol\theta} \mathcal{L})}\)
\EndFor
\State \(\lambda \gets \lambda - \kappa^s/\sum_{s=0}^{n_{steps}-1} \kappa^s\)
\Comment{Decrease homotopy parameter with power law decrements}
\EndFor
\Ensure Trained model parameters \(\boldsymbol{\theta}^*\), \(\lambda = 0\)
\end{algorithmic}
| \begin{algorithmic}
\Require Data \(\{t^{(i)}, \hat{\mathbf{u}}^{(i)}\}_{i=0}^N\), untrained model \(\mathbf{U}(...; \boldsymbol{\theta})\)\\
\Return Coupling strength(\(k\)), homotopy parameter decrement ratio(\(\kappa\)), number of homotopy steps(\(s\)), epochs per homotopy step(\(n_{epoch}\)), learning rate(\(\eta\))
\State \(\hat{\mathbf{u}}(t)=CubicSmoothingSpline(\{t^{(i)}, \hat{\mathbf{u}}^{(i)}\}_{i=0}^N)\)
\Comment{Construct data interpolant}
\State \(\lambda \gets 1\)
\Comment Initialize homotopy parameter
\For{\(s\) in \(0\dots n_{step}-1\)}
\For{\(epoch\) in \(0\dots n_{epoch}-1\)}
\State \(\{\mathbf{u}^{(i)}\}_{i=0}^N = ODESolve(\dot{\mathbf{u}} = \mathbf{U}(t, \mathbf{u} ; \boldsymbol{\theta})- \lambda k \mathbf{I}_n(\mathbf{u}-\hat{\mathbf{u}}(t)))\)
\Comment{Solve coupled dynamics}
\State \(\{\tilde{\mathbf{u}}^{(i)}\}_{i=0}^N = ODESolve(\dot{\tilde{\mathbf{u}}} = \mathbf{U}(t, \tilde{\mathbf{u}}; \boldsymbol{\theta}))\)
\Comment{Also solve uncoupled dynamics}
\State \(MSE(\boldsymbol{\theta})=\frac{1}{N+1}\sum_i\left|\tilde{\mathbf{u}}^{(i)}(\boldsymbol{\theta})-\hat{\mathbf{u}}^{(i)}\right|^2\)
\If{\(MSE \leq MSE_{best}\)}
\State \(MSE_{best} \gets MSE\)
\Comment{Model performance is gauged by uncoupled dynamics error}
\State \(\boldsymbol{\theta}^* \gets \boldsymbol{\theta}\)
\Comment{Checkpoint best model parameters}
\EndIf
\State \(\mathcal{L}(\boldsymbol{\theta})=\frac{1}{N+1} \sum_i \left|\mathbf{u}^{(i)}(\boldsymbol{\theta}) - \hat{\mathbf{u}}^{(i)} \right|^2\)
\Comment{Loss function is calculated using coupled dynamics}
\State \({\boldsymbol{\theta} \gets OptimizerStep(\eta, \boldsymbol{\theta}, \nabla_{\boldsymbol\theta} \mathcal{L})}\)
\EndFor
\State \(\lambda \gets \lambda - \kappa^s/\sum_{s=0}^{n_{steps}-1} \kappa^s\)
\Comment{Decrease homotopy parameter with power law decrements}
\EndFor
\Ensure Trained model parameters \(\boldsymbol{\theta}^*\), \(\lambda = 0\)
\end{algorithmic} | "https://arxiv.org/src/2210.01407" | "2210.01407.tar.gz" | "2024-01-23" | {
"title": "homotopy-based training of neuralodes for accurate dynamics discovery",
"id": "2210.01407",
"abstract": "neural ordinary differential equations (neuralodes) present an attractive way to extract dynamical laws from time series data, as they bridge neural networks with the differential equation-based modeling paradigm of the physical sciences. however, these models often display long training times and suboptimal results, especially for longer duration data. while a common strategy in the literature imposes strong constraints to the neuralode architecture to inherently promote stable model dynamics, such methods are ill-suited for dynamics discovery as the unknown governing equation is not guaranteed to satisfy the assumed constraints. in this paper, we develop a new training method for neuralodes, based on synchronization and homotopy optimization, that does not require changes to the model architecture. we show that synchronizing the model dynamics and the training data tames the originally irregular loss landscape, which homotopy optimization can then leverage to enhance training. through benchmark experiments, we demonstrate our method achieves competitive or better training loss while often requiring less than half the number of training epochs compared to other model-agnostic techniques. furthermore, models trained with our method display better extrapolation capabilities, highlighting the effectiveness of our method.",
"categories": "cs.lg math.ds math.oc physics.app-ph",
"doi": "",
"created": "2022-10-04",
"updated": "2024-01-23",
"authors": [
"joon-hyuk ko",
"hankyul koh",
"nojun park",
"wonho jhe"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2210.01407"
} | "2024-03-15T07:14:36.473195" | {
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} | [] | "algorithm" | "6b1faeaf-94f1-4b8b-9f17-a0e1d72ca38a" | 1942 | hard |
|
\begin{algorithmic}[1]
\State Initialize the weights of an RL agent and a Self-Explainer (SE-Net)
\State Initialize buffers $\mathcal{D}_{success}$ and $\mathcal{D}_{failure}$ for training the Self-Explainer and $D_{RL}$ for RL from Demonstrations as in the RLfD works \cite{hester2017deep,vecerik2017leveraging}
\State Store expert experiences into $\mathcal{D}_{success}$ and $\mathcal{D}_{RL}$. Pretrain the RL agent with experiences sampled from $\mathcal{D}_{RL}$
\State Sample $K$ trajectories with a random policy and add them to $D_{RL}$. Also add successful and unsuccessful trajectories to $\mathcal{D}_{success}$ and $\mathcal{D}_{failure}$ respectively.
\For{\texttt{$episode=1; episode \leq N; episode++$}}
\State Sample experiences (including grounded predicate values) from $\mathcal{D}_{success}$ and $\mathcal{D}_{failure}$ \Comment{\textbf{Train Self-Explainer}}
\State Compute utility weights $u$ and shaped reward prediction $\hat{r}_\theta(s_t,u_t,a_t,s_{t+1},u_{t+1})$ by using SE-Net, Eqs. \ref{eq:dot-prod} and \ref{eq:serl_rwd}
\State Update the SE-Net via binary cross entropy loss $L_{SE}$ (Eq. \ref{eq:l_se}) to distinguish successful experiences from unsuccessful experiences
\State Sample experiences with grounded predicate values from $\mathcal{D}_{RL}$ \Comment{\textbf{Train RL agent}}
\State Run SE-Net on sampled states to obtain utility weights $u$
\State Augment input states with grounded predicate values and utility weight values
\State Augment rewards with predicted shaped reward by using Eq. \ref{eq:serl_rwd}
\State Update RL agent with the augmented experiences
\State Use RL agent to sample a new trajectory and add it to $D_{RL}$. If the trajectory is successful, it would also be added to $\mathcal{D}_{success}$. Otherwise, it would also be added to $\mathcal{D}_{failure}$ \Comment{\textbf{Sample a new trajectory}}
\EndFor \\
\Return a trained RL agent and SE-Net
\end{algorithmic}
| \begin{algorithmic}[1]
\State Initialize the weights of an RL agent and a Self-Explainer (SE-Net)
\State Initialize buffers $\mathcal{D}_{success}$ and $\mathcal{D}_{failure}$ for training the Self-Explainer and $D_{RL}$ for RL from Demonstrations as in the RLfD works \cite{hester2017deep,vecerik2017leveraging}
\State Store expert experiences into $\mathcal{D}_{success}$ and $\mathcal{D}_{RL}$. Pretrain the RL agent with experiences sampled from $\mathcal{D}_{RL}$
\State Sample $K$ trajectories with a random policy and add them to $D_{RL}$. Also add successful and unsuccessful trajectories to $\mathcal{D}_{success}$ and $\mathcal{D}_{failure}$ respectively.
\For{\texttt{$episode=1; episode \leq N; episode++$}}
\State Sample experiences (including grounded predicate values) from $\mathcal{D}_{success}$ and $\mathcal{D}_{failure}$ \Comment{\textbf{Train Self-Explainer}}
\State Compute utility weights $u$ and shaped reward prediction $\hat{r}_\theta(s_t,u_t,a_t,s_{t+1},u_{t+1})$ by using SE-Net, Eqs. \ref{eq:dot-prod} and \ref{eq:serl_rwd}
\State Update the SE-Net via binary cross entropy loss $L_{SE}$ (Eq. \ref{eq:l_se}) to distinguish successful experiences from unsuccessful experiences
\State Sample experiences with grounded predicate values from $\mathcal{D}_{RL}$ \Comment{\textbf{Train RL agent}}
\State Run SE-Net on sampled states to obtain utility weights $u$
\State Augment input states with grounded predicate values and utility weight values
\State Augment rewards with predicted shaped reward by using Eq. \ref{eq:serl_rwd}
\State Update RL agent with the augmented experiences
\State Use RL agent to sample a new trajectory and add it to $D_{RL}$. If the trajectory is successful, it would also be added to $\mathcal{D}_{success}$. Otherwise, it would also be added to $\mathcal{D}_{failure}$ \Comment{\textbf{Sample a new trajectory}}
\EndFor \\
\Return a trained RL agent and SE-Net
\end{algorithmic} | "https://arxiv.org/src/2110.05286" | "2110.05286.tar.gz" | "2024-02-07" | {
"title": "learning from ambiguous demonstrations with self-explanation guided reinforcement learning",
"id": "2110.05286",
"abstract": "our work aims at efficiently leveraging ambiguous demonstrations for the training of a reinforcement learning (rl) agent. an ambiguous demonstration can usually be interpreted in multiple ways, which severely hinders the rl-agent from learning stably and efficiently. since an optimal demonstration may also suffer from being ambiguous, previous works that combine rl and learning from demonstration (rlfd works) may not work well. inspired by how humans handle such situations, we propose to use self-explanation (an agent generates explanations for itself) to recognize valuable high-level relational features as an interpretation of why a successful trajectory is successful. this way, the agent can provide some guidance for its rl learning. our main contribution is to propose the self-explanation for rl from demonstrations (serlfd) framework, which can overcome the limitations of traditional rlfd works. our experimental results show that an rlfd model can be improved by using our serlfd framework in terms of training stability and performance.",
"categories": "cs.lg",
"doi": "",
"created": "2021-10-11",
"updated": "2024-02-07",
"authors": [
"yantian zha",
"lin guan",
"subbarao kambhampati"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2110.05286"
} | "2024-03-15T07:11:54.770777" | {
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} | [] | "algorithm" | "9c262d00-9dd9-4757-8546-807d775a66cf" | 1933 | hard |
|
\begin{algorithmic}[1]
\State Choose a proper filter function $f$ to project data on the real line, $f: X \rightarrow \mathbb{R}$.
\State Choose a component number $n$ and overlap percentage ratio $p$.
\State Construct a cover $\mathcal{U} = (u_i), i=1...n$ on projected data $f(X)$ based on the parameter $n$ and $p$.
\State Pull back the intervals of projected data, $f^{-1}(\mathcal{U})$.
\State Cluster on the refined cover and build the nerves with the clustering result.
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Choose a proper filter function $f$ to project data on the real line, $f: X \rightarrow \mathbb{R}$.
\State Choose a component number $n$ and overlap percentage ratio $p$.
\State Construct a cover $\mathcal{U} = (u_i), i=1...n$ on projected data $f(X)$ based on the parameter $n$ and $p$.
\State Pull back the intervals of projected data, $f^{-1}(\mathcal{U})$.
\State Cluster on the refined cover and build the nerves with the clustering result.
\end{algorithmic} | "https://arxiv.org/src/2401.12237" | "2401.12237.tar.gz" | "2024-01-19" | {
"title": "a distribution-guided mapper algorithm",
"id": "2401.12237",
"abstract": "motivation: the mapper algorithm is an essential tool to explore shape of data in topology data analysis. with a dataset as an input, the mapper algorithm outputs a graph representing the topological features of the whole dataset. this graph is often regarded as an approximation of a reeb graph of data. the classic mapper algorithm uses fixed interval lengths and overlapping ratios, which might fail to reveal subtle features of data, especially when the underlying structure is complex. results: in this work, we introduce a distribution guided mapper algorithm named d-mapper, that utilizes the property of the probability model and data intrinsic characteristics to generate density guided covers and provides enhanced topological features. our proposed algorithm is a probabilistic model-based approach, which could serve as an alternative to non-prababilistic ones. moreover, we introduce a metric accounting for both the quality of overlap clustering and extended persistence homology to measure the performance of mapper type algorithm. our numerical experiments indicate that the d-mapper outperforms the classical mapper algorithm in various scenarios. we also apply the d-mapper to a sars-cov-2 coronavirus rna sequences dataset to explore the topological structure of different virus variants. the results indicate that the d-mapper algorithm can reveal both vertical and horizontal evolution processes of the viruses. availability: our package is available at https://github.com/shufeige/d-mapper.",
"categories": "math.at cs.lg q-bio.qm",
"doi": "",
"created": "2024-01-19",
"updated": "",
"authors": [
"yuyang tao",
"shufei ge"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.12237"
} | "2024-03-15T06:54:42.856784" | {
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} | [] | "algorithm" | "f611d244-1f76-4ec1-b58e-03a6c29d6bcb" | 495 | easy |
|
\begin{algorithm}
\caption{}\label{alg2}
\begin{algorithmic}[1]
\State Let $\mathcal{J}=\{I_1,I_2,\ldots,I_m\}$ be the set of subintervals formed the chore $[0,1]$.
\State Solve the following linear program:
\begin{align}\label{eq1}
\min \quad
& \sum_{i,j =1}^{n} \sum_{k=1}^m x_{j,I_k} V_{i,j}(I_k)
\end{align}
s.t.
\begin{align}
\sum_{i=1}^n x_{i,I_k}&
= 1 && \forall k\in [m] \label{eq:2} \\
x_{i,k} &\geq 0&& \forall i\in N, \forall k\in [m] \label{eq:3}\\
\sum_{k=1}^m \sum_{j=1}^n x_{j,I_k}V_{i,j}(I_k)&\leq \frac{1}{n} && \forall i\in N \label{eq:4}
\end{align}
\begin{equation} \label{eq:5}
\begin{split}
\sum_{k=1}^m x_{i,I_k}V_{i,i}(I_k)+x_{j,I_k} V_{i,j}(I_k) & \leq\sum_{k=1}^m x_{j,I_k}V_{i,i}(I_k)+x_{i,I_k} V_{i,j}(I_k)\\ & \forall i,j \in N
\end{split}
\end{equation}
\State Return an allocation which for all $i\in N$ and $I_k\in \mathcal{J}$ allocates an $x_{i,k}$ fraction of subinterval $I_k$ to agent $i$.
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{}\begin{algorithmic}
[1]
\State Let $\mathcal{J}=\{I_1,I_2,\ldots,I_m\}$ be the set of subintervals formed the chore $[0,1]$.
\State Solve the following linear program:
\begin{align*}
\min \quad
& \sum_{i,j =1}^{n} \sum_{k=1}^m x_{j,I_k} V_{i,j}(I_k)
\end{align*}
s.t.
\begin{align*}
\sum_{i=1}^n x_{i,I_k}&
= 1 && \forall k\in [m] \\
x_{i,k} &\geq 0&& \forall i\in N, \forall k\in [m] \\
\sum_{k=1}^m \sum_{j=1}^n x_{j,I_k}V_{i,j}(I_k)&\leq \frac{1}{n} && \forall i\in N \end{align*}
\begin{equation*}
\begin{split}
\sum_{k=1}^m x_{i,I_k}V_{i,i}(I_k)+x_{j,I_k} V_{i,j}(I_k) & \leq\sum_{k=1}^m x_{j,I_k}V_{i,i}(I_k)+x_{i,I_k} V_{i,j}(I_k)\\ & \forall i,j \in N
\end{split}
\end{equation*}
\State Return an allocation which for all $i\in N$ and $I_k\in \mathcal{J}$ allocates an $x_{i,k}$ fraction of subinterval $I_k$ to agent $i$.
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2303.12446" | "2303.12446.tar.gz" | "2024-02-24" | {
"title": "externalities in chore division",
"id": "2303.12446",
"abstract": "the chore division problem simulates the fair division of a heterogeneous, undesirable resource among several agents. in the fair division of chores, each agent only gets the disutility from its own piece. agents may, however, also be concerned with the pieces given to other agents; these externalities naturally appear in fair division situations. we first demonstrate the generalization of the classical concepts of proportionality and envy-freeness while extending the classical model by taking externalities into account.",
"categories": "cs.gt cs.ai cs.ma",
"doi": "",
"created": "2023-03-22",
"updated": "2024-02-24",
"authors": [
"mohammad azharuddin sanpui"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2303.12446"
} | "2024-03-15T03:42:06.657255" | {
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} | [] | "algorithm" | "a4e77adb-9d77-484f-b875-345aa06ccf95" | 892 | medium |
|
\begin{algorithmic}
\Require{$\{M, x_0, x_M, r,\lambda_t, D_{\alpha}, \alpha, \nu, \beta, \lambda, \mu\}$ (Table \ref{tab:parameters})}
\State{1: Compute Time Steps: $\{\Delta t_k\}_{k=1}^M$ and $\Delta t$}
\State{2: Compute State Steps: $\{ \Delta x_k \}_{k=1}^M$ and $\Delta x$ (Eqn. [\ref{eq:latticesize}]) }
\State{3: Initialise Background Lattice: $(x_i,t_n)$}
\State{4: Compute Initial Conditions: $\varphi^i_0$}
\State{\ForAll{$n$}
\State{5: Set Time and State Steps: $\Delta t_n, \Delta x_n$}
\State{6: Compute Boltzmann Potentials: $V_t$}
\State{7: Compute Jump Probabilities: $r$, $F_n$}
\State{8: Update Sources: $s(x_i,t_n,p_n)$}
\State{9: Update Boundary Conditions: $\varphi^0_n$, $\varphi^M_n$}
\State{10: Update Interior Points: $\varphi^i_n$ (Eqn. [\ref{eq:UpdateEquationExpArrival},\ref{eq:onjumplattice},\ref{eq:MemKerRecursive}])}
\State{11: Find mid-price: $p_n=\{ x_i : \min \{|\varphi^i_n|\} \}$}
\EndFor} \\
\State{\Return{$\varphi^i_n$ and $p_n$ on lattice $(x_i,t_n)$}}
\end{algorithmic}
| \begin{algorithmic}
\Require{$\{M, x_0, x_M, r,\lambda_t, D_{\alpha}, \alpha, \nu, \beta, \lambda, \mu\}$ (Table \ref{tab:parameters})}
\State{1: Compute Time Steps: $\{\Delta t_k\}_{k=1}^M$ and $\Delta t$}
\State{2: Compute State Steps: $\{ \Delta x_k \}_{k=1}^M$ and $\Delta x$ (Eqn. [\ref{eq:latticesize}]) }
\State{3: Initialise Background Lattice: $(x_i,t_n)$}
\State{4: Compute Initial Conditions: $\varphi^i_0$}
\State{\ForAll{$n$}
\State{5: Set Time and State Steps: $\Delta t_n, \Delta x_n$}
\State{6: Compute Boltzmann Potentials: $V_t$}
\State{7: Compute Jump Probabilities: $r$, $F_n$}
\State{8: Update Sources: $s(x_i,t_n,p_n)$}
\State{9: Update Boundary Conditions: $\varphi^0_n$, $\varphi^M_n$}
\State{10: Update Interior Points: $\varphi^i_n$ (Eqn. [\ref{eq:UpdateEquationExpArrival},\ref{eq:onjumplattice},\ref{eq:MemKerRecursive}])}
\State{11: Find mid-price: $p_n=\{ x_i : \min \{|\varphi^i_n|\} \}$}
\EndFor} \\
\State{\Return{$\varphi^i_n$ and $p_n$ on lattice $(x_i,t_n)$}}
\end{algorithmic} | "https://arxiv.org/src/2310.06079" | "2310.06079.tar.gz" | "2024-01-16" | {
"title": "anomalous diffusion and price impact in the fluid-limit of an order book",
"id": "2310.06079",
"abstract": "we extend a discrete time random walk (dtrw) numerical scheme to simulate the anomalous diffusion of financial market orders in a simulated order book. here using random walks with sibuya waiting times to include a time-dependent stochastic forcing function with non-uniformly sampled times between order book events in the setting of fractional diffusion. this models the fluid limit of an order book by modelling the continuous arrival, cancellation and diffusion of orders in the presence of information shocks. we study the impulse response and stylised facts of orders undergoing anomalous diffusion for different forcing functions and model parameters. concretely, we demonstrate the price impact for flash limit-orders and market orders and show how the numerical method generate kinks in the price impact. we use cubic spline interpolation to generate smoothed price impact curves. the work promotes the use of non-uniform sampling in the presence of diffusive dynamics as the preferred simulation method.",
"categories": "q-fin.cp cs.ce nlin.ao q-fin.tr",
"doi": "",
"created": "2023-10-09",
"updated": "2024-01-16",
"authors": [
"derick diana",
"tim gebbie"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2310.06079"
} | "2024-03-15T06:07:24.790122" | {
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} | [] | "algorithm" | "9ab15a52-eaff-4cae-8077-1df3ee5e394c" | 1013 | medium |
|
\begin{algorithmic}[1]
\State Input: Two probability distributions $\P_B,\P_R$ supported on $B,R\subset Q_d$, and a tilt factor $\alpha\in(0,1)$.
\State Output: Probability distribution $\P_B'$ supported on $B$. $\P_B'$ is close to $\alpha\P_R+(1-\alpha)\P_B$ in $W_1$, under assumptions of Theorem~\ref{main1:thm}.
\For{$r\in R$}
\State $\mathrm{Supply}(r)\gets C\cdot\alpha\P_R(r)$
\EndFor
\For{$b\in B$}
\State $\mathrm{Demand(b)}\gets C - C\cdot(1-\alpha)\P_B(r)$
\If{$\mathrm{Demand}(b) < 0$}
\State $\mathrm{Demand(b)}\gets 0$
\EndIf
\EndFor
\State Create multi-set $B',R'$ with multiplicities of each element being equal to their Demand and Supply respectively.
\State Use $\mathrm{GreedyMatch}(R', B')$ to compute the met (matched) demands, i.e., the extent to which the demands of $B$ that are actually fulfilled by $R$.
\State Normalize the weights of met demands to obtain a probability distribution $\P_B'$ supported on $B$.
\State \textbf{return} $\P_B'$.
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Input: Two probability distributions $\P_B,\P_R$ supported on $B,R\subset Q_d$, and a tilt factor $\alpha\in(0,1)$.
\State Output: Probability distribution $\P_B'$ supported on $B$. $\P_B'$ is close to $\alpha\P_R+(1-\alpha)\P_B$ in $W_1$, under assumptions of Theorem~\ref{main1:thm}.
\For{$r\in R$}
\State $\mathrm{Supply}(r)\gets C\cdot\alpha\P_R(r)$
\EndFor
\For{$b\in B$}
\State $\mathrm{Demand(b)}\gets C - C\cdot(1-\alpha)\P_B(r)$
\If{$\mathrm{Demand}(b) < 0$}
\State $\mathrm{Demand(b)}\gets 0$
\EndIf
\EndFor
\State Create multi-set $B',R'$ with multiplicities of each element being equal to their Demand and Supply respectively.
\State Use $\mathrm{GreedyMatch}(R', B')$ to compute the met (matched) demands, i.e., the extent to which the demands of $B$ that are actually fulfilled by $R$.
\State Normalize the weights of met demands to obtain a probability distribution $\P_B'$ supported on $B$.
\State \textbf{return} $\P_B'$.
\end{algorithmic} | "https://arxiv.org/src/2401.11562" | "2401.11562.tar.gz" | "2024-01-21" | {
"title": "enhancing selectivity using wasserstein distance based reweighing",
"id": "2401.11562",
"abstract": "given two labeled data-sets $\\mathcal{s}$ and $\\mathcal{t}$, we design a simple and efficient greedy algorithm to reweigh the loss function such that the limiting distribution of the neural network weights that result from training on $\\mathcal{s}$ approaches the limiting distribution that would have resulted by training on $\\mathcal{t}$. on the theoretical side, we prove that when the metric entropy of the input data-sets is bounded, our greedy algorithm outputs a close to optimal reweighing, i.e., the two invariant distributions of network weights will be provably close in total variation distance. moreover, the algorithm is simple and scalable, and we prove bounds on the efficiency of the algorithm as well. our algorithm can deliberately introduce distribution shift to perform (soft) multi-criteria optimization. as a motivating application, we train a neural net to recognize small molecule binders to mnk2 (a map kinase, responsible for cell signaling) which are non-binders to mnk1 (a highly similar protein). we tune the algorithm's parameter so that overall change in holdout loss is negligible, but the selectivity, i.e., the fraction of top 100 mnk2 binders that are mnk1 non-binders, increases from 54\\% to 95\\%, as a result of our reweighing. of the 43 distinct small molecules predicted to be most selective from the enamine catalog, 2 small molecules were experimentally verified to be selective, i.e., they reduced the enzyme activity of mnk2 below 50\\% but not mnk1, at 10$\\mu$m -- a 5\\% success rate.",
"categories": "stat.ml cs.lg q-bio.qm",
"doi": "",
"created": "2024-01-21",
"updated": "",
"authors": [
"pratik worah"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.11562"
} | "2024-03-15T07:03:20.799704" | {
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} | [] | "algorithm" | "c391ee7b-2e5f-4597-8dea-02a54f2af3df" | 987 | medium |
|
\begin{algorithm}[t]
\caption{\textbf{SplitSGD}($\eta, w, l, q, B, t_1, \theta_0, \gamma$)}
\label{procedure}
{\fontsize{10}{15} \selectfont
\begin{algorithmic}[1]
\State $\eta_1 = \eta$
\State $\theta_1^{in} = \theta_0$
\For{$b = 1,..., B$}
\State Run SGD with constant step size $\eta_b$ for $t_b$ steps, starting from $\theta_{b}^{in}$
\State Let the last update be $\theta_{b}^{last}$
\State $D_b = \textbf{Diagnostic}(\eta_b, w, l, q, \theta_{b}^{last})$
\State $\theta_{b+1}^{in} = \theta_{D_b}$
\If{$T_{D_b} = S$}
\State $\eta_{b+1} = \gamma\cdot\eta_b$ and $t_{b+1} = \lfloor t_b/\gamma \rfloor$
\Else
\State $\eta_{b+1} = \eta_b$ and $t_{b+1} = t_b$
\EndIf
\EndFor
\end{algorithmic}
}
\end{algorithm}
| \begin{algorithm}
[t]
\caption{\textbf{SplitSGD}($\eta, w, l, q, B, t_1, \theta_0, \gamma$)}
{\fontsize{10}{15} \selectfont
\begin{algorithmic}
[1]
\State $\eta_1 = \eta$
\State $\theta_1^{in} = \theta_0$
\For{$b = 1,..., B$}
\State Run SGD with constant step size $\eta_b$ for $t_b$ steps, starting from $\theta_{b}^{in}$
\State Let the last update be $\theta_{b}^{last}$
\State $D_b = \textbf{Diagnostic}(\eta_b, w, l, q, \theta_{b}^{last})$
\State $\theta_{b+1}^{in} = \theta_{D_b}$
\If{$T_{D_b} = S$}
\State $\eta_{b+1} = \gamma\cdot\eta_b$ and $t_{b+1} = \lfloor t_b/\gamma \rfloor$
\Else
\State $\eta_{b+1} = \eta_b$ and $t_{b+1} = t_b$
\EndIf
\EndFor
\end{algorithmic}
}
\end{algorithm} | "https://arxiv.org/src/1910.08597" | "1910.08597.tar.gz" | "2024-02-16" | {
"title": "robust learning rate selection for stochastic optimization via splitting diagnostic",
"id": "1910.08597",
"abstract": "this paper proposes splitsgd, a new dynamic learning rate schedule for stochastic optimization. this method decreases the learning rate for better adaptation to the local geometry of the objective function whenever a stationary phase is detected, that is, the iterates are likely to bounce at around a vicinity of a local minimum. the detection is performed by splitting the single thread into two and using the inner product of the gradients from the two threads as a measure of stationarity. owing to this simple yet provably valid stationarity detection, splitsgd is easy-to-implement and essentially does not incur additional computational cost than standard sgd. through a series of extensive experiments, we show that this method is appropriate for both convex problems and training (non-convex) neural networks, with performance compared favorably to other stochastic optimization methods. importantly, this method is observed to be very robust with a set of default parameters for a wide range of problems and, moreover, can yield better generalization performance than other adaptive gradient methods such as adam.",
"categories": "stat.ml cs.lg math.oc stat.me",
"doi": "",
"created": "2019-10-18",
"updated": "2024-02-16",
"authors": [
"matteo sordello",
"niccol\u00f2 dalmasso",
"hangfeng he",
"weijie su"
],
"affiliation": [],
"url": "https://arxiv.org/abs/1910.08597"
} | "2024-03-15T04:35:48.772484" | {
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} | [] | "algorithm" | "bb78be88-561e-4048-a126-61b45570103a" | 693 | easy |
|
\begin{algorithm}[!ht]
\caption{3d Subspace Intersects Box}
\begin{algorithmic}
\Require
\State \hspace{5mm}Boundary $\mathcal{S} = [-B,B[\times[-B,B[\times[-B,B[\times[-B,B[$
\State \hspace{5mm}4d normal $N=(n_x,n_y,n_z,n_t)$ to 3d subspace $\mathcal{S_N}$
\State \hspace{5mm}Point $V=(x,y,z,t)$ contained in $\mathcal{S_N}$
\Ensure
True if $\mathcal{S_N} \cap \mathcal{S} \neq \emptyset$, False otherwise
\vspace{1mm}
\Procedure{}{}
\vspace{1mm}
\State $d \gets n_xx + n_yy + n_zz + n_tt$
\State $nxB0 \gets -n_xB$
\State $nyB0 \gets -n_yB$
\State $nzB0 \gets -n_zB$
\State $ntB0 \gets -n_tB$
\State $nxB1 \gets n_x(B-1)$
\State $nyB1 \gets n_y(B-1)$
\State $nzB1 \gets n_z(B-1)$
\State $ntB1 \gets n_t(B-1)$
\State $s_0 \gets nxB0 + nyB0 + nzB0 + ntB0 - d$
\State $s_1 \gets nxB1 + nyB0 + nzB0 + ntB0 - d$
\State $s_2 \gets nxB0 + nyB1 + nzB0 + ntB0 - d$
\State $s_3 \gets nxB1 + nyB1 + nzB0 + ntB0 - d$
\State $s_4 \gets nxB0 + nyB0 + nzB1 + ntB0 - d$
\State $s_5 \gets nxB1 + nyB0 + nzB1 + ntB0 - d$
\State $s_6 \gets nxB0 + nyB1 + nzB1 + ntB0 - d$
\State $s_7 \gets nxB1 + nyB1 + nzB1 + ntB0 - d$
\State $s_8 \gets nxB0 + nyB0 + nzB0 + ntB1 - d$
\State $s_9 \gets nxB1 + nyB0 + nzB0 + ntB1 - d$
\State $s_a \gets nxB0 + nyB1 + nzB0 + ntB1 - d$
\State $s_b \gets nxB1 + nyB1 + nzB0 + ntB1 - d$
\State $s_c \gets nxB0 + nyB0 + nzB1 + ntB1 - d$
\State $s_d \gets nxB1 + nyB0 + nzB1 + ntB1 - d$
\State $s_e \gets nxB0 + nyB1 + nzB1 + ntB1 - d$
\State $s_f \gets nxB1 + nyB1 + nzB1 + ntB1 - d$
\State If all of $s_0,\dots,s_f$ have the same sign, return False, otherwise return True
\EndProcedure
\end{algorithmic}\label{alg1}
\end{algorithm}
| \begin{algorithm}
[!ht]
\caption{3d Subspace Intersects Box}
\begin{algorithmic}
\Require
\State \hspace{5mm}Boundary $\mathcal{S} = [-B,B[\times[-B,B[\times[-B,B[\times[-B,B[$
\State \hspace{5mm}4d normal $N=(n_x,n_y,n_z,n_t)$ to 3d subspace $\mathcal{S_N}$
\State \hspace{5mm}Point $V=(x,y,z,t)$ contained in $\mathcal{S_N}$
\Ensure
True if $\mathcal{S_N} \cap \mathcal{S} \neq \emptyset$, False otherwise
\vspace{1mm}
\Procedure{}{}
\vspace{1mm}
\State $d \gets n_xx + n_yy + n_zz + n_tt$
\State $nxB0 \gets -n_xB$
\State $nyB0 \gets -n_yB$
\State $nzB0 \gets -n_zB$
\State $ntB0 \gets -n_tB$
\State $nxB1 \gets n_x(B-1)$
\State $nyB1 \gets n_y(B-1)$
\State $nzB1 \gets n_z(B-1)$
\State $ntB1 \gets n_t(B-1)$
\State $s_0 \gets nxB0 + nyB0 + nzB0 + ntB0 - d$
\State $s_1 \gets nxB1 + nyB0 + nzB0 + ntB0 - d$
\State $s_2 \gets nxB0 + nyB1 + nzB0 + ntB0 - d$
\State $s_3 \gets nxB1 + nyB1 + nzB0 + ntB0 - d$
\State $s_4 \gets nxB0 + nyB0 + nzB1 + ntB0 - d$
\State $s_5 \gets nxB1 + nyB0 + nzB1 + ntB0 - d$
\State $s_6 \gets nxB0 + nyB1 + nzB1 + ntB0 - d$
\State $s_7 \gets nxB1 + nyB1 + nzB1 + ntB0 - d$
\State $s_8 \gets nxB0 + nyB0 + nzB0 + ntB1 - d$
\State $s_9 \gets nxB1 + nyB0 + nzB0 + ntB1 - d$
\State $s_a \gets nxB0 + nyB1 + nzB0 + ntB1 - d$
\State $s_b \gets nxB1 + nyB1 + nzB0 + ntB1 - d$
\State $s_c \gets nxB0 + nyB0 + nzB1 + ntB1 - d$
\State $s_d \gets nxB1 + nyB0 + nzB1 + ntB1 - d$
\State $s_e \gets nxB0 + nyB1 + nzB1 + ntB1 - d$
\State $s_f \gets nxB1 + nyB1 + nzB1 + ntB1 - d$
\State If all of $s_0,\dots,s_f$ have the same sign, return False, otherwise return True
\EndProcedure
\end{algorithmic}\end{algorithm} | "https://arxiv.org/src/2212.04999" | "2212.04999.tar.gz" | "2024-02-06" | {
"title": "an implementation of the extended tower number field sieve using 4d sieving in a box and a record computation in fp4",
"id": "2212.04999",
"abstract": "we report on an implementation of the extended tower number field sieve (extnfs) and record computation in a medium characteristic finite field $\\mathbb{f}_{p^4}$ of 512 bits size. empirically, we show that sieving in a 4-dimensional box (orthotope) for collecting relations for extnfs in $\\mathbb{f}_{p^4}$ is faster than sieving in a 4-dimensional hypersphere. we also give a new intermediate descent method, `descent using random vectors', without which the descent stage in our extnfs computation would have been difficult/impossible, and analyze its complexity.",
"categories": "cs.cr",
"doi": "",
"created": "2022-12-09",
"updated": "2024-02-06",
"authors": [
"oisin robinson"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2212.04999"
} | "2024-03-15T07:40:23.873860" | {
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} | [] | "algorithm" | "e1a0de20-c044-4ffb-b88b-b19504ea14fa" | 1631 | hard |
|
\begin{algorithm}[H]
\caption{ TADRED Forward \& Backward Pass (FBP) in Step $ t $}\label{FBP:alg}
\textbf{Requires:}
\\ Input and Target Data $ X_{\bar{D}}, Y $, Mask $ \textbf{m}_{t} $
\\ Scoring and Task Networks $ \mathcal{S}_{t}, \mathcal{T}_{t} $, Loss $ L $
\\ Sample-independent Feature Score $ \bar{\textbf{s}}_{t} $
\\ Mix Parameter $ \alpha \in [0,1] $, Feature Fill $ X_{\bar{D}}^{\text{fill}} $
\begin{algorithmic}[1]
\State{$ \tilde{s} = \sigma(\mathcal{S}_{t}(X_{\bar{D}})) $}
\State{$ \textbf{s} = \alpha \odot \tilde{s} + (1-\alpha) \odot \bar{\textbf{s}}_{t} $ \hfill \# Equation~\ref{score_both:eq}}
\State{$ X_{D_{t}} = \textbf{m}_{t} \odot X_{\bar{D}} + (\mathbf{1}_{\bar{C}} - \textbf{m}_{t}) \odot X_{\bar{D}}^{\text{fill}} $}
\State{$ \widehat{Y} = \mathcal{T}_{t}(\textbf{s} \odot X_{D_{t}})$ }
\State{Compute $ L(\widehat{Y},Y) $ and backpropagate}
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[H]
\caption{ TADRED Forward \& Backward Pass (FBP) in Step $ t $}\textbf{Requires:}
\\ Input and Target Data $ X_{\bar{D}}, Y $, Mask $ \textbf{m}_{t} $
\\ Scoring and Task Networks $ \mathcal{S}_{t}, \mathcal{T}_{t} $, Loss $ L $
\\ Sample-independent Feature Score $ \bar{\textbf{s}}_{t} $
\\ Mix Parameter $ \alpha \in [0,1] $, Feature Fill $ X_{\bar{D}}^{\text{fill}} $
\begin{algorithmic}
[1]
\State{$ \tilde{s} = \sigma(\mathcal{S}_{t}(X_{\bar{D}})) $}
\State{$ \textbf{s} = \alpha \odot \tilde{s} + (1-\alpha) \odot \bar{\textbf{s}}_{t} $ \hfill \# Equation~\ref{score_both:eq}}
\State{$ X_{D_{t}} = \textbf{m}_{t} \odot X_{\bar{D}} + (\mathbf{1}_{\bar{C}} - \textbf{m}_{t}) \odot X_{\bar{D}}^{\text{fill}} $}
\State{$ \widehat{Y} = \mathcal{T}_{t}(\textbf{s} \odot X_{D_{t}})$ }
\State{Compute $ L(\widehat{Y},Y) $ and backpropagate}
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2210.06891" | "2210.06891.tar.gz" | "2024-02-23" | {
"title": "experimental design for multi-channel imaging via task-driven feature selection",
"id": "2210.06891",
"abstract": "this paper presents a data-driven, task-specific paradigm for experimental design, to shorten acquisition time, reduce costs, and accelerate the deployment of imaging devices. current approaches in experimental design focus on model-parameter estimation and require specification of a particular model, whereas in imaging, other tasks may drive the design. furthermore, such approaches often lead to intractable optimization problems in real-world imaging applications. here we present a new paradigm for experimental design that simultaneously optimizes the design (set of image channels) and trains a machine-learning model to execute a user-specified image-analysis task. the approach obtains data densely-sampled over the measurement space (many image channels) for a small number of acquisitions, then identifies a subset of channels of prespecified size that best supports the task. we propose a method: tadred for task-driven experimental design in imaging, to identify the most informative channel-subset whilst simultaneously training a network to execute the task given the subset. experiments demonstrate the potential of tadred in diverse imaging applications: several clinically-relevant tasks in magnetic resonance imaging; and remote sensing and physiological applications of hyperspectral imaging. results show substantial improvement over classical experimental design, two recent application-specific methods within the new paradigm, and state-of-the-art approaches in supervised feature selection. we anticipate further applications of our approach. code is available: https://github.com/sbb-gh/experimental-design-multichannel",
"categories": "cs.lg cs.ai q-bio.nc",
"doi": "",
"created": "2022-10-13",
"updated": "2024-02-23",
"authors": [
"stefano b. blumberg",
"paddy j. slator",
"daniel c. alexander"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2210.06891"
} | "2024-03-15T03:59:49.884455" | {
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} | [] | "algorithm" | "9f78d3a2-6b6a-4033-bf41-5cd0dccc765e" | 894 | medium |
|
\begin{algorithmic}[1]
\State possible pair list $\gets$ conventional neighbour list
\State new pair list $\gets \varnothing$
\ForAll{stickers $i$}
\State $N_{bonds}[i]\gets0$
\EndFor
\State shuffle possible pair list
\ForAll{pairs $(i,j) \in$ possible pair list}
\State $\Delta E_{ij} \gets U_{bound}(r_{ij})-U_{unbound}(r_{ij})$
\If {$(i,j) \in$ previous pair list}
\If {$X\sim U(0,1)>\exp(-\Delta E_{ij})$}
\State append $(i,j)$ to new pair list
\State $N_{bonds}[i]\gets N_{bonds}[i]+1$
\State $N_{bonds}[j]\gets N_{bonds}[j]+1$
\EndIf
\ElsIf{$N_{bonds}[i]<functionality$ \textbf{ and } $N_{bonds}[j]<functionality$}
\If {$X\sim U(0,1)<\exp(-\Delta E_{ij})$}
\State append $(i,j)$ to new pair list
\State $N_{bonds}[i]\gets N_{bonds}[i]+1$
\State $N_{bonds}[j]\gets N_{bonds}[j]+1$
\EndIf
\EndIf
\EndFor
\State previous pair list $\gets$ new pair list
\end{algorithmic}
| \begin{algorithmic}
[1]
\State possible pair list $\gets$ conventional neighbour list
\State new pair list $\gets \varnothing$
\ForAll{stickers $i$}
\State $N_{bonds}[i]\gets0$
\EndFor
\State shuffle possible pair list
\ForAll{pairs $(i,j) \in$ possible pair list}
\State $\Delta E_{ij} \gets U_{bound}(r_{ij})-U_{unbound}(r_{ij})$
\If {$(i,j) \in$ previous pair list}
\If {$X\sim U(0,1)>\exp(-\Delta E_{ij})$}
\State append $(i,j)$ to new pair list
\State $N_{bonds}[i]\gets N_{bonds}[i]+1$
\State $N_{bonds}[j]\gets N_{bonds}[j]+1$
\EndIf
\ElsIf{$N_{bonds}[i]<functionality$ \textbf{ and } $N_{bonds}[j]<functionality$}
\If {$X\sim U(0,1)<\exp(-\Delta E_{ij})$}
\State append $(i,j)$ to new pair list
\State $N_{bonds}[i]\gets N_{bonds}[i]+1$
\State $N_{bonds}[j]\gets N_{bonds}[j]+1$
\EndIf
\EndIf
\EndFor
\State previous pair list $\gets$ new pair list
\end{algorithmic} | "https://arxiv.org/src/2302.13623" | "2302.13623.tar.gz" | "2024-02-10" | {
"title": "evanescent gels: competition between sticker dynamics and single chain relaxation",
"id": "2302.13623",
"abstract": "solutions of polymer chains are modelled using non-equilibrium brownian dynamics simulations, with physically associative beads which form reversible crosslinks to establish a system-spanning physical gel network. rheological properties such as the zero-shear-rate viscosity and relaxation modulus are investigated systematically as functions of polymer concentration and the binding energy between associative sites. it is shown that a system-spanning network can form regardless of binding energy at sufficiently high concentration. however, the contribution to the stress sustained by this physical network can decay faster than other relaxation processes, even single chain relaxations. if the polymer relaxation time scales overlap with short-lived associations, the mechanical response of a gel becomes ``evanescent'', decaying before it can be rheologically observed, even though the network is instantaneously mechanically rigid. in our simulations, the concentration of elastically active chains and the dynamic modulii are computed independently. this makes it possible to combine structural and rheological information to identify the concentration at which the sol-gel transition occurs as a function of binding energy. further, it is shown that the competition of scales between the sticker dissociation time and the single-polymer relaxation time determines if the gel is in the evanescent regime.",
"categories": "cond-mat.soft",
"doi": "",
"created": "2023-02-27",
"updated": "2024-02-10",
"authors": [
"dominic robe",
"aritra santra",
"gareth h. mckinley",
"j. ravi prakash"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2302.13623"
} | "2024-03-15T05:06:25.025312" | {
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} | [] | "algorithm" | "33c72b1d-a532-4c5d-9e1a-c090a0bd9c84" | 874 | medium |
|
\begin{algorithm}
\caption{Synthetic bid validation / Double validation}
\begin{algorithmic}[1]
\State $\beta \gets \beta^*$ \Comment{load best set of parameters for BidNet}
\State $\alpha \gets \alpha^*$ \Comment{load optimized set of parameters for synthesizer}
\State $\tilde{\mathbf{c}}\sim A_{\alpha^*}(\mathbf{z})$\Comment{sample synthetic examples from the trained synthesizer}
\State $\mathbf{c} \sim D_{test}$\Comment{sample a test-set of real instances}
\State $\hat{b} \sim B_{\beta^*}(\mathbf{c})$\Comment{sample predicted bids from the test-set of real instances using BidNet}
\State $\tilde{b} \sim B_{\beta^*}(\tilde{\mathbf{c}})$\Comment{sample fake bids with the synthetic data emanating from the synthesizer}
\State $Dist(p(b) || p(\tilde{b}))$\Comment{compute the statistical distance between the fake and real distributions of bids}
\State $Dist(p(b) || p(\hat{b}))$\Comment{compute the statistical distance between the predicted and real distributions of bids}
\State $Dist(p(\hat{b}) || p(\tilde{b}))$\Comment{compute the statistical distance between the predicted and fake distributions of bids}
\end{algorithmic}
\label{alg:doubleval}
\end{algorithm}
| \begin{algorithm}
\caption{Synthetic bid validation / Double validation}
\begin{algorithmic}
[1]
\State $\beta \gets \beta^*$ \Comment{load best set of parameters for BidNet}
\State $\alpha \gets \alpha^*$ \Comment{load optimized set of parameters for synthesizer}
\State $\tilde{\mathbf{c}}\sim A_{\alpha^*}(\mathbf{z})$\Comment{sample synthetic examples from the trained synthesizer}
\State $\mathbf{c} \sim D_{test}$\Comment{sample a test-set of real instances}
\State $\hat{b} \sim B_{\beta^*}(\mathbf{c})$\Comment{sample predicted bids from the test-set of real instances using BidNet}
\State $\tilde{b} \sim B_{\beta^*}(\tilde{\mathbf{c}})$\Comment{sample fake bids with the synthetic data emanating from the synthesizer}
\State $Dist(p(b) || p(\tilde{b}))$\Comment{compute the statistical distance between the fake and real distributions of bids}
\State $Dist(p(b) || p(\hat{b}))$\Comment{compute the statistical distance between the predicted and real distributions of bids}
\State $Dist(p(\hat{b}) || p(\tilde{b}))$\Comment{compute the statistical distance between the predicted and fake distributions of bids}
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2207.12255" | "2207.12255.tar.gz" | "2024-02-15" | {
"title": "implementing a hierarchical deep learning approach for simulating multi-level auction data",
"id": "2207.12255",
"abstract": "we present a deep learning solution to address the challenges of simulating realistic synthetic first-price sealed-bid auction data. the complexities encountered in this type of auction data include high-cardinality discrete feature spaces and a multilevel structure arising from multiple bids associated with a single auction instance. our methodology combines deep generative modeling (dgm) with an artificial learner that predicts the conditional bid distribution based on auction characteristics, contributing to advancements in simulation-based research. this approach lays the groundwork for creating realistic auction environments suitable for agent-based learning and modeling applications. our contribution is twofold: we introduce a comprehensive methodology for simulating multilevel discrete auction data, and we underscore the potential of dgm as a powerful instrument for refining simulation techniques and fostering the development of economic models grounded in generative ai.",
"categories": "econ.gn q-fin.ec",
"doi": "",
"created": "2022-07-25",
"updated": "2024-02-15",
"authors": [
"igor sadoune",
"andrea lodi",
"marcelin joanis"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2207.12255"
} | "2024-03-15T04:00:57.383729" | {
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} | [] | "algorithm" | "9534119b-ef69-4ff8-936a-b1ab80205947" | 1153 | medium |
|
\begin{algorithmic}[1]
\State {\bf data structure} \textsc{LSH}
\State {\bf members}
\State \hspace{4mm} $d,n \in \mathbb{N}_+$ \Comment{$d$ is dimension, $n$ is number of data points}
\State \hspace{4mm} $K,L\in \mathbb{N}_+$ \Comment{$K$ is amplification factor, $L$ is number of repetition for hashing}
\State \hspace{4mm} $p_{\mathrm{near}},p_{\mathrm{far}}\in (0,1)$ \Comment{Collision probability}
\State \hspace{4mm} For $l \in L$, $\mathcal{T}_l:=[n]$ \Comment{Hashtable recording data points hashed by $\mathcal{H}_l$}
\State \hspace{4mm} $\mathcal{R}:=[n]$ \Comment{retrieved points}
\State \hspace{4mm} $\mathcal{H}:=\{f\in\mathcal{H}:\mathbb{R}^{d}\rightarrow[M]\}$ \Comment{$M$ is number of buckets for hashing family $\mathcal{H}$}
\State \hspace{4mm} For $l \in [L]$, $\mathcal{H}_{l} \in \mathcal{H}^K$ \label{lin:basic_hash_family} \Comment{Family of amplified hash functions with at most $M^K$ non-empty buckets}
\State \hspace{4mm} For $b \in [M^K]$, $\mathcal{S}_b:=$AVL tree \Comment{Use AVL tree to store points in bucket}
\State {\bf end members}
\State
\State {\bf public}
\Procedure{\textsc{Initialize}}{$\{x_i\}_{i\in[n]}\subset \mathbb{R}^d, k,L\in \mathbb{N}_+$}\label{lin:LSH_initialize}
\State \textsc{ChooseHashFunc}($k,L$)\label{lin:LSH_intialize_choose_hash_func}
\State \textsc{ConstructHashTable}($\{x_i\}_{i\in[n]}$)\label{lin:LSH_initialize_construct_hash_table}
\EndProcedure
\State
\Procedure{\textsc{Recover}}{$q\in\mathbb{R}^d$}\label{alg:LSH_recover}
\State $\mathcal{R} \leftarrow 0$
\For{$l\in[L]$}
\State $\mathcal{R}\leftarrow \mathcal{R} \cup \mathcal{T}_{l}$.\textsc{Retrieve}($\mathcal{H}_{l}(q)$) \Comment{Find the bucket $\mathcal{H}_{l}(q)$ in $\mathcal{T}_l$ and retrieve all points}\label{lin:LSH_retrieve}
\EndFor
\EndProcedure
\State
\Procedure{\textsc{UpdateHashTable}}{$z\in\mathbb{R}^d, i\in[n]$}\label{lin:update_hashtable}
\For{$l\in [L]$}
\State $\mathcal{H}_{l}(z)$.\textsc{Insert}($z$)\label{lin:insert} \Comment{$\mathcal{H}_{l}(z)$ denotes the bucket that $z$ is mapped to}
\State $\mathcal{H}_{l}(x_i)$.\textsc{Delete}($x_i$)\label{lin:delete}
\EndFor
\EndProcedure
\State {\bf end data structure}
\end{algorithmic}
| \begin{algorithmic}
[1]
\State {\bf data structure} \textsc{LSH}
\State {\bf members}
\State \hspace{4mm} $d,n \in \mathbb{N}_+$ \Comment{$d$ is dimension, $n$ is number of data points}
\State \hspace{4mm} $K,L\in \mathbb{N}_+$ \Comment{$K$ is amplification factor, $L$ is number of repetition for hashing}
\State \hspace{4mm} $p_{\mathrm{near}},p_{\mathrm{far}}\in (0,1)$ \Comment{Collision probability}
\State \hspace{4mm} For $l \in L$, $\mathcal{T}_l:=[n]$ \Comment{Hashtable recording data points hashed by $\mathcal{H}_l$}
\State \hspace{4mm} $\mathcal{R}:=[n]$ \Comment{retrieved points}
\State \hspace{4mm} $\mathcal{H}:=\{f\in\mathcal{H}:\mathbb{R}^{d}\rightarrow[M]\}$ \Comment{$M$ is number of buckets for hashing family $\mathcal{H}$}
\State \hspace{4mm} For $l \in [L]$, $\mathcal{H}_{l} \in \mathcal{H}^K$ \Comment{Family of amplified hash functions with at most $M^K$ non-empty buckets}
\State \hspace{4mm} For $b \in [M^K]$, $\mathcal{S}_b:=$AVL tree \Comment{Use AVL tree to store points in bucket}
\State {\bf end members}
\State
\State {\bf public}
\Procedure{\textsc{Initialize}}{$\{x_i\}_{i\in[n]}\subset \mathbb{R}^d, k,L\in \mathbb{N}_+$}
\State \textsc{ChooseHashFunc}($k,L$) \State \textsc{ConstructHashTable}($\{x_i\}_{i\in[n]}$)\EndProcedure
\State
\Procedure{\textsc{Recover}}{$q\in\mathbb{R}^d$} \State $\mathcal{R} \leftarrow 0$
\For{$l\in[L]$}
\State $\mathcal{R}\leftarrow \mathcal{R} \cup \mathcal{T}_{l}$.\textsc{Retrieve}($\mathcal{H}_{l}(q)$) \Comment{Find the bucket $\mathcal{H}_{l}(q)$ in $\mathcal{T}_l$ and retrieve all points} \EndFor
\EndProcedure
\State
\Procedure{\textsc{UpdateHashTable}}{$z\in\mathbb{R}^d, i\in[n]$} \For{$l\in [L]$}
\State $\mathcal{H}_{l}(z)$.\textsc{Insert}($z$)\Comment{$\mathcal{H}_{l}(z)$ denotes the bucket that $z$ is mapped to}
\State $\mathcal{H}_{l}(x_i)$.\textsc{Delete}($x_i$) \EndFor
\EndProcedure
\State {\bf end data structure}
\end{algorithmic} | "https://arxiv.org/src/2208.03915" | "2208.03915.tar.gz" | "2024-02-13" | {
"title": "dynamic maintenance of kernel density estimation data structure: from practice to theory",
"id": "2208.03915",
"abstract": "kernel density estimation (kde) stands out as a challenging task in machine learning. the problem is defined in the following way: given a kernel function $f(x,y)$ and a set of points $\\{x_1, x_2, \\cdots, x_n \\} \\subset \\mathbb{r}^d$, we would like to compute $\\frac{1}{n}\\sum_{i=1}^{n} f(x_i,y)$ for any query point $y \\in \\mathbb{r}^d$. recently, there has been a growing trend of using data structures for efficient kde. however, the proposed kde data structures focus on static settings. the robustness of kde data structures over dynamic changing data distributions is not addressed. in this work, we focus on the dynamic maintenance of kde data structures with robustness to adversarial queries. especially, we provide a theoretical framework of kde data structures. in our framework, the kde data structures only require subquadratic spaces. moreover, our data structure supports the dynamic update of the dataset in sublinear time. furthermore, we can perform adaptive queries with the potential adversary in sublinear time.",
"categories": "cs.lg stat.ml",
"doi": "",
"created": "2022-08-08",
"updated": "2024-02-13",
"authors": [
"jiehao liang",
"zhao song",
"zhaozhuo xu",
"junze yin",
"danyang zhuo"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2208.03915"
} | "2024-03-15T05:43:39.046127" | {
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} | [] | "algorithm" | "87fe858d-35b2-4465-ba95-37fbdc8131e7" | 1925 | hard |
|
\begin{algorithm}
\caption{Penalized G-estimation algorithm}\label{penG.algorithm}
\begin{algorithmic}[1]
\Procedure{penalizedG}{$\vec A, \vec H, \vec Y, \lambda$,\,corstr,\,$\kappa$} %Put comment if you want: \Comment{The g.c.d. of a and b}
\State Compute $E(\vec A_i|\vec H_i)$ for $i=1,\ldots,n$ \Comment{logistic regression on the pooled data}
\State $\vec\theta^{\text{up}} \gets \{\sum_{i=1}^n\vec D_i^\top(\vec H_i\;\;\vec A_i\cdot\vec H_i)\}^{-1}\sum_{i=1}^n\vec D_i^\top \vec Y_i$ \Comment{univariate unpenalized G-estimator}
\ForAll{$\lambda \in (\lambda_{max}, \ldots, \lambda_{min})$} %\Comment{We have the answer if r is 0}
\State Initialize: $t = 0$, $\vec\theta^0 \gets \vec\theta^{\text{up}}$
\Repeat
\State $\vec e_i \gets \vec Y_i - (\vec H_i\;\;\vec A_i\cdot\vec H_i)\vec\theta^t$ for $i=1,\ldots,n$%\Comment{comment}
\State Compute $\sigma^t$ and $\alpha^t$ under corstr using \ref{moment.method} \Comment{method of moments estimator}
\State Compute $\hat{\vec V}_i$ according to corstr for $i=1,\ldots,n$ \Comment{$\hat{\vec V}_i=\hat{\vec V}$ $\forall i$ if $J$ is fixed}
\State Compute $\vec S^{\text{eff}}(\vec\theta^t)$ using (\ref{form})
\State Compute $\vec H_n(\vec\theta^t)$ and $\vec E_n(\vec\theta^t)$ using (\ref{eq.Hn}) and (\ref{eq.En}), respectively.
\State Update $\vec\theta^{t}$ according to (\ref{update.penalizedG}) and obtain $\vec\theta^{t+1}$
\State $t \gets t+1$
\Until{$||\vec\theta^{t} - \vec\theta^{t-1}|| < \kappa$}\Comment{we set $\kappa=10^{-4}$}
\State $\tilde{\vec\theta}_\lambda \gets \vec\theta^t$, $\tilde{\sigma}_\lambda \gets \sigma^t$, and $\tilde{\alpha}_\lambda \gets \alpha^t$
\State Compute $\text{DRIC}_{\lambda}$ according to (\ref{dric})
\EndFor
\State $\tilde{\vec\theta} \gets \tilde{\vec\theta}_\lambda^*$ such that $\tilde{\vec\theta}_\lambda^*$ corresponds to the minimum of $\text{DRIC}_{\lambda}$
\State \textbf{return} $\tilde{\vec\theta}$
\EndProcedure
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Penalized G-estimation algorithm}\begin{algorithmic}
[1]
\Procedure{penalizedG}{$\vec A, \vec H, \vec Y, \lambda$,\,corstr,\,$\kappa$} %Put comment if you want: \Comment{The g.c.d. of a and b}
\State Compute $E(\vec A_i|\vec H_i)$ for $i=1,\ldots,n$ \Comment{logistic regression on the pooled data}
\State $\vec\theta^{\text{up}} \gets \{\sum_{i=1}^n\vec D_i^\top(\vec H_i\;\;\vec A_i\cdot\vec H_i)\}^{-1}\sum_{i=1}^n\vec D_i^\top \vec Y_i$ \Comment{univariate unpenalized G-estimator}
\ForAll{$\lambda \in (\lambda_{max}, \ldots, \lambda_{min})$} %\Comment{We have the answer if r is 0}
\State Initialize: $t = 0$, $\vec\theta^0 \gets \vec\theta^{\text{up}}$
\Repeat
\State $\vec e_i \gets \vec Y_i - (\vec H_i\;\;\vec A_i\cdot\vec H_i)\vec\theta^t$ for $i=1,\ldots,n$%\Comment{comment}
\State Compute $\sigma^t$ and $\alpha^t$ under corstr using \ref{moment.method} \Comment{method of moments estimator}
\State Compute $\hat{\vec V}_i$ according to corstr for $i=1,\ldots,n$ \Comment{$\hat{\vec V}_i=\hat{\vec V}$ $\forall i$ if $J$ is fixed}
\State Compute $\vec S^{\text{eff}}(\vec\theta^t)$ using (\ref{form})
\State Compute $\vec H_n(\vec\theta^t)$ and $\vec E_n(\vec\theta^t)$ using (\ref{eq.Hn}) and (\ref{eq.En}), respectively.
\State Update $\vec\theta^{t}$ according to (\ref{update.penalizedG}) and obtain $\vec\theta^{t+1}$
\State $t \gets t+1$
\Until{$||\vec\theta^{t} - \vec\theta^{t-1}|| < \kappa$}\Comment{we set $\kappa=10^{-4}$}
\State $\tilde{\vec\theta}_\lambda \gets \vec\theta^t$, $\tilde{\sigma}_\lambda \gets \sigma^t$, and $\tilde{\alpha}_\lambda \gets \alpha^t$
\State Compute $\text{DRIC}_{\lambda}$ according to (\ref{dric})
\EndFor
\State $\tilde{\vec\theta} \gets \tilde{\vec\theta}_\lambda^*$ such that $\tilde{\vec\theta}_\lambda^*$ corresponds to the minimum of $\text{DRIC}_{\lambda}$
\State \textbf{return} $\tilde{\vec\theta}$
\EndProcedure
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2402.00154" | "2402.00154.tar.gz" | "2024-02-16" | {
"title": "penalized g-estimation for effect modifier selection in a structural nested mean model for repeated outcomes",
"id": "2402.00154",
"abstract": "effect modification occurs when the impact of the treatment on an outcome varies based on the levels of other covariates known as effect modifiers. modeling of these effect differences is important for etiological goals and for purposes of optimizing treatment. structural nested mean models (snmms) are useful causal models for estimating the potentially heterogeneous effect of a time-varying exposure on the mean of an outcome in the presence of time-varying confounding. a data-driven approach for selecting the effect modifiers of an exposure may be necessary if these effect modifiers are a priori unknown and need to be identified. although variable selection techniques are available in the context of estimating conditional average treatment effects using marginal structural models, or in the context of estimating optimal dynamic treatment regimens, all of these methods consider an outcome measured at a single point in time. in the context of an snmm for repeated outcomes, we propose a doubly robust penalized g-estimator for the causal effect of a time-varying exposure with a simultaneous selection of effect modifiers and use this estimator to analyze the effect modification in a study of hemodiafiltration. we prove the oracle property of our estimator, and conduct a simulation study for evaluation of its performance in finite samples and for verification of its double-robustness property. our work is motivated by and applied to the study of hemodiafiltration for treating patients with end-stage renal disease at the centre hospitalier de l'universit\\'e de montr\\'eal. we apply the proposed method to investigate the effect heterogeneity of dialysis facility on the repeated session-specific hemodiafiltration outcomes.",
"categories": "stat.me",
"doi": "",
"created": "2024-01-31",
"updated": "2024-02-16",
"authors": [
"ajmery jaman",
"guanbo wang",
"ashkan ertefaie",
"mich\u00e8le bally",
"ren\u00e9e l\u00e9vesque",
"robert w. platt",
"mireille e. schnitzer"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.00154"
} | "2024-03-15T05:18:15.887063" | {
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} | [] | "algorithm" | "24758dfb-f2c5-491c-a6b7-16eac0570e33" | 1938 | hard |
|
\begin{algorithmic}[1]
\While{$\mbox{bias}(\hat{\theta}_{0,p}, \tilde{\theta}_{b,p}) > 0.3 \times S_{p}$, for all $p$}
\State Sample $\theta_{n,p} \sim \mbox{Unif}(a_{1,p}, a_{2,p}), n = 1, \ldots, N$
\State Simulate $\mathbf{x}_n^* \sim p(;\boldsymbol{\theta}_n), n = 1, \ldots, N$
\State Train $\mathcal{F}_{\phi}(\mathbf{x})$ and obtain $\hat{\boldsymbol{\theta}}_0$ from $\mathcal{F}_{\hat{\phi}}(\mathbf{x}_0)$
\State Simulate $\mathbf{x}_b \sim p(;\hat{\boldsymbol{\theta}}_0)$ and obtain $\hat{\boldsymbol{\theta}}_{b}$ from $\mathcal{F}_{\hat{\phi}}(\mathbf{x}_b), b = 1, \ldots, B$
\State $a_{1,p} = \hat{\theta}_{0,p} + \mbox{bias}(\hat{\theta}_{0,p}, \tilde{\theta}_{p}) - \mathcal{Q}^{0.05}_p(\hat{\theta}_{0,p} - \theta^1_{p}, \ldots, \hat{\theta}_{0,p} -\theta^B_p)$
\State $a_{2,p} = \hat{\theta}_{0,p} + \mbox{bias}(\hat{\theta}_{0,p}, \tilde{\theta}_{p}) + \mathcal{Q}^{0.975}_p(\hat{\theta}_{0,p} - \theta^1_{p}, \ldots, \hat{\theta}_{0,p} -\theta^B_p)$
\State Increase $N$ by $5\%$
\EndWhile
\end{algorithmic}
| \begin{algorithmic}
[1]
\While{$\mbox{bias}(\hat{\theta}_{0,p}, \tilde{\theta}_{b,p}) > 0.3 \times S_{p}$, for all $p$}
\State Sample $\theta_{n,p} \sim \mbox{Unif}(a_{1,p}, a_{2,p}), n = 1, \ldots, N$
\State Simulate $\mathbf{x}_n^* \sim p(;\boldsymbol{\theta}_n), n = 1, \ldots, N$
\State Train $\mathcal{F}_{\phi}(\mathbf{x})$ and obtain $\hat{\boldsymbol{\theta}}_0$ from $\mathcal{F}_{\hat{\phi}}(\mathbf{x}_0)$
\State Simulate $\mathbf{x}_b \sim p(;\hat{\boldsymbol{\theta}}_0)$ and obtain $\hat{\boldsymbol{\theta}}_{b}$ from $\mathcal{F}_{\hat{\phi}}(\mathbf{x}_b), b = 1, \ldots, B$
\State $a_{1,p} = \hat{\theta}_{0,p} + \mbox{bias}(\hat{\theta}_{0,p}, \tilde{\theta}_{p}) - \mathcal{Q}^{0.05}_p(\hat{\theta}_{0,p} - \theta^1_{p}, \ldots, \hat{\theta}_{0,p} -\theta^B_p)$
\State $a_{2,p} = \hat{\theta}_{0,p} + \mbox{bias}(\hat{\theta}_{0,p}, \tilde{\theta}_{p}) + \mathcal{Q}^{0.975}_p(\hat{\theta}_{0,p} - \theta^1_{p}, \ldots, \hat{\theta}_{0,p} -\theta^B_p)$
\State Increase $N$ by $5\%$
\EndWhile
\end{algorithmic} | "https://arxiv.org/src/2303.15041" | "2303.15041.tar.gz" | "2024-02-19" | {
"title": "towards black-box parameter estimation",
"id": "2303.15041",
"abstract": "deep learning algorithms have recently shown to be a successful tool in estimating parameters of statistical models for which simulation is easy, but likelihood computation is challenging. but the success of these approaches depends on simulating parameters that sufficiently reproduce the observed data, and, at present, there is a lack of efficient methods to produce these simulations. we develop new black-box procedures to estimate parameters of statistical models based only on weak parameter structure assumptions. for well-structured likelihoods with frequent occurrences, such as in time series, this is achieved by pre-training a deep neural network on an extensive simulated database that covers a wide range of data sizes. for other types of complex dependencies, an iterative algorithm guides simulations to the correct parameter region in multiple rounds. these approaches can successfully estimate and quantify the uncertainty of parameters from non-gaussian models with complex spatial and temporal dependencies. the success of our methods is a first step towards a fully flexible automatic black-box estimation framework.",
"categories": "stat.ml cs.lg",
"doi": "",
"created": "2023-03-27",
"updated": "2024-02-19",
"authors": [
"amanda lenzi",
"haavard rue"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2303.15041"
} | "2024-03-15T05:01:49.289931" | {
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} | [] | "algorithm" | "c8268520-098b-4a66-8404-827a27550013" | 1029 | medium |
|
\begin{algorithmic}[1]
\State
Set $\mathcal{D} \gets \emptyset$ \Comment{{\it Initialize dataset.}}
\For{$t=1,\ldots, T$} \Comment{{\it Training $T$ rounds}}
\State $\beta_1,\ldots,\beta_M \sim P_{\text{exp}}(\beta)$ \Comment{{\it Sample temperatures from exploration query prior.}}
\For{$m=1,\ldots,M$}
\State $\tau_m \sim P_F(\tau|\beta = \beta_m;\theta)$ \Comment{{\it Sample trajectories from Logit-GFN.}}
\State $\mathcal{D} \gets \mathcal{D} \cup \{\tau_m\}$
\EndFor
\For{$k = 1, \ldots K$} \Comment{{\it Training $K$ epochs per each training rounds}}
\State Use ADAM for gradually minimizing $\mathcal{L}(\theta;\mathcal{D})$.
\EndFor
\EndFor
\State Output: $\mathcal{D}$
\end{algorithmic}
| \begin{algorithmic}
[1]
\State
Set $\mathcal{D} \gets \emptyset$ \Comment{{\it Initialize dataset.}}
\For{$t=1,\ldots, T$} \Comment{{\it Training $T$ rounds}}
\State $\beta_1,\ldots,\beta_M \sim P_{\text{exp}}(\beta)$ \Comment{{\it Sample temperatures from exploration query prior.}}
\For{$m=1,\ldots,M$}
\State $\tau_m \sim P_F(\tau|\beta = \beta_m;\theta)$ \Comment{{\it Sample trajectories from Logit-GFN.}}
\State $\mathcal{D} \gets \mathcal{D} \cup \{\tau_m\}$
\EndFor
\For{$k = 1, \ldots K$} \Comment{{\it Training $K$ epochs per each training rounds}}
\State Use ADAM for gradually minimizing $\mathcal{L}(\theta;\mathcal{D})$.
\EndFor
\EndFor
\State Output: $\mathcal{D}$
\end{algorithmic} | "https://arxiv.org/src/2310.02823" | "2310.02823.tar.gz" | "2024-02-04" | {
"title": "learning to scale logits for temperature-conditional gflownets",
"id": "2310.02823",
"abstract": "gflownets are probabilistic models that sequentially generate compositional structures through a stochastic policy. among gflownets, temperature-conditional gflownets can introduce temperature-based controllability for exploration and exploitation. we propose \\textit{logit-scaling gflownets} (logit-gfn), a novel architectural design that greatly accelerates the training of temperature-conditional gflownets. it is based on the idea that previously proposed approaches introduced numerical challenges in the deep network training, since different temperatures may give rise to very different gradient profiles as well as magnitudes of the policy's logits. we find that the challenge is greatly reduced if a learned function of the temperature is used to scale the policy's logits directly. also, using logit-gfn, gflownets can be improved by having better generalization capabilities in offline learning and mode discovery capabilities in online learning, which is empirically verified in various biological and chemical tasks. our code is available at \\url{https://github.com/dbsxodud-11/logit-gfn}",
"categories": "cs.lg stat.ml",
"doi": "",
"created": "2023-10-04",
"updated": "2024-02-04",
"authors": [
"minsu kim",
"joohwan ko",
"taeyoung yun",
"dinghuai zhang",
"ling pan",
"woochang kim",
"jinkyoo park",
"emmanuel bengio",
"yoshua bengio"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2310.02823"
} | "2024-03-15T07:30:57.250575" | {
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} | [] | "algorithm" | "ede6d8f2-a767-4b4f-8a0c-91464d30530a" | 697 | easy |
|
\begin{algorithmic}
\Function{Transport}{$\bold{M}, \boldsymbol{\beta},\bold{g}, \Delta t$} \Comment{Input moments, natural parameters, and gauge parameters for all cells}
\State $\boldsymbol{\beta}\gets \Call{NewtonOptimization}{\bold{M},\boldsymbol{\beta}, \boldsymbol{\phi}(\bold{u} ;\mathbf{g})}$ \Comment{Solve the natural parameters by Alg. \ref{Newton method} in the gauge $\mathbf{g}$}
\State $\bold{F} \gets \Call{ComputeFluxes}{\boldsymbol{\beta}, \boldsymbol{\phi}(\bold{u} ;\mathbf{g})}$\Comment{Compute fluxes of the statistics $\boldsymbol{\phi}(\bold{u} ;\mathbf{g})$ by \eqref{The ME equation:subeq3} }
\State $\bold{M}_{\pm1}, \bold{F}_{\pm1} \gets \Call{SpatialGaugeTransformation}{\bold{M}, \bold{F}, \bold{g}}$\Comment{Perform gauge transformation as in \eqref{The lax F convert} }
\State $\bold{M} \gets \Call{FiniteVolumeStep}{\bold{M}, \bold{F},\bold{M}_{\pm1}, \bold{F}_{\pm1}, \bold{g}, \Delta t}$\Comment{One step forward in time by \eqref{The ME equation fvm 2} }
\State \textbf{return} $\bold{M}, \boldsymbol{\beta}, \bold{g}$
\EndFunction
\Function{Collision}{$\bold{M}, \boldsymbol{\beta},\bold{g}, \Delta t$} \Comment{Input moments, natural parameters, and gauge parameters for all cells}
\State $\bold{M} \gets \Call{SourceTerm}{\bold{M}, \bold{g}, \Delta t}$\Comment{Compute source term by operator splitting \eqref{source update} }
\State \textbf{return} $\bold{M}, \boldsymbol{\beta}, \bold{g}$
\EndFunction
\Function{Step}{$\bold{M}, \boldsymbol{\beta},\bold{g}$} \Comment{Input moments, natural parameters, and gauge parameters for all cells}
\State $\bold{M}, \boldsymbol{\beta}, \bold{g} \gets \Call{Collision}{\bold{M},\boldsymbol{\beta},\bold{g}, \Delta t/2}$\Comment{Compute collision term by operator splitting}
\State $\bold{M}, \boldsymbol{\beta}, \bold{g} \gets \Call{Transport}{\bold{M},\boldsymbol{\beta},\bold{g}, \Delta t}$\Comment{Compute Transport term by operator splitting}
\State $\bold{M}, \boldsymbol{\beta}, \bold{g} \gets \Call{Collision}{\bold{M},\boldsymbol{\beta},\bold{g}, \Delta t/2}$\Comment{Compute collision term by operator splitting}
\State $\bold{g}_H \gets \Call{ComputeGaugeParameters}{\bold{M}, \bold{g}}$\Comment{Compute the Hermite gauge parameters by \eqref{Hermite parameters in moments} }
\State $\bold{M}_H,\boldsymbol{\beta}_H \gets \Call{GaugeTransformation}{\bold{M}, \boldsymbol{\beta}, \bold{g}_H, \bold{g}}$\Comment{Transform into the Hermite gauge using \eqref{Change gauge M F} and \eqref{Maximal Likelihood equation for Exponential Family Distributions: form transformation}}
\State \textbf{return} $\bold{M}_H, \boldsymbol{\beta}_H, \bold{g}_H$
\EndFunction
\end{algorithmic}
| \begin{algorithmic}
\Function{Transport}{$\bold{M}, \boldsymbol{\beta},\bold{g}, \Delta t$} \Comment{Input moments, natural parameters, and gauge parameters for all cells}
\State $\boldsymbol{\beta}\gets \Call{NewtonOptimization}{\bold{M},\boldsymbol{\beta}, \boldsymbol{\phi}(\bold{u} ;\mathbf{g})}$ \Comment{Solve the natural parameters by Alg. \ref{Newton method} in the gauge $\mathbf{g}$}
\State $\bold{F} \gets \Call{ComputeFluxes}{\boldsymbol{\beta}, \boldsymbol{\phi}(\bold{u} ;\mathbf{g})}$\Comment{Compute fluxes of the statistics $\boldsymbol{\phi}(\bold{u} ;\mathbf{g})$ by \eqref{The ME equation:subeq3} }
\State $\bold{M}_{\pm1}, \bold{F}_{\pm1} \gets \Call{SpatialGaugeTransformation}{\bold{M}, \bold{F}, \bold{g}}$\Comment{Perform gauge transformation as in \eqref{The lax F convert} }
\State $\bold{M} \gets \Call{FiniteVolumeStep}{\bold{M}, \bold{F},\bold{M}_{\pm1}, \bold{F}_{\pm1}, \bold{g}, \Delta t}$\Comment{One step forward in time by \eqref{The ME equation fvm 2} }
\State \textbf{return} $\bold{M}, \boldsymbol{\beta}, \bold{g}$
\EndFunction
\Function{Collision}{$\bold{M}, \boldsymbol{\beta},\bold{g}, \Delta t$} \Comment{Input moments, natural parameters, and gauge parameters for all cells}
\State $\bold{M} \gets \Call{SourceTerm}{\bold{M}, \bold{g}, \Delta t}$\Comment{Compute source term by operator splitting \eqref{source update} }
\State \textbf{return} $\bold{M}, \boldsymbol{\beta}, \bold{g}$
\EndFunction
\Function{Step}{$\bold{M}, \boldsymbol{\beta},\bold{g}$} \Comment{Input moments, natural parameters, and gauge parameters for all cells}
\State $\bold{M}, \boldsymbol{\beta}, \bold{g} \gets \Call{Collision}{\bold{M},\boldsymbol{\beta},\bold{g}, \Delta t/2}$\Comment{Compute collision term by operator splitting}
\State $\bold{M}, \boldsymbol{\beta}, \bold{g} \gets \Call{Transport}{\bold{M},\boldsymbol{\beta},\bold{g}, \Delta t}$\Comment{Compute Transport term by operator splitting}
\State $\bold{M}, \boldsymbol{\beta}, \bold{g} \gets \Call{Collision}{\bold{M},\boldsymbol{\beta},\bold{g}, \Delta t/2}$\Comment{Compute collision term by operator splitting}
\State $\bold{g}_H \gets \Call{ComputeGaugeParameters}{\bold{M}, \bold{g}}$\Comment{Compute the Hermite gauge parameters by \eqref{Hermite parameters in moments} }
\State $\bold{M}_H,\boldsymbol{\beta}_H \gets \Call{GaugeTransformation}{\bold{M}, \boldsymbol{\beta}, \bold{g}_H, \bold{g}}$\Comment{Transform into the Hermite gauge using \eqref{Change gauge M F} and \eqref{Maximal Likelihood equation for Exponential Family Distributions: form transformation}}
\State \textbf{return} $\bold{M}_H, \boldsymbol{\beta}_H, \bold{g}_H$
\EndFunction
\end{algorithmic} | "https://arxiv.org/src/2303.02898" | "2303.02898.tar.gz" | "2024-02-19" | {
"title": "stabilizing the maximal entropy moment method for rarefied gas dynamics at single-precision",
"id": "2303.02898",
"abstract": "the maximal entropy moment method (mem) is systematic solution of the challenging problem: generating extended hydrodynamic equations valid for both dense and rarefied gases. however, simulating mem suffers from a computational expensive and ill-conditioned maximal entropy problem. it causes numerical overflow and breakdown when the numerical precision is insufficient, especially for flows like high-speed shock waves. it also prevents modern gpus from accelerating mem with their enormous single floating-point precision computation power. this paper aims to stabilize mem, making it possible to simulating very strong normal shock waves on modern gpus at single precision. we improve the condition number of the maximal entropy problem by proposing gauge transformations, which moves not only flow fields but also hydrodynamic equations into a more optimal coordinate system. we addressed numerical overflow and breakdown in the maximal entropy problem by employing the canonical form of distribution and a modified newton optimization method. moreover, we discovered a counter-intuitive phenomenon that over-refined spatial mesh beyond mean free path degrades the stability of mem. with these techniques, we accomplished single-precision gpu simulations of high speed shock wave up to mach 10 utilizing 35 moments mem, while previous methods only achieved mach 4 on double-precision.",
"categories": "physics.flu-dyn cs.lg",
"doi": "",
"created": "2023-03-06",
"updated": "2024-02-19",
"authors": [
"candi zheng",
"wang yang",
"shiyi chen"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2303.02898"
} | "2024-03-15T03:56:31.323537" | {
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} | [] | "algorithm" | "c7b25e2d-eada-4336-adc6-ccf52d67f217" | 2664 | hard |
|
\begin{algorithmic}[1]
\State Inputs: $M, K, \epsilon, \mathcal{P}$ (the page dataset)
\State $H_P := \varnothing, \forall P\in \mathcal{P}$
\State $\mathrm{nn\_model} := \mathrm{model\_init}()$
\For {$epoch = 1,2,\ldots$}
\State $S_{train} := \varnothing$
\For {\textbf{each} webpage $P \in \mathcal{P}$}
\State $P\triangleq (V, E)$, $V\triangleq V_{labelled}\cup V_{unlabelled}$
\State $S_P := \mathrm{UniformRand}(V_{unlabelled}, \mathrm{n_{samples}}=M)$
\If {$epoch = K$} %\Comment{At epoch $K$, add \emph{hard} elements to training}
\For {$l:=1,\dots, L$}
\State $preds = \{\mathrm{nn\_model}(v)[l], \forall
\mathrm{elements}\ v\in V\})$
\State $H_P := H_P\cup\mathrm{rank}(preds)[:K]$
\EndFor
\EndIf
\State $S_{train} := S_{train}\cup S_P \cup V_{labelled} \cup H_P$
\EndFor
\State Train nn\_model for $1$ epoch on dataset $S_{train}$.
\EndFor
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Inputs: $M, K, \epsilon, \mathcal{P}$ (the page dataset)
\State $H_P := \varnothing, \forall P\in \mathcal{P}$
\State $\mathrm{nn\_model} := \mathrm{model\_init}()$
\For {$epoch = 1,2,\ldots$}
\State $S_{train} := \varnothing$
\For {\textbf{each} webpage $P \in \mathcal{P}$}
\State $P\triangleq (V, E)$, $V\triangleq V_{labelled}\cup V_{unlabelled}$
\State $S_P := \mathrm{UniformRand}(V_{unlabelled}, \mathrm{n_{samples}}=M)$
\If {$epoch = K$} %\Comment{At epoch $K$, add \emph{hard} elements to training}
\For {$l:=1,\dots, L$}
\State $preds = \{\mathrm{nn\_model}(v)[l], \forall
\mathrm{elements}\ v\in V\})$
\State $H_P := H_P\cup\mathrm{rank}(preds)[:K]$
\EndFor
\EndIf
\State $S_{train} := S_{train}\cup S_P \cup V_{labelled} \cup H_P$
\EndFor
\State Train nn\_model for $1$ epoch on dataset $S_{train}$.
\EndFor
\end{algorithmic} | "https://arxiv.org/src/2111.02168" | "2111.02168.tar.gz" | "2024-02-23" | {
"title": "the klarna product page dataset: web element nomination with graph neural networks and large language models",
"id": "2111.02168",
"abstract": "web automation holds the potential to revolutionize how users interact with the digital world, offering unparalleled assistance and simplifying tasks via sophisticated computational methods. central to this evolution is the web element nomination task, which entails identifying unique elements on webpages. unfortunately, the development of algorithmic designs for web automation is hampered by the scarcity of comprehensive and realistic datasets that reflect the complexity faced by real-world applications on the web. to address this, we introduce the klarna product page dataset, a comprehensive and diverse collection of webpages that surpasses existing datasets in richness and variety. the dataset features 51,701 manually labeled product pages from 8,175 e-commerce websites across eight geographic regions, accompanied by a dataset of rendered page screenshots. to initiate research on the klarna product page dataset, we empirically benchmark a range of graph neural networks (gnns) on the web element nomination task. we make three important contributions. first, we found that a simple convolutional gnn (gcn) outperforms complex state-of-the-art nomination methods. second, we introduce a training refinement procedure that involves identifying a small number of relevant elements from each page using the aforementioned gcn. these elements are then passed to a large language model for the final nomination. this procedure significantly improves the nomination accuracy by 16.8 percentage points on our challenging dataset, without any need for fine-tuning. finally, in response to another prevalent challenge in this field - the abundance of training methodologies suitable for element nomination - we introduce the challenge nomination training procedure, a novel training approach that further boosts nomination accuracy.",
"categories": "cs.lg cs.cl cs.cv cs.hc cs.ir",
"doi": "",
"created": "2021-11-03",
"updated": "2024-02-23",
"authors": [
"alexandra hotti",
"riccardo sven risuleo",
"stefan magureanu",
"aref moradi",
"jens lagergren"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2111.02168"
} | "2024-03-15T02:50:08.214851" | {
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} | [] | "algorithm" | "79f588ba-e2cf-48bd-9b7a-8b1338fded12" | 868 | medium |
|
\begin{algorithmic}[1]
\Require Observations, history $d_{1:2} = (d_1, d_2)$, {\tt model} $\in$ {\tt \{full interactions, linear\}}.
\If{{\tt model} $=$ {\tt full interactions}}
\State Estimate $\beta_{d_{1:2}}^{(2)} $ by regressing $Y_{i,2}$ onto $H_{i,2}$ for all $i: (D_{i, 1:2} = d_{1:2})$;
\State Estimate $\beta_{d_{1:2}}^{(1)} $ by regression $H_{i,2} \hat{\beta}_{d_{1:2}}^2$ onto $X_{i,1}$ for $i$ that has $D_{i,1} = d_{1}$.
\Else
\State Estimate $\beta^{(2)} $ by regressing $Y_{i,2}$ onto $(H_{i,2}, D_{i,2})$ for all $i$ (without penalizing $(D_{i,1}, D_{i,2})$) and define $H_{i,2} \hat{\beta}_{d_1, d_2} = (H_{i,2}, d_2) \hat{\beta}^{(2)}$ for all $i: D_{i,1} = d_1$ ;
\State Estimate $\beta^{(1)} $ by regressing $(H_{i,2}, d_2) \hat{\beta}^2$ onto $(X_{i,1}, D_{i,1})$ for all $i$ (without penalizing $D_{i,1}$) and define $X_{i,1} \hat{\beta}_{d_1, d_2}^{(1)} = (X_{i,1}, d_1)\hat{\beta}^{(1)}$ for all $i$.
\EndIf
\end{algorithmic}
| \begin{algorithmic}
[1]
\Require Observations, history $d_{1:2} = (d_1, d_2)$, {\tt model} $\in$ {\tt \{full interactions, linear\}}.
\If{{\tt model} $=$ {\tt full interactions}}
\State Estimate $\beta_{d_{1:2}}^{(2)} $ by regressing $Y_{i,2}$ onto $H_{i,2}$ for all $i: (D_{i, 1:2} = d_{1:2})$;
\State Estimate $\beta_{d_{1:2}}^{(1)} $ by regression $H_{i,2} \hat{\beta}_{d_{1:2}}^2$ onto $X_{i,1}$ for $i$ that has $D_{i,1} = d_{1}$.
\Else
\State Estimate $\beta^{(2)} $ by regressing $Y_{i,2}$ onto $(H_{i,2}, D_{i,2})$ for all $i$ (without penalizing $(D_{i,1}, D_{i,2})$) and define $H_{i,2} \hat{\beta}_{d_1, d_2} = (H_{i,2}, d_2) \hat{\beta}^{(2)}$ for all $i: D_{i,1} = d_1$ ;
\State Estimate $\beta^{(1)} $ by regressing $(H_{i,2}, d_2) \hat{\beta}^2$ onto $(X_{i,1}, D_{i,1})$ for all $i$ (without penalizing $D_{i,1}$) and define $X_{i,1} \hat{\beta}_{d_1, d_2}^{(1)} = (X_{i,1}, d_1)\hat{\beta}^{(1)}$ for all $i$.
\EndIf
\end{algorithmic} | "https://arxiv.org/src/2103.01280" | "2103.01280.tar.gz" | "2024-01-26" | {
"title": "dynamic covariate balancing: estimating treatment effects over time with potential local projections",
"id": "2103.01280",
"abstract": "this paper studies the estimation and inference of treatment histories in panel data settings when treatments change dynamically over time. we propose a method that allows for (i) treatments to be assigned dynamically over time based on high-dimensional covariates, past outcomes and treatments; (ii) outcomes and time-varying covariates to depend on treatment trajectories; (iii) heterogeneity of treatment effects. our approach recursively projects potential outcomes' expectations on past histories. it then controls the bias by balancing dynamically observable characteristics. we study the asymptotic and numerical properties of the estimator and illustrate the benefits of the procedure in an empirical application.",
"categories": "econ.em math.st stat.me stat.ml stat.th",
"doi": "",
"created": "2021-03-01",
"updated": "2024-01-26",
"authors": [
"davide viviano",
"jelena bradic"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2103.01280"
} | "2024-03-15T05:21:52.236887" | {
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} | [] | "algorithm" | "8775e21c-b899-489a-b60e-4c9afec1f0ef" | 951 | medium |
|
\begin{algorithm}[h]
\caption{Particle Filter}
\label{alg:pf}
\begin{enumerate}
\item{Input: data $y_{1:T}$, level $l\in\mathbb{N}_0$, particle number $N\in\mathbb{N}$ and parameter $\theta\in\Theta$.}
\item{Initialize: For $i\in\{1,\dots,N\}$, independently generate $\overline{W}_{\Delta_l:1}^i$ from $\mathcal{N}(0,\Delta_l)$. Set $t=1$, {$\hat{p}^N(y_{1:0})=1$ for convention} and go to step 3.}
\item{Iterate: For $i\in\{1,\dots,N\}$ compute
$$
u_t^i = \frac{\kappa_{t,l}(\overline{w}_{\Delta_l:t}^i)}{\sum_{j=1}^N\kappa_{t,l}(\overline{w}_{\Delta_l:t}^j)}.
$$
Set $\hat{p}^N(y_{1:t})={\hat{p}^N(y_{1:t-1})}\tfrac{1}{N}\sum_{i=1}^N\kappa_{t,l}(\overline{w}_{\Delta_l:t}^i)$.
Then sample $\overline{w}_{\Delta_l:t}^{1:N}$ with replacement from $\overline{w}_{\Delta_l:t}^{1:N}$ using probabilities
$u_t^{1:N}$. For $i\in\{1,\dots,N\}$, independently generate $\overline{W}_{t+\Delta_l:t+1}^i$ from $\mathcal{N}(0,\Delta_l)$.
Set $t=t+1$ and if $t=T$ go to step 4, otherwise restart step 3.}
\item{Grand Selection: For $i\in\{1,\dots,N\}$ compute
$
u_T^i = \frac{\kappa_{T,l}(\overline{w}_{\Delta_l:T}^i)}{\sum_{j=1}^N\kappa_{T,l}(\overline{w}_{\Delta_l:T}^j)}.
$
Set $\hat{p}^N(y_{1:T})=\hat{p}^N(y_{1:T-1})\tfrac{1}{N}\sum_{i=1}^N\kappa_{t,l}(\overline{w}_{\Delta_l:T}^i)$.
Sample one $\overline{w}_{\Delta_l:T}$ from $\overline{w}_{\Delta_l:T}^{1:N}$ using $u_T^{1:N}$ and go to step 5.}
\item{Output: trajectory $\overline{w}_{\Delta_l:T}$ and normalizing constant estimate $\hat{p}^N(y_{1:T})$.}
\end{enumerate}
\end{algorithm}
| \begin{algorithm}
[h]
\caption{Particle Filter}
\begin{enumerate}
\item{Input: data $y_{1:T}$, level $l\in\mathbb{N}_0$, particle number $N\in\mathbb{N}$ and parameter $\theta\in\Theta$.}
\item{Initialize: For $i\in\{1,\dots,N\}$, independently generate $\overline{W}_{\Delta_l:1}^i$ from $\mathcal{N}(0,\Delta_l)$. Set $t=1$, {$\hat{p}^N(y_{1:0})=1$ for convention} and go to step 3.}
\item{Iterate: For $i\in\{1,\dots,N\}$ compute
$$
u_t^i = \frac{\kappa_{t,l}(\overline{w}_{\Delta_l:t}^i)}{\sum_{j=1}^N\kappa_{t,l}(\overline{w}_{\Delta_l:t}^j)}.
$$
Set $\hat{p}^N(y_{1:t})={\hat{p}^N(y_{1:t-1})}\tfrac{1}{N}\sum_{i=1}^N\kappa_{t,l}(\overline{w}_{\Delta_l:t}^i)$.
Then sample $\overline{w}_{\Delta_l:t}^{1:N}$ with replacement from $\overline{w}_{\Delta_l:t}^{1:N}$ using probabilities
$u_t^{1:N}$. For $i\in\{1,\dots,N\}$, independently generate $\overline{W}_{t+\Delta_l:t+1}^i$ from $\mathcal{N}(0,\Delta_l)$.
Set $t=t+1$ and if $t=T$ go to step 4, otherwise restart step 3.}
\item{Grand Selection: For $i\in\{1,\dots,N\}$ compute
$
u_T^i = \frac{\kappa_{T,l}(\overline{w}_{\Delta_l:T}^i)}{\sum_{j=1}^N\kappa_{T,l}(\overline{w}_{\Delta_l:T}^j)}.
$
Set $\hat{p}^N(y_{1:T})=\hat{p}^N(y_{1:T-1})\tfrac{1}{N}\sum_{i=1}^N\kappa_{t,l}(\overline{w}_{\Delta_l:T}^i)$.
Sample one $\overline{w}_{\Delta_l:T}$ from $\overline{w}_{\Delta_l:T}^{1:N}$ using $u_T^{1:N}$ and go to step 5.}
\item{Output: trajectory $\overline{w}_{\Delta_l:T}$ and normalizing constant estimate $\hat{p}^N(y_{1:T})$.}
\end{enumerate}
\end{algorithm} | "https://arxiv.org/src/2310.03114" | "2310.03114.tar.gz" | "2024-02-19" | {
"title": "bayesian parameter inference for partially observed stochastic volterra equations",
"id": "2310.03114",
"abstract": "in this article we consider bayesian parameter inference for a type of partially observed stochastic volterra equation (sve). sves are found in many areas such as physics and mathematical finance. in the latter field they can be used to represent long memory in unobserved volatility processes. in many cases of practical interest, sves must be time-discretized and then parameter inference is based upon the posterior associated to this time-discretized process. based upon recent studies on time-discretization of sves (e.g. richard et al. 2021), we use euler-maruyama methods for the afore-mentioned discretization. we then show how multilevel markov chain monte carlo (mcmc) methods (jasra et al. 2018) can be applied in this context. in the examples we study, we give a proof that shows that the cost to achieve a mean square error (mse) of $\\mathcal{o}(\\epsilon^2)$, $\\epsilon>0$, is {$\\mathcal{o}(\\epsilon^{-\\tfrac{4}{2h+1}})$, where $h$ is the hurst parameter. if one uses a single level mcmc method then the cost is $\\mathcal{o}(\\epsilon^{-\\tfrac{2(2h+3)}{2h+1}})$} to achieve the same mse. we illustrate these results in the context of state-space and stochastic volatility models, with the latter applied to real data.",
"categories": "stat.co stat.me",
"doi": "",
"created": "2023-10-04",
"updated": "2024-02-19",
"authors": [
"ajay jasra",
"hamza ruzayqat",
"amin wu"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2310.03114"
} | "2024-03-15T05:09:03.161347" | {
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} | [] | "algorithm" | "1659b1f9-da27-461f-82a7-7289e2470234" | 1521 | hard |
|
\begin{algorithmic}[1]
\Require{$\{(A_i,Y_i)\}_{i=1}^m$ , $\delta \in (0,1)$}{}
\State Set $k=1$, and $U_k = V$
\While{$|U_k|>1$}
\For{$u \in U_k$ }
\State $X_i=A_{i}(U_{k})[u,\cdot]$
\State $\beta(u) = Dcor(\{X_i,Y_i\}_{i=1}^m )$
\EndFor
\State Set $t$ be the $\delta$ quantile among $\{\beta(u), u \in U_k\}$
\State Set $U_{k+1} = \{u \in U_k|\beta(u) > t\}$
\State Set $k = k+1$
\EndWhile
\State $k^{*}=\arg\max_{k} Dcor(\{(A_{i}(U_{k}),Y_i)\}_{i=1}^{m})$
\State Output the signal vertices $\hat{S} = U_{k^{*}}$.
\end{algorithmic}
| \begin{algorithmic}
[1]
\Require{$\{(A_i,Y_i)\}_{i=1}^m$ , $\delta \in (0,1)$}{}
\State Set $k=1$, and $U_k = V$
\While{$|U_k|>1$}
\For{$u \in U_k$ }
\State $X_i=A_{i}(U_{k})[u,\cdot]$
\State $\beta(u) = Dcor(\{X_i,Y_i\}_{i=1}^m )$
\EndFor
\State Set $t$ be the $\delta$ quantile among $\{\beta(u), u \in U_k\}$
\State Set $U_{k+1} = \{u \in U_k|\beta(u) > t\}$
\State Set $k = k+1$
\EndWhile
\State $k^{*}=\arg\max_{k} Dcor(\{(A_{i}(U_{k}),Y_i)\}_{i=1}^{m})$
\State Output the signal vertices $\hat{S} = U_{k^{*}}$.
\end{algorithmic} | "https://arxiv.org/src/1801.07683" | "1801.07683.tar.gz" | "2024-02-05" | {
"title": "discovering the signal subgraph: an iterative screening approach on graphs",
"id": "1801.07683",
"abstract": "supervised learning on graphs is a challenging task due to the high dimensionality and inherent structural dependencies in the data, where each edge depends on a pair of vertices. existing conventional methods designed for euclidean data do not account for this graph dependency structure. to address this issue, this paper proposes an iterative vertex screening method to identify the signal subgraph that is most informative for the given graph attributes. the method screens the rows and columns of the adjacency matrix concurrently and stops when the resulting distance correlation is maximized. we establish the theoretical foundation of our method by proving that it estimates the true signal subgraph with high probability. additionally, we establish the convergence rate of classification error under the erdos-renyi random graph model and prove that the subsequent classification can be asymptotically optimal, outperforming the entire graph under high-dimensional conditions. our method is evaluated on various simulated datasets and real-world human and murine graphs derived from functional and structural magnetic resonance images. the results demonstrate its excellent performance in estimating the ground-truth signal subgraph and achieving superior classification accuracy.",
"categories": "stat.me",
"doi": "",
"created": "2018-01-23",
"updated": "2024-02-05",
"authors": [
"cencheng shen",
"shangsi wang",
"alexandra badea",
"carey e. priebe",
"joshua t. vogelstein"
],
"affiliation": [],
"url": "https://arxiv.org/abs/1801.07683"
} | "2024-03-15T06:55:05.801196" | {
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} | [] | "algorithm" | "982d67a9-cb83-40df-81dd-501d13c15bf7" | 534 | easy |
|
\begin{algorithm}[t]
\small
\caption{On-the-fly DA Denoising (ODDA)}\label{alg:alg}
\begin{tabular}{p{2em}p{20em}}
\textbf{Input:} & Teacher model $f_T(\cdot)$, student model $f(\cdot)$, original dataset $\mathcal{D}=\{(x_i, y_i)\}, i=1,\cdots,n$, augmented dataset $\mathcal{D}'=\{(x_i', y_i')\}, i=1,\cdots,kn$, OD temperature $\tau$, SR coefficient $\alpha$. Max training steps for the organic teacher $s_T$ and the student $s_S$. \\
\textbf{Output:} & \hspace{0.5em} The trained student model $f(\cdot)$ \\
\end{tabular}
\begin{algorithmic}[1]
\State Initialize the teacher model $f_T(\cdot)$
\State $s \gets 0$ \Comment{Training steps for OD}
\While{$s < s_T$}
\State Sample a batch $\mathcal{B}$ from $\{(x_i, y_i)\}$
\State Train $f_T(\cdot)$ with cross-entropy loss on $\mathcal{B}$
\EndWhile
\State $s \gets 0$ \Comment{Training steps for Denoising}
\State $\mathcal{D}^+ \gets \{(x_i, y_i)\} \cup \{(x_i', y_i')\}$ \Comment{Mix $\mathcal{D}$ \& $\mathcal{D}'$}
\While{$s < s_S$}
\State Sample a batch $\mathcal{B}'$ from $\mathcal{D}^+$
\State Train $f(\cdot)$ with loss in Eq.~(\ref{eq:overall_loss}) on $\mathcal{B}'$ with Organic Distillation and Self-Regularization to do deonising
\EndWhile
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[t]
\small
\caption{On-the-fly DA Denoising (ODDA)}\begin{tabular}
{p{2em}p{20em}}
\textbf{Input:} & Teacher model $f_T(\cdot)$, student model $f(\cdot)$, original dataset $\mathcal{D}=\{(x_i, y_i)\}, i=1,\cdots,n$, augmented dataset $\mathcal{D}'=\{(x_i', y_i')\}, i=1,\cdots,kn$, OD temperature $\tau$, SR coefficient $\alpha$. Max training steps for the organic teacher $s_T$ and the student $s_S$. \\
\textbf{Output:} & \hspace{0.5em} The trained student model $f(\cdot)$ \\
\end{tabular}
\begin{algorithmic}
[1]
\State Initialize the teacher model $f_T(\cdot)$
\State $s \gets 0$ \Comment{Training steps for OD}
\While{$s < s_T$}
\State Sample a batch $\mathcal{B}$ from $\{(x_i, y_i)\}$
\State Train $f_T(\cdot)$ with cross-entropy loss on $\mathcal{B}$
\EndWhile
\State $s \gets 0$ \Comment{Training steps for Denoising}
\State $\mathcal{D}^+ \gets \{(x_i, y_i)\} \cup \{(x_i', y_i')\}$ \Comment{Mix $\mathcal{D}$ \& $\mathcal{D}'$}
\While{$s < s_S$}
\State Sample a batch $\mathcal{B}'$ from $\mathcal{D}^+$
\State Train $f(\cdot)$ with loss in Eq.~(\ref{eq:overall_loss}) on $\mathcal{B}'$ with Organic Distillation and Self-Regularization to do deonising
\EndWhile
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2212.10558" | "2212.10558.tar.gz" | "2024-01-31" | {
"title": "on-the-fly denoising for data augmentation in natural language understanding",
"id": "2212.10558",
"abstract": "data augmentation (da) is frequently used to provide additional training data without extra human annotation automatically. however, data augmentation may introduce noisy data that impairs training. to guarantee the quality of augmented data, existing methods either assume no noise exists in the augmented data and adopt consistency training or use simple heuristics such as training loss and diversity constraints to filter out \"noisy\" data. however, those filtered examples may still contain useful information, and dropping them completely causes a loss of supervision signals. in this paper, based on the assumption that the original dataset is cleaner than the augmented data, we propose an on-the-fly denoising technique for data augmentation that learns from soft augmented labels provided by an organic teacher model trained on the cleaner original data. to further prevent overfitting on noisy labels, a simple self-regularization module is applied to force the model prediction to be consistent across two distinct dropouts. our method can be applied to general augmentation techniques and consistently improve the performance on both text classification and question-answering tasks.",
"categories": "cs.cl cs.ai",
"doi": "",
"created": "2022-12-20",
"updated": "2024-01-31",
"authors": [
"tianqing fang",
"wenxuan zhou",
"fangyu liu",
"hongming zhang",
"yangqiu song",
"muhao chen"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2212.10558"
} | "2024-03-15T08:24:23.744468" | {
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} | [] | "algorithm" | "0b2cd615-032c-4ee5-8359-9d6c4bc16d55" | 1226 | hard |
|
\begin{algorithm}
\caption{Algorithm for detecting equilibrium}\label{algo2}
\begin{algorithmic}[1]
\State Initialize an empty list $l$
\For{\textbf{each} $i$ \textbf{in} $producers$}
\For{$t$ \textbf{in} $[500, 900)$}
\If{$\forall x \in \{p_{it},p_{i(t+1)},\dots,p_{i1000}\}(x < \epsilon)$}
\State $l$\textbf{.push}(True)
\State \textbf{break}
\EndIf
\EndFor
\State $l$\textbf{.push}(False)
\EndFor
\If{$\forall \text{y} \in l$\text{(y==True)}}
\State \textbf{return} $"Equilibrium"$
\Else
\State \textbf{return} $"Disequilibrium"$
\EndIf
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Algorithm for detecting equilibrium}\begin{algorithmic}
[1]
\State Initialize an empty list $l$
\For{\textbf{each} $i$ \textbf{in} $producers$}
\For{$t$ \textbf{in} $[500, 900)$}
\If{$\forall x \in \{p_{it},p_{i(t+1)},\dots,p_{i1000}\}(x < \epsilon)$}
\State $l$\textbf{.push}(True)
\State \textbf{break}
\EndIf
\EndFor
\State $l$\textbf{.push}(False)
\EndFor
\If{$\forall \text{y} \in l$\text{(y==True)}}
\State \textbf{return} $"Equilibrium"$
\Else
\State \textbf{return} $"Disequilibrium"$
\EndIf
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2401.07070" | "2401.07070.tar.gz" | "2024-01-13" | {
"title": "a dynamic agent based model of the real economy with monopolistic competition, perfect product differentiation, heterogeneous agents, increasing returns to scale and trade in disequilibrium",
"id": "2401.07070",
"abstract": "we have used agent-based modeling as our numerical method to artificially simulate a dynamic real economy where agents are rational maximizers of an objective function of cobb-douglas type. the economy is characterised by heterogeneous agents, acting out of local or imperfect information, monopolistic competition, perfect product differentiation, allowance for increasing returns to scale technology and trade in disequilibrium. an algorithm for economic activity in each period is devised and a general purpose open source agent-based model is developed which allows for counterfactual inquiries, testing out treatments, analysing causality of various economic processes, outcomes and studying emergent properties. 10,000 simulations, with 10 firms and 80 consumers are run with varying parameters and the results show that from only a few initial conditions the economy reaches equilibrium while in most of the other cases it remains in perpetual disequilibrium. it also shows that from a few initial conditions the economy reaches a disaster where all the consumer wealth falls to zero or only a single producer remains. furthermore, from some initial conditions, an ideal economy with high wage rate, high consumer utility and no unemployment is also reached. it was also observed that starting from an equal endowment of wealth in consumers and in producers, inequality emerged in the economy. in majority of the cases most of the firms(6-7) shut down because they were not profitable enough and only a few firms remained. our results highlight that all these varying outcomes are possible for a decentralized market economy with rational optimizing agents.",
"categories": "econ.th cs.ma",
"doi": "",
"created": "2024-01-13",
"updated": "",
"authors": [
"subhamon supantha",
"naresh kumar sharma"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.07070"
} | "2024-03-15T06:13:08.276479" | {
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} | [] | "algorithm" | "65962d6b-c013-4a90-b2ed-f36af9e242dc" | 560 | easy |
|
\begin{algorithmic}
\State \textbf{Input:} Two graphs $\mathcal{G}=(V, E, \boldsymbol{X})$ and $\mathcal{H}=(P, F, \boldsymbol{Y})$
\State $c_{\boldsymbol{v}}^{(0)} \leftarrow \textsc{Hash}(\mathcal{G}[\boldsymbol{v}]), \forall \boldsymbol{v} \in V^k$
\State $d_{\boldsymbol{p}}^{(0)} \leftarrow \textsc{Hash}(\mathcal{H}[\boldsymbol{p}]), \forall \boldsymbol{p} \in P^k$
\Repeat \ ($\ell=1,2,\cdots$)
\If{$\{\!\{c_{\boldsymbol{v}}^{(\ell-1)}|\boldsymbol{v} \in V^k\}\!\} \neq \{\!\{d_{\boldsymbol{p}}^{(\ell-1)}|\boldsymbol{v} \in P^k\}\!\}$}
\State \Return $\mathcal{G} \not\simeq \mathcal{H}$
\EndIf
\For{$\boldsymbol{v}\in V^k$}
\State $c_{\boldsymbol{v},i}^{(\ell)}=\{\!\{c_{\boldsymbol{u}}^{(\ell-1)}|\boldsymbol{u}\in \mathcal{N}_{{\boldsymbol{v}},i}\}\!\}$, \quad for $i=1,2,\cdots,k$
\State $c_{\boldsymbol{v}}^{(\ell)} \leftarrow \textsc{Hash}\Bigl(c_{\boldsymbol{v}}^{(\ell-1)}, c_{\boldsymbol{v},1}^{(\ell)}, c_{\boldsymbol{v},2}^{(\ell)}, \cdots, c_{\boldsymbol{v},k}^{(\ell)}\Bigr)$
\EndFor
\For{$\boldsymbol{p} \in P^k$}
\State $d_{\boldsymbol{p},i}^{(\ell)}=\{\!\{d_{\boldsymbol{q}}^{(\ell-1)}|\boldsymbol{q}\in \mathcal{N}_{\boldsymbol{p},i}\}\!\}$, \quad for $i=1,2,\cdots,k$
\State $d_{\boldsymbol{p}}^{(\ell)} \leftarrow \textsc{Hash}\Bigl(d_{\boldsymbol{p}}^{(\ell-1)}, d_{\boldsymbol{p},1}^{(\ell)}, d_{\boldsymbol{p},2}^{(\ell)}, \cdots, d_{\boldsymbol{p},k}^{(\ell)}\Bigr)$
\EndFor
\Until convergence
\State \Return $\mathcal{G} \simeq \mathcal{H}$
\end{algorithmic}
| \begin{algorithmic}
\State \textbf{Input:} Two graphs $\mathcal{G}=(V, E, \boldsymbol{X})$ and $\mathcal{H}=(P, F, \boldsymbol{Y})$
\State $c_{\boldsymbol{v}}^{(0)} \leftarrow \textsc{Hash}(\mathcal{G}[\boldsymbol{v}]), \forall \boldsymbol{v} \in V^k$
\State $d_{\boldsymbol{p}}^{(0)} \leftarrow \textsc{Hash}(\mathcal{H}[\boldsymbol{p}]), \forall \boldsymbol{p} \in P^k$
\Repeat \ ($\ell=1,2,\cdots$)
\If{$\{\!\{c_{\boldsymbol{v}}^{(\ell-1)}|\boldsymbol{v} \in V^k\}\!\} \neq \{\!\{d_{\boldsymbol{p}}^{(\ell-1)}|\boldsymbol{v} \in P^k\}\!\}$}
\State \Return $\mathcal{G} \not\simeq \mathcal{H}$
\EndIf
\For{$\boldsymbol{v}\in V^k$}
\State $c_{\boldsymbol{v},i}^{(\ell)}=\{\!\{c_{\boldsymbol{u}}^{(\ell-1)}|\boldsymbol{u}\in \mathcal{N}_{{\boldsymbol{v}},i}\}\!\}$, \quad for $i=1,2,\cdots,k$
\State $c_{\boldsymbol{v}}^{(\ell)} \leftarrow \textsc{Hash}\Bigl(c_{\boldsymbol{v}}^{(\ell-1)}, c_{\boldsymbol{v},1}^{(\ell)}, c_{\boldsymbol{v},2}^{(\ell)}, \cdots, c_{\boldsymbol{v},k}^{(\ell)}\Bigr)$
\EndFor
\For{$\boldsymbol{p} \in P^k$}
\State $d_{\boldsymbol{p},i}^{(\ell)}=\{\!\{d_{\boldsymbol{q}}^{(\ell-1)}|\boldsymbol{q}\in \mathcal{N}_{\boldsymbol{p},i}\}\!\}$, \quad for $i=1,2,\cdots,k$
\State $d_{\boldsymbol{p}}^{(\ell)} \leftarrow \textsc{Hash}\Bigl(d_{\boldsymbol{p}}^{(\ell-1)}, d_{\boldsymbol{p},1}^{(\ell)}, d_{\boldsymbol{p},2}^{(\ell)}, \cdots, d_{\boldsymbol{p},k}^{(\ell)}\Bigr)$
\EndFor
\Until convergence
\State \Return $\mathcal{G} \simeq \mathcal{H}$
\end{algorithmic} | "https://arxiv.org/src/2206.02059" | "2206.02059.tar.gz" | "2024-01-23" | {
"title": "empowering gnns via edge-aware weisfeiler-leman algorithm",
"id": "2206.02059",
"abstract": "message passing graph neural networks (gnns) are known to have their expressiveness upper-bounded by 1-dimensional weisfeiler-leman (1-wl) algorithm. to achieve more powerful gnns, existing attempts either require ad hoc features, or involve operations that incur high time and space complexities. in this work, we propose a general and provably powerful gnn framework that preserves the scalability of the message passing scheme. in particular, we first propose to empower 1-wl for graph isomorphism test by considering edges among neighbors, giving rise to nc-1-wl. the expressiveness of nc-1-wl is shown to be strictly above 1-wl and below 3-wl theoretically. further, we propose the nc-gnn framework as a differentiable neural version of nc-1-wl. our simple implementation of nc-gnn is provably as powerful as nc-1-wl. experiments demonstrate that our nc-gnn performs effectively and efficiently on various benchmarks.",
"categories": "cs.lg cs.ai",
"doi": "",
"created": "2022-06-04",
"updated": "2024-01-23",
"authors": [
"meng liu",
"haiyang yu",
"shuiwang ji"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2206.02059"
} | "2024-03-15T09:04:06.314342" | {
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} | [] | "algorithm" | "8052e22a-9519-4f39-bc84-ef117dfe5879" | 1490 | hard |
|
\begin{algorithmic}[1]
\State \textbf{Input:} Initial parameters $\left(\theta^P_0, \theta^Q_0,\ldots, \theta^Q_{N-1}\right)$, learning rate $\eta$; batch size $M$; number of iteration $K$.
\State \textbf{Data:} Simulated Brownian increments $\left\{ \Delta W_{t_i, k} \right\}_{0\leq i\leq N-1, 1\leq k\leq K}$
\State \textbf{Output:} The triple $(X_{t_i}, P_{t_i}, Q_{t_i})$
\For{$k = 1$ to $K$}
\State $X_{t_0, k}^{\pi} = x_0$, $P_{t_0, k}^{\pi} = \mu_0^\pi(x_0; \theta^P_{0} ) $
\For{$i = 0$ to $N-1$}
\State $ Q_{t_i, k}^{\pi} = \phi_i^\pi\left(X_{t_i}^\pi; \theta^Q_{i}\right) $
\State $ u_{t_i, k}^{\pi} = \mathcal{M}\left(t_i, X_{t_i, k}^{\pi}, P_{t_i,k}^{\pi}, Q_{t_i,k}^{\pi} \right)$
\State $ X_{t_{i+1},k}^{\pi} = X_{t_i,k}^{\pi} + \bar{b} \left(t_i, X_{t_i,k}^{\pi},u_{t_i, k}^{\pi} \right) \Delta t_i + \bar{\sigma} \left(t_i, X_{t_i,k}^{\pi}, u_{t_i, k}^{\pi} \right) \Delta W_{t_i, k} $
\State $ P_{t_{i+1},k}^{\pi} = P_{t_i,k}^{\pi} - \bar{F} \left(t_i, X_{t_i,k}^{\pi}, u_{t_i, k}^{\pi} \right) \Delta t_i + Q_{t_i,k}^{\pi} \Delta W_{t_i, k} $
\EndFor
\State $\text{Loss} = \frac{1}{M} \sum_{j=1}^M \left\| -\nabla_x g\left( X_{t_N,k}^{\pi} \right) - P_{t_N,k}^{\pi}\right\|^2 $
\State $ \left(\theta^P_0, \theta^Q_0,\ldots, \theta^Q_{N-1} \right) \longleftarrow \left(\theta^P_0, \theta^Q_0,\ldots, \theta^Q_{N-1} \right) - \eta \nabla \text{Loss} $
\EndFor
\end{algorithmic}
| \begin{algorithmic}[1]
\State \textbf{Input:} Initial parameters $\left(\theta^P_0, \theta^Q_0,\ldots, \theta^Q_{N-1}\right)$, learning rate $\eta$; batch size $M$; number of iteration $K$.
\State \textbf{Data:} Simulated Brownian increments $\left\{ \Delta W_{t_i, k} \right\}_{0\leq i\leq N-1, 1\leq k\leq K}$
\State \textbf{Output:} The triple $(X_{t_i}, P_{t_i}, Q_{t_i})$
\For{$k = 1$ to $K$}
\State $X_{t_0, k}^{\pi} = x_0$, $P_{t_0, k}^{\pi} = \mu_0^\pi(x_0; \theta^P_{0} ) $
\For{$i = 0$ to $N-1$}
\State $ Q_{t_i, k}^{\pi} = \phi_i^\pi\left(X_{t_i}^\pi; \theta^Q_{i}\right) $
\State $ u_{t_i, k}^{\pi} = \mathcal{M}\left(t_i, X_{t_i, k}^{\pi}, P_{t_i,k}^{\pi}, Q_{t_i,k}^{\pi} \right)$
\State $ X_{t_{i+1},k}^{\pi} = X_{t_i,k}^{\pi} + \bar{b} \left(t_i, X_{t_i,k}^{\pi},u_{t_i, k}^{\pi} \right) \Delta t_i + \bar{\sigma} \left(t_i, X_{t_i,k}^{\pi}, u_{t_i, k}^{\pi} \right) \Delta W_{t_i, k} $
\State $ P_{t_{i+1},k}^{\pi} = P_{t_i,k}^{\pi} - \bar{F} \left(t_i, X_{t_i,k}^{\pi}, u_{t_i, k}^{\pi} \right) \Delta t_i + Q_{t_i,k}^{\pi} \Delta W_{t_i, k} $
\EndFor
\State $\text{Loss} = \frac{1}{M} \sum_{j=1}^M \left\| -\nabla_x g\left( X_{t_N,k}^{\pi} \right) - P_{t_N,k}^{\pi}\right\|^2 $
\State $ \left(\theta^P_0, \theta^Q_0,\ldots, \theta^Q_{N-1} \right) \longleftarrow \left(\theta^P_0, \theta^Q_0,\ldots, \theta^Q_{N-1} \right) - \eta \nabla \text{Loss} $
\EndFor
\end{algorithmic} | "https://arxiv.org/src/2401.17472" | "2401.17472.tar.gz" | "2024-01-30" | {
"title": "convergence of the deep bsde method for stochastic control problems formulated through the stochastic maximum principle",
"id": "2401.17472",
"abstract": "it is well-known that decision-making problems from stochastic control can be formulated by means of forward-backward stochastic differential equation (fbsde). recently, the authors of ji et al. 2022 proposed an efficient deep learning-based algorithm which was based on the stochastic maximum principle (smp). in this paper, we provide a convergence result for this deep smp-bsde algorithm and compare its performance with other existing methods. in particular, by adopting a similar strategy as in han and long 2020, we derive a posteriori error estimate, and show that the total approximation error can be bounded by the value of the loss functional and the discretization error. we present numerical examples for high-dimensional stochastic control problems, both in case of drift- and diffusion control, which showcase superior performance compared to existing algorithms.",
"categories": "math.oc cs.na math.na q-fin.cp",
"doi": "",
"created": "2024-01-30",
"updated": "",
"authors": [
"zhipeng huang",
"balint negyesi",
"cornelis w. oosterlee"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.17472"
} | "2024-03-15T05:11:50.224129" | {
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|
\begin{algorithm}[h]
\caption{LMC method algorithm for the computation of the bid reservation price}
\begin{algorithmic}
\Require $n > 0$
\State \textbf{Step 1} : Choose $u$ and $v$ such that the hypothesis of Theorem \ref{prop_dec_gen} are satisfied
\State \textbf{Step 2} : Generate a vector $U$ of $n$ i.i.d random variables of law $\mathcal{N}(0,1)$
\State \textbf{Step 3} : Set $V := \exp\bigg[-\theta\bigg(\hat{\zeta}\left(\frac{W(\theta v \eta^2 T)}{\theta v\eta^2 T}e^{\eta\sqrt{T}U}\right)-u - \frac{W(\theta v \eta^2 T)}{\theta \eta^2 T}e^{\eta\sqrt{T}U}\bigg) 1_{U\leq \frac{\ln(\hat{K})}{\eta\sqrt{T}}+\frac{W(\theta v \eta^2 T)}{\eta\sqrt{T}}}\bigg] \phi_{\hat{K}}( U,\theta)$ with the parameters $\hat{\zeta}$, $\hat{K}$ and the function $\phi_{\hat{K}}$ specified in Theorem \ref{prop_dec_gen} and $\theta:= \lambda\gamma (1-\rho^2)$.
\State \textbf{Step 4} : Compute the mean $m$ of $V$
\State \textbf{Step 5} : Compute the approximation of the random part $M:=-\frac{e^{-rT}}{\gamma(1-\rho^{2})}\ln\left(m\right)$
\State \textbf{Step 6} : Return the approximation of the bid reservation price $D_{\zeta,K}+M$.
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[h]
\caption{LMC method algorithm for the computation of the bid reservation price}
\begin{algorithmic}
\Require $n > 0$
\State \textbf{Step 1} : Choose $u$ and $v$ such that the hypothesis of Theorem \ref{prop_dec_gen} are satisfied
\State \textbf{Step 2} : Generate a vector $U$ of $n$ i.i.d random variables of law $\mathcal{N}(0,1)$
\State \textbf{Step 3} : Set $V := \exp\bigg[-\theta\bigg(\hat{\zeta}\left(\frac{W(\theta v \eta^2 T)}{\theta v\eta^2 T}e^{\eta\sqrt{T}U}\right)-u - \frac{W(\theta v \eta^2 T)}{\theta \eta^2 T}e^{\eta\sqrt{T}U}\bigg) 1_{U\leq \frac{\ln(\hat{K})}{\eta\sqrt{T}}+\frac{W(\theta v \eta^2 T)}{\eta\sqrt{T}}}\bigg] \phi_{\hat{K}}( U,\theta)$ with the parameters $\hat{\zeta}$, $\hat{K}$ and the function $\phi_{\hat{K}}$ specified in Theorem \ref{prop_dec_gen} and $\theta:= \lambda\gamma (1-\rho^2)$.
\State \textbf{Step 4} : Compute the mean $m$ of $V$
\State \textbf{Step 5} : Compute the approximation of the random part $M:=-\frac{e^{-rT}}{\gamma(1-\rho^{2})}\ln\left(m\right)$
\State \textbf{Step 6} : Return the approximation of the bid reservation price $D_{\zeta,K}+M$.
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2105.08804" | "2105.08804.tar.gz" | "2024-02-20" | {
"title": "efficient approximations for utility-based pricing",
"id": "2105.08804",
"abstract": "in a context of illiquidity, the reservation price is a well-accepted alternative to the usual martingale approach which does not apply. however, this price is not available in closed form and requires numerical methods such as monte carlo or polynomial approximations to evaluate it. we show that these methods can be inaccurate and propose a deterministic decomposition of the reservation price using the lambert function. this decomposition allows us to perform an improved monte carlo method, which we name lambert monte carlo (lmc) and to give deterministic approximations of the reservation price and of the optimal strategies based on the lambert function. we also give an answer to the problem of selecting a hedging asset that minimizes the reservation price and also the cash invested. our theoretical results are illustrated by numerical simulations.",
"categories": "q-fin.cp q-fin.pr",
"doi": "",
"created": "2021-05-18",
"updated": "2024-02-20",
"authors": [
"laurence carassus",
"massinissa ferhoune"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2105.08804"
} | "2024-03-15T03:14:06.406557" | {
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