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\begin{algorithmic}[1]
\State Input: Two multi-sets of $n$ points $R,B$ in $Q_d$.
\State Output: A matching from $R$ to $B$.
\State$\triangleright$ The set B is shared across all threads
\Procedure{WeightedMatch}{$R,B$}
\For {$r \in R$}\Comment{All for loop statements run in parallel}
\State $b\gets\mathrm{BreadthFirstSearch}(r,B)$
\State $M\gets M\cup \{r\to b\}$
\EndFor
\State \textbf{return} $M$\Comment{M is the matching}
\EndProcedure
\Procedure{BreadthFirstSearch}{$r,B$}
\For{$i=1,...,d$}
\For{$v\in Q_d$, $\|v-r\|_1=i$}
\If{$v\in B$}
\State $B\gets B\setminus{v}$
\State \textbf{return} $v$\Comment{r matches to v}
\EndIf
\EndFor
\EndFor
\EndProcedure
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Input: Two multi-sets of $n$ points $R,B$ in $Q_d$.
\State Output: A matching from $R$ to $B$.
\State$\triangleright$ The set B is shared across all threads
\Procedure{WeightedMatch}{$R,B$}
\For {$r \in R$}\Comment{All for loop statements run in parallel}
\State $b\gets\mathrm{BreadthFirstSearch}(r,B)$
\State $M\gets M\cup \{r\to b\}$
\EndFor
\State \textbf{return} $M$\Comment{M is the matching}
\EndProcedure
\Procedure{BreadthFirstSearch}{$r,B$}
\For{$i=1,...,d$}
\For{$v\in Q_d$, $\|v-r\|_1=i$}
\If{$v\in B$}
\State $B\gets B\setminus{v}$
\State \textbf{return} $v$\Comment{r matches to v}
\EndIf
\EndFor
\EndFor
\EndProcedure
\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" | "6198b44e-7ef3-4092-abff-15603e4a2143" | 681 | easy |
|
\begin{algorithmic}[1]
\Require current node $u$, candidate node $v$, Walker $W$, {\sf HuGE} parameter $\mu$
\Ensure walker state updates
{\flushleft{{\bf sendStateQuery($u$, $v$, $W$)}}} %//{submit the walker-to-vertex query messages and process the state queries}
\State{$P(u,v) = Z\left(\frac{1}{deg(u)-Cm(u, v)}\cdot \max \left\{\frac{deg(u)}{deg(v)}, \frac{deg(v)}{deg(u)} \right\} \right)$} // Eq.~\ref{accept_CNHRW}
{\flushleft{{\bf getStateQueryResult($W, P(u,v)$)}}} %// {return results to querying walkers for retrieving the state and decide sampling outcome}
\State{generate a random number $\eta \in\left[0,1\right]$}
\If{$P(u,v)> \eta $}
\State{$W.path$.append($v$), $W.cur$ = $v$, $W.steps$ ++}
\State{$L$ = $W.steps$}
\State compute $H(W)$ and $R\left(H(W),L\right)$ // Eq.~\ref{path_entropy}, \ref{path_corr}
\If{$R^2(H(W),L) < \mu$}
\State terminate the walk
\Else
\State{generate another candidate node $t$ of $v$}
\State{sendStateQuery($v$, $t$, $W$)}
\EndIf
\Else
\State{backtrack to $u$ and generate another candidate node $v'$ of $u$}
\State{sendStateQuery($u$, $v'$, $W$)}
\EndIf
\end{algorithmic}
| \begin{algorithmic}
[1]
\Require current node $u$, candidate node $v$, Walker $W$, {\sf HuGE} parameter $\mu$
\Ensure walker state updates
{\flushleft{{\bf sendStateQuery($u$, $v$, $W$)}}} %//{submit the walker-to-vertex query messages and process the state queries}
\State{$P(u,v) = Z\left(\frac{1}{deg(u)-Cm(u, v)}\cdot \max \left\{\frac{deg(u)}{deg(v)}, \frac{deg(v)}{deg(u)} \right\} \right)$} // Eq.~\ref{accept_CNHRW}
{\flushleft{{\bf getStateQueryResult($W, P(u,v)$)}}} %// {return results to querying walkers for retrieving the state and decide sampling outcome}
\State{generate a random number $\eta \in\left[0,1\right]$}
\If{$P(u,v)> \eta $}
\State{$W.path$.append($v$), $W.cur$ = $v$, $W.steps$ ++}
\State{$L$ = $W.steps$}
\State compute $H(W)$ and $R\left(H(W),L\right)$ // Eq.~\ref{path_entropy}, \ref{path_corr}
\If{$R^2(H(W),L) < \mu$}
\State terminate the walk
\Else
\State{generate another candidate node $t$ of $v$}
\State{sendStateQuery($v$, $t$, $W$)}
\EndIf
\Else
\State{backtrack to $u$ and generate another candidate node $v'$ of $u$}
\State{sendStateQuery($u$, $v'$, $W$)}
\EndIf
\end{algorithmic} | "https://arxiv.org/src/2303.15702" | "2303.15702.tar.gz" | "2024-02-25" | {
"title": "distributed graph embedding with information-oriented random walks",
"id": "2303.15702",
"abstract": "graph embedding maps graph nodes to low-dimensional vectors, and is widely adopted in machine learning tasks. the increasing availability of billion-edge graphs underscores the importance of learning efficient and effective embeddings on large graphs, such as link prediction on twitter with over one billion edges. most existing graph embedding methods fall short of reaching high data scalability. in this paper, we present a general-purpose, distributed, information-centric random walk-based graph embedding framework, distger, which can scale to embed billion-edge graphs. distger incrementally computes information-centric random walks. it further leverages a multi-proximity-aware, streaming, parallel graph partitioning strategy, simultaneously achieving high local partition quality and excellent workload balancing across machines. distger also improves the distributed skip-gram learning model to generate node embeddings by optimizing the access locality, cpu throughput, and synchronization efficiency. experiments on real-world graphs demonstrate that compared to state-of-the-art distributed graph embedding frameworks, including knightking, distdgl, and pytorch-biggraph, distger exhibits 2.33x-129x acceleration, 45% reduction in cross-machines communication, and > 10% effectiveness improvement in downstream tasks.",
"categories": "cs.dc cs.lg",
"doi": "",
"created": "2023-03-27",
"updated": "2024-02-25",
"authors": [
"peng fang",
"arijit khan",
"siqiang luo",
"fang wang",
"dan feng",
"zhenli li",
"wei yin",
"yuchao cao"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2303.15702"
} | "2024-03-15T03:43:03.810720" | {
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} | [] | "algorithm" | "495ba26c-9d13-4916-8708-fb41c8065401" | 1121 | medium |
|
\begin{algorithmic}[1]
\Procedure{ModifiedGD}{$\nabla F, \hat{L}_{i, 0}, \delta_{(i, \cdot)}, R, \theta_{i, 0}, \kappa_{(i,\cdot)}, T^*, \ell, \gamma$}
\State $ \Delta \leftarrow 0 $ \Comment{Measure of predicted decrease of objective}
\For{$j = 0, 1, ..., T^*-1$}
\State $\alpha_{i,j} \leftarrow \delta_{(i,\cdot)} (2||\nabla F(\theta_{i,j})||^3 + ||\nabla F(\theta_{i,j})||^2\hat{L}_{i,j} )^{-1}$ \Comment{Step size computation}
\State $\theta_{i, j+1} \leftarrow \theta_{i,j} - \alpha_{i,j} \nabla F(\theta_{i,j})$ \Comment{Gradient step}
\State $\Delta \leftarrow \Delta - \delta_{(i,\cdot)}^2\left( 4||\nabla F(\theta_{i,j})||^3 + 2\hat{L}_{i,j}||\nabla F(\theta_{i,j}) ||^2 \right)^{-1}$ \Comment{Update predicted decrease}
\If{ $|| \theta_{i,j} - \theta_{i,j+1} || \ge 10^{-10}$ }
\State $\hat{L}_{i,j+1} \leftarrow \Call{UpdateL}{\nabla F, \theta_{i,j}, \theta_{i,j+1}, \hat{L}_{i,j}, \kappa_{(i,\cdot)}, \ell}$ \Comment{Update local Lipschitz estimate}
\Else
\State $\hat{L}_{i,j+1} \leftarrow \hat{L}_{i,j}$
\EndIf
\State $ \delta_{cond} \leftarrow ||\nabla F(\theta_{i,j+1})||^2 \not\in (\delta_{(i,\cdot)}, \gamma\delta_{(i,\cdot)})$
\If{$\delta_{cond}$ or $||\theta_{i,j+1}-\theta_{i,0}|| > R$ or stop condition} \Comment{Check triggering events}
\State \Return{$\theta_{i,j+1},\hat{L}_{i,j+1},\delta_{cond},\Delta$}
\EndIf
\EndFor
\State
\Return{$\theta_{i,T^*},\hat{L}_{i,T^*},\delta_{cond},\Delta$}
\EndProcedure
\end{algorithmic}
| \begin{algorithmic}
[1]
\Procedure{ModifiedGD}{$\nabla F, \hat{L}_{i, 0}, \delta_{(i, \cdot)}, R, \theta_{i, 0}, \kappa_{(i,\cdot)}, T^*, \ell, \gamma$}
\State $ \Delta \leftarrow 0 $ \Comment{Measure of predicted decrease of objective}
\For{$j = 0, 1, ..., T^*-1$}
\State $\alpha_{i,j} \leftarrow \delta_{(i,\cdot)} (2||\nabla F(\theta_{i,j})||^3 + ||\nabla F(\theta_{i,j})||^2\hat{L}_{i,j} )^{-1}$ \Comment{Step size computation}
\State $\theta_{i, j+1} \leftarrow \theta_{i,j} - \alpha_{i,j} \nabla F(\theta_{i,j})$ \Comment{Gradient step}
\State $\Delta \leftarrow \Delta - \delta_{(i,\cdot)}^2\left( 4||\nabla F(\theta_{i,j})||^3 + 2\hat{L}_{i,j}||\nabla F(\theta_{i,j}) ||^2 \right)^{-1}$ \Comment{Update predicted decrease}
\If{ $|| \theta_{i,j} - \theta_{i,j+1} || \ge 10^{-10}$ }
\State $\hat{L}_{i,j+1} \leftarrow \Call{UpdateL}{\nabla F, \theta_{i,j}, \theta_{i,j+1}, \hat{L}_{i,j}, \kappa_{(i,\cdot)}, \ell}$ \Comment{Update local Lipschitz estimate}
\Else
\State $\hat{L}_{i,j+1} \leftarrow \hat{L}_{i,j}$
\EndIf
\State $ \delta_{cond} \leftarrow ||\nabla F(\theta_{i,j+1})||^2 \not\in (\delta_{(i,\cdot)}, \gamma\delta_{(i,\cdot)})$
\If{$\delta_{cond}$ or $||\theta_{i,j+1}-\theta_{i,0}|| > R$ or stop condition} \Comment{Check triggering events}
\State \Return{$\theta_{i,j+1},\hat{L}_{i,j+1},\delta_{cond},\Delta$}
\EndIf
\EndFor
\State
\Return{$\theta_{i,T^*},\hat{L}_{i,T^*},\delta_{cond},\Delta$}
\EndProcedure
\end{algorithmic} | "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"
} | "2024-03-15T05:23:50.845023" | {
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} | [] | "algorithm" | "d5824813-2875-4568-bb05-f16712f12f47" | 1447 | hard |
|
\begin{algorithmic}[1]
\State \textbf{Input:} Stock data for two assets $S_1$ and $S_2$, buy threshold, sell threshold
\State \textbf{Output:} Trade signals for pairs trading
\State
\Procedure{Compute Hedge Ratio}{data1, data2}
\State model $\gets$ perform OLS regression (data1, data2)
\State \Return model.params$[1]$
\EndProcedure
\State
\Procedure{Initialize}{fast, slow}
\State hedge$\_$ratio $\gets$ \Call{Compute Hedge Ratio}{$S_1$, $S_2$}
\State Calculate spread $\gets$ $S_1$$-$hedge$\_$ratio $\times$ $S_2$
\State fast$\_$ema $\gets$ \Call{EMA}{spread, fast}
\State slow$\_$ema $\gets$ \Call{EMA}{spread, slow}
\State apo$\_$spread $\gets$ fast$\_$ema$-$slow$\_$ema
\State position $\gets 0$
\EndProcedure
\State
\Procedure{Next}{buy threshold, sell threshold}
\State \textbf{if}{~apo$\_$spread $<$ buy$\_$threshold} \textbf{then}
\State \hspace{1cm} Execute Buy for $S_1$ and Sell Short for $S_2$
\State \textbf{else if}{apo$\_$spread $>$ sell$\_$threshold} \textbf{then}
\State \hspace{1cm} Execute Sell Short for $S_1$ and Buy for $S_2$
\State \textbf{end if}
\EndProcedure
\end{algorithmic}
| \begin{algorithmic}
[1]
\State \textbf{Input:} Stock data for two assets $S_1$ and $S_2$, buy threshold, sell threshold
\State \textbf{Output:} Trade signals for pairs trading
\State
\Procedure{Compute Hedge Ratio}{data1, data2}
\State model $\gets$ perform OLS regression (data1, data2)
\State \Return model.params$[1]$
\EndProcedure
\State
\Procedure{Initialize}{fast, slow}
\State hedge$\_$ratio $\gets$ \Call{Compute Hedge Ratio}{$S_1$, $S_2$}
\State Calculate spread $\gets$ $S_1$$-$hedge$\_$ratio $\times$ $S_2$
\State fast$\_$ema $\gets$ \Call{EMA}{spread, fast}
\State slow$\_$ema $\gets$ \Call{EMA}{spread, slow}
\State apo$\_$spread $\gets$ fast$\_$ema$-$slow$\_$ema
\State position $\gets 0$
\EndProcedure
\State
\Procedure{Next}{buy threshold, sell threshold}
\State \textbf{if}{~apo$\_$spread $<$ buy$\_$threshold} \textbf{then}
\State \hspace{1cm} Execute Buy for $S_1$ and Sell Short for $S_2$
\State \textbf{else if}{apo$\_$spread $>$ sell$\_$threshold} \textbf{then}
\State \hspace{1cm} Execute Sell Short for $S_1$ and Buy for $S_2$
\State \textbf{end if}
\EndProcedure
\end{algorithmic} | "https://arxiv.org/src/2401.14761" | "2401.14761.tar.gz" | "2024-01-26" | {
"title": "esg driven pairs algorithm for sustainable trading: analysis from the indian market",
"id": "2401.14761",
"abstract": "this paper proposes an algorithmic trading framework integrating environmental, social, and governance (esg) ratings with a pairs trading strategy. it addresses the demand for socially responsible investment solutions by developing a unique algorithm blending esg data with methods for identifying co-integrated stocks. this allows selecting profitable pairs adhering to esg principles. further, it incorporates technical indicators for optimal trade execution within this sustainability framework. extensive back-testing provides evidence of the model's effectiveness, consistently generating positive returns exceeding conventional pairs trading strategies, while upholding esg principles. this paves the way for a transformative approach to algorithmic trading, offering insights for investors, policymakers, and academics.",
"categories": "q-fin.tr",
"doi": "",
"created": "2024-01-26",
"updated": "",
"authors": [
"eeshaan dutta",
"sarthak diwan",
"siddhartha p. chakrabarty"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.14761"
} | "2024-03-15T05:30:05.430403" | {
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} | [] | "algorithm" | "d4f074dd-00b8-4ebd-9eff-3126db854c98" | 1105 | medium |
|
\begin{algorithm}
GPB(N) Algorithm
\end{algorithm}
| \begin{algorithm}
GPB(N) Algorithm
\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" | "75bee723-8648-4b9d-82cd-341a3bad5259" | 50 | easy |
|
\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}
| \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} | "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" | "596d1a2a-5955-45c6-abc2-8a6ffce88a00" | 481 | easy |
|
\begin{algorithm}[!ht]
\caption{Discrete empirical interpolation method (DEIM)}\label{alg:DEIM}
\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}
\end{algorithm}
| \begin{algorithm}
[!ht]
\caption{Discrete empirical interpolation method (DEIM)}\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}
\end{algorithm} | "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" | "080b212f-f820-4ed0-803b-0cd7ba5e82d4" | 467 | easy |
|
\begin{algorithm}
\caption{Multi-Period Transition Framework}\label{alg:MPTF}
\begin{algorithmic}[H]
\Require $P_0, \mathcal{T}, Y_{-L:0}, \mathbf{X}_{-L:0}, V_0, \mathbf{T}, C_0$, OPT, Forecaster, MarketObserver
\Ensure $Y_0^T\mathcal{T} + C_0 \leq V_0$
\State $t \gets 0$
\State $P_t \gets P_0$
\State $C_t \gets C_0$
\State $Y \gets Y_{-L:t}$
\While{$t \leq \mathbf{T}$}
\State $V_t \gets Y_t^TP_t + C_t$ \Comment{Calculate portfolio value at current timestep}
\State $\hat{Y}_{t+1:\mathbf{T}}\gets \text{Forecaster}(Y_{-L:t}, \mathbf{X}_{-L:t})$ \Comment{Predict unknown time steps with known information}
\State $Z_{t:\mathbf{T}}, W_{t:\mathbf{T}} \gets \text{OPT}([Y_t\ \hat{Y}_{t+1:\mathbf{T}}], P_t, C_t, \mathcal{T})$ \Comment{Run Optimization Policy}
\State $P_{t+1} \gets P_t + Z_t$ \Comment{Execute trades at current timestep}
\State $C_{t+1} \gets C_t - Y_t\cdot Z_t - F\Vec{1} \cdot W_t$ \Comment{Calculate cash}
\State $Y_{t+1} \gets \text{MarketObserver}()$ \Comment{Observe the market for new price information}
\State $t \gets t + 1$
\EndWhile
\Ensure $P_\mathbf{T} \geq \mathcal{T}$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Multi-Period Transition Framework}\begin{algorithmic}
[H]
\Require $P_0, \mathcal{T}, Y_{-L:0}, \mathbf{X}_{-L:0}, V_0, \mathbf{T}, C_0$, OPT, Forecaster, MarketObserver
\Ensure $Y_0^T\mathcal{T} + C_0 \leq V_0$
\State $t \gets 0$
\State $P_t \gets P_0$
\State $C_t \gets C_0$
\State $Y \gets Y_{-L:t}$
\While{$t \leq \mathbf{T}$}
\State $V_t \gets Y_t^TP_t + C_t$ \Comment{Calculate portfolio value at current timestep}
\State $\hat{Y}_{t+1:\mathbf{T}}\gets \text{Forecaster}(Y_{-L:t}, \mathbf{X}_{-L:t})$ \Comment{Predict unknown time steps with known information}
\State $Z_{t:\mathbf{T}}, W_{t:\mathbf{T}} \gets \text{OPT}([Y_t\ \hat{Y}_{t+1:\mathbf{T}}], P_t, C_t, \mathcal{T})$ \Comment{Run Optimization Policy}
\State $P_{t+1} \gets P_t + Z_t$ \Comment{Execute trades at current timestep}
\State $C_{t+1} \gets C_t - Y_t\cdot Z_t - F\Vec{1} \cdot W_t$ \Comment{Calculate cash}
\State $Y_{t+1} \gets \text{MarketObserver}()$ \Comment{Observe the market for new price information}
\State $t \gets t + 1$
\EndWhile
\Ensure $P_\mathbf{T} \geq \mathcal{T}$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2401.13126" | "2401.13126.tar.gz" | "2024-01-24" | {
"title": "optimizing transition strategies for small to medium sized portfolios",
"id": "2401.13126",
"abstract": "this work discusses the benefits of constrained portfolio turnover strategies for small to medium-sized portfolios. we propose a dynamic multi-period model that aims to minimize transaction costs and maximize terminal wealth levels whilst adhering to strict portfolio turnover constraints. our results demonstrate that using our framework in combination with a reasonable forecast, can lead to higher portfolio values and lower transaction costs on average when compared to a naive, single-period model. such results were maintained given different problem cases, such as, trading horizon, assets under management, wealth levels, etc. in addition, the proposed model lends itself to a reformulation that makes use of the column generation algorithm which can be strategically leveraged to reduce complexity and solving times.",
"categories": "q-fin.cp",
"doi": "",
"created": "2024-01-23",
"updated": "2024-01-24",
"authors": [
"nakul upadhya",
"alexandre granzer-guay"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.13126"
} | "2024-03-15T05:38:12.261498" | {
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} | [] | "algorithm" | "9d6c0f2d-70af-4e25-9cee-9bec2c661226" | 1119 | medium |
|
\begin{algorithm}
\caption{getNextStage(candidates, k)}\label{alg:te2rules_stagek}
\begin{algorithmic}
\State $newCandidates \gets []$
\\
\For{$r_1 \gets candidates$}
\For{$r_2 \gets candidates$}
\State $nodes_1 = r_1.sourceNodes$
\State $nodes_2 = r_2.sourceNodes$
\If{$|nodes_1 \cap nodes_2| = k - 2$}
\State $r \gets r_1 \& r_2$
\State $r.sourceNodes \gets n_1 \cup n_2$
\If{$|r.support| > \epsilon$}
\State $candidates.append(r)$
\EndIf
\EndIf
\EndFor
\EndFor
\\
\Return $newCandidates$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{getNextStage(candidates, k)}\begin{algorithmic}
\State $newCandidates \gets []$
\\
\For{$r_1 \gets candidates$}
\For{$r_2 \gets candidates$}
\State $nodes_1 = r_1.sourceNodes$
\State $nodes_2 = r_2.sourceNodes$
\If{$|nodes_1 \cap nodes_2| = k - 2$}
\State $r \gets r_1 \& r_2$
\State $r.sourceNodes \gets n_1 \cup n_2$
\If{$|r.support| > \epsilon$}
\State $candidates.append(r)$
\EndIf
\EndIf
\EndFor
\EndFor
\\
\Return $newCandidates$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2206.14359" | "2206.14359.tar.gz" | "2024-01-23" | {
"title": "te2rules: explaining tree ensembles using rules",
"id": "2206.14359",
"abstract": "tree ensemble (te) models, such as gradient boosted trees, often achieve optimal performance on tabular datasets, yet their lack of transparency poses challenges for comprehending their decision logic. this paper introduces te2rules (tree ensemble to rules), a novel approach for explaining binary classification tree ensemble models through a list of rules, particularly focusing on explaining the minority class. many state-of-the-art explainers struggle with minority class explanations, making te2rules valuable in such cases. the rules generated by te2rules closely approximate the original model, ensuring high fidelity, providing an accurate and interpretable means to understand decision-making. experimental results demonstrate that te2rules scales effectively to tree ensembles with hundreds of trees, achieving higher fidelity within runtimes comparable to baselines. te2rules allows for a trade-off between runtime and fidelity, enhancing its practical applicability. the implementation is available here: https://github.com/linkedin/te2rules.",
"categories": "cs.lg cs.ai",
"doi": "",
"created": "2022-06-28",
"updated": "2024-01-23",
"authors": [
"g roshan lal",
"xiaotong chen",
"varun mithal"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2206.14359"
} | "2024-03-15T09:04:28.850184" | {
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} | [] | "algorithm" | "4838572e-3197-4b9d-96d2-c4263ddd219d" | 496 | easy |
|
\begin{algorithmic}[1]
\State Simulate $N$ random variables from $\text{Uniform}(0,1)$; Denote $\tilde{U}=(\tilde{U}_{(1)},...,\tilde{U}_{(N)})$ as the vector of $N$ simulated Uniformly distributed random variables
\State Denote $\tilde{Y}^{*}_{ij}=(\tilde{Y}^{*}_{ij,(1)},...,\tilde{Y}^{*}_{ij,(N)})$ as the vector of $N$ simulated variables for cell $(i,j)$ from the ensemble
\For{$n=1,..,N$}
\If{$\tilde{U}_{(n)} \in (\sum_{m=1}^{l-1}w_m,\sum_{m=1}^{l}w_m]$}
\State simulate a random variable from the $l^{th}$ component distribution, denoted as $\tilde{Y}_{ij}^{(l)}$
\State Set $\tilde{Y}^{*}_{ij,(n)}=\tilde{Y}_{ij}^{(l)}$
\EndIf
\EndFor
\State Repeat the above two steps for each cell $(i,j)$
\State Calculate the simulated reserve based on the simulated random variables for each cell $(i,j)$: $\tilde{R}^{*}=(\tilde{R}^{*}_{(1)},\tilde{R}^{*}_{(2)},...,\tilde{R}^{*}_{(N)})=(\sum_{i,j\in D^{out}}\tilde{Y}_{ij,(1)}^{*},\sum_{i,j\in D^{out}}\tilde{Y}_{ij,(2)}^{*},...,\sum_{i,j\in D^{out}}\tilde{Y}_{ij,(N)}^{*})$
\State Calculate the empirical $75^{th}$ quantile of the $N$ simulated reserves for the ensemble: $R^{*}_{75}$
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Simulate $N$ random variables from $\text{Uniform}(0,1)$; Denote $\tilde{U}=(\tilde{U}_{(1)},...,\tilde{U}_{(N)})$ as the vector of $N$ simulated Uniformly distributed random variables
\State Denote $\tilde{Y}^{*}_{ij}=(\tilde{Y}^{*}_{ij,(1)},...,\tilde{Y}^{*}_{ij,(N)})$ as the vector of $N$ simulated variables for cell $(i,j)$ from the ensemble
\For{$n=1,..,N$}
\If{$\tilde{U}_{(n)} \in (\sum_{m=1}^{l-1}w_m,\sum_{m=1}^{l}w_m]$}
\State simulate a random variable from the $l^{th}$ component distribution, denoted as $\tilde{Y}_{ij}^{(l)}$
\State Set $\tilde{Y}^{*}_{ij,(n)}=\tilde{Y}_{ij}^{(l)}$
\EndIf
\EndFor
\State Repeat the above two steps for each cell $(i,j)$
\State Calculate the simulated reserve based on the simulated random variables for each cell $(i,j)$: $\tilde{R}^{*}=(\tilde{R}^{*}_{(1)},\tilde{R}^{*}_{(2)},...,\tilde{R}^{*}_{(N)})=(\sum_{i,j\in D^{out}}\tilde{Y}_{ij,(1)}^{*},\sum_{i,j\in D^{out}}\tilde{Y}_{ij,(2)}^{*},...,\sum_{i,j\in D^{out}}\tilde{Y}_{ij,(N)}^{*})$
\State Calculate the empirical $75^{th}$ quantile of the $N$ simulated reserves for the ensemble: $R^{*}_{75}$
\end{algorithmic} | "https://arxiv.org/src/2206.08541" | "2206.08541.tar.gz" | "2024-02-19" | {
"title": "ensemble distributional forecasting for insurance loss reserving",
"id": "2206.08541",
"abstract": "loss reserving generally focuses on identifying a single model that can generate superior predictive performance. however, different loss reserving models specialise in capturing different aspects of loss data. this is recognised in practice in the sense that results from different models are often considered, and sometimes combined. for instance, actuaries may take a weighted average of the prediction outcomes from various loss reserving models, often based on subjective assessments. in this paper, we propose a systematic framework to objectively combine (i.e. ensemble) multiple _stochastic_ loss reserving models such that the strengths offered by different models can be utilised effectively. our framework contains two main innovations compared to existing literature and practice. firstly, our criteria model combination considers the full distributional properties of the ensemble and not just the central estimate - which is of particular importance in the reserving context. secondly, our framework is that it is tailored for the features inherent to reserving data. these include, for instance, accident, development, calendar, and claim maturity effects. crucially, the relative importance and scarcity of data across accident periods renders the problem distinct from the traditional ensembling techniques in statistical learning. our framework is illustrated with a complex synthetic dataset. in the results, the optimised ensemble outperforms both (i) traditional model selection strategies, and (ii) an equally weighted ensemble. in particular, the improvement occurs not only with central estimates but also relevant quantiles, such as the 75th percentile of reserves (typically of interest to both insurers and regulators).",
"categories": "stat.me q-fin.rm stat.ap",
"doi": "",
"created": "2022-06-17",
"updated": "2024-02-19",
"authors": [
"benjamin avanzi",
"yanfeng li",
"bernard wong",
"alan xian"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2206.08541"
} | "2024-03-15T03:14:29.396980" | {
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} | [] | "algorithm" | "1d289ead-1c69-4045-8011-bd2568d3d304" | 1151 | medium |
|
\begin{algorithmic}
\vspace{1mm}
\State{// \texttt{Iterate over all the haloes in catalogue}}
\For{ halo in catalogue }
\vspace{3mm}
\State{// \texttt{Compute probability of central}}
\State{$p_\text{cen} \leftarrow \text{model.}N_\text{cen}( $ halo.mass $ )$ }
\vspace{3mm}
\State{// \texttt{Define a binomial random variable}}
\State{select $\leftarrow$ random.Binomial(1, $p_\text{cen}$)}
\If{ select }
\State{halo $\leftarrow$ central}
\EndIf
\vspace{3mm}
\State{// \texttt{Compute average number of satellites}}
\State{$\overline{N}_\text{sat} \leftarrow \text{model.}N_\text{sat}( $ halo.mass $ )$}
\vspace{3mm}
\State{// \texttt{Define a Poisson random variable}}
\State{$N_\text{sat} = $ random.Poisson( $\overline{N}_\text{sat}$ )}
\State{halo $\leftarrow$ select randomly $N_\text{sat}$ objects among satellites}
\EndFor
\vspace{3mm}
\end{algorithmic}
| \begin{algorithmic}
\vspace{1mm}
\State{// \texttt{Iterate over all the haloes in catalogue}}
\For{ halo in catalogue }
\vspace{3mm}
\State{// \texttt{Compute probability of central}}
\State{$p_\text{cen} \leftarrow \text{model.}N_\text{cen}( $ halo.mass $ )$ }
\vspace{3mm}
\State{// \texttt{Define a binomial random variable}}
\State{select $\leftarrow$ random.Binomial(1, $p_\text{cen}$)}
\If{ select }
\State{halo $\leftarrow$ central}
\EndIf
\vspace{3mm}
\State{// \texttt{Compute average number of satellites}}
\State{$\overline{N}_\text{sat} \leftarrow \text{model.}N_\text{sat}( $ halo.mass $ )$}
\vspace{3mm}
\State{// \texttt{Define a Poisson random variable}}
\State{$N_\text{sat} = $ random.Poisson( $\overline{N}_\text{sat}$ )}
\State{halo $\leftarrow$ select randomly $N_\text{sat}$ objects among satellites}
\EndFor
\vspace{3mm}
\end{algorithmic} | "https://arxiv.org/src/2002.07179" | "2002.07179.tar.gz" | "2024-02-14" | {
"title": "scampy -- a sub-halo clustering & abundance matching based python interface for painting galaxies on the dark matter halo/sub-halo hierarchy",
"id": "2002.07179",
"abstract": "we present a computational framework for \"painting\" galaxies on top of the dark matter halo/sub-halo hierarchy obtained from n-body simulations. the method we use is based on the sub-halo clustering and abundance matching (scam) scheme which requires observations of the 1- and 2-point statistics of the target (observed) population we want to reproduce. this method is particularly tailored for high redshift studies and thereby relies on the observed high-redshift galaxy luminosity functions and correlation properties. the core functionalities are written in c++ and exploit object oriented programming, with a wide use of polymorphism, to achieve flexibility and high computational efficiency. in order to have an easily accessible interface, all the libraries are wrapped in python and provided with an extensive documentation. we validate our results and provide a simple and quantitative application to reionization, with an investigation of physical quantities related to the galaxy population, ionization fraction and bubble size distribution.",
"categories": "astro-ph.co",
"doi": "10.1093/mnras/staa2201",
"created": "2020-02-17",
"updated": "2024-02-14",
"authors": [
"tommaso ronconi",
"andrea lapi",
"matteo viel",
"alberto sartori"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2002.07179"
} | "2024-03-15T04:34:46.153353" | {
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} | [] | "algorithm" | "845af096-d4f2-4f54-96bd-5d99fe1e642a" | 861 | medium |
|
\begin{algorithmic}[1]
\Require $n \geq 0 \vee x \neq 0$
\Ensure $y = x^n$
\State $y \Leftarrow 1$
\If{$n < 0$}\label{algln2}
\State $X \Leftarrow 1 / x$
\State $N \Leftarrow -n$
\Else
\State $X \Leftarrow x$
\State $N \Leftarrow n$
\EndIf
\While{$N \neq 0$}
\If{$N$ is even}
\State $X \Leftarrow X \times X$
\State $N \Leftarrow N / 2$
\Else[$N$ is odd]
\State $y \Leftarrow y \times X$
\State $N \Leftarrow N - 1$
\EndIf
\EndWhile
\end{algorithmic}
| \begin{algorithmic}
[1]
\Require $n \geq 0 \vee x \neq 0$
\Ensure $y = x^n$
\State $y \Leftarrow 1$
\If{$n < 0$} \State $X \Leftarrow 1 / x$
\State $N \Leftarrow -n$
\Else
\State $X \Leftarrow x$
\State $N \Leftarrow n$
\EndIf
\While{$N \neq 0$}
\If{$N$ is even}
\State $X \Leftarrow X \times X$
\State $N \Leftarrow N / 2$
\Else[$N$ is odd]
\State $y \Leftarrow y \times X$
\State $N \Leftarrow N - 1$
\EndIf
\EndWhile
\end{algorithmic} | "https://arxiv.org/src/2312.05063" | "2312.05063.tar.gz" | "2024-02-25" | {
"title": "individualizing glioma radiotherapy planning by optimization of data and physics-informed discrete loss",
"id": "2312.05063",
"abstract": "brain tumor growth is unique to each patient and extends beyond what is visible in imaging scans, infiltrating surrounding brain tissue. understanding these hidden patient-specific progressions is essential for effective therapies. current treatment plans for brain tumors, such as radiotherapy, typically involve delineating a uniform margin around the visible tumor on pre-treatment scans to target this invisible tumor growth. this \"one size fits all\" approach is derived from population studies and often fails to account for the nuances of individual patient conditions. we present the framework gliodil which infers the full spatial distribution of tumor cell concentration from available multi-modal imaging. this is achieved through the newly introduced method of optimizing the discrete loss (odil), where both data and physics-based constraints are softly assimilated into the solution. our test dataset comprises 152 glioblastoma patients with pre-treatment imaging and post-treatment follow-ups for tumor recurrence monitoring. by blending data-driven techniques with physics-based constraints adapted for complex cases, gliodil enhances recurrence prediction in radiotherapy planning, offering a superior alternative to traditional uniform margins and strict pde adherence.",
"categories": "physics.med-ph cs.na math.na q-bio.qm",
"doi": "",
"created": "2023-12-08",
"updated": "2024-02-25",
"authors": [
"michal balcerak",
"jonas weidner",
"petr karnakov",
"ivan ezhov",
"sergey litvinov",
"petros koumoutsakos",
"ray zirui zhang",
"john s. lowengrub",
"bene wiestler",
"bjoern menze"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2312.05063"
} | "2024-03-15T03:04:49.138400" | {
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} | [] | "algorithm" | "37f9ec91-081a-4799-9d19-7a6595228dc9" | 437 | easy |
|
\begin{algorithmic}[1]
\State Compute the set
\begin{equation*}
I(\mathbf{x}) = \left\{i \in \{1, \dots, N\} : \mathbf{x} \in \mathcal{B}_i\right\}.
\end{equation*}
\If{$|I(\mathbf{x})|=1$}
\State Assign $C(\mathbf{x})$ the unique element of $I(\mathbf{x})$.
\EndIf
\If{$|I(\mathbf{x})| = 0$}
\State $C(\mathbf{x}) = \arg\min_i d(\mathbf{x},\mathcal{B}_i)$.
\EndIf
\If{$|I(\mathbf{x})| > 1$}
\State $C(\mathbf{x}) = \arg\min_i \tilde{d}(\mathbf{x},\mathcal{B}_i)$.
\EndIf
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Compute the set
\begin{equation*}
I(\mathbf{x}) = \left\{i \in \{1, \dots, N\} : \mathbf{x} \in \mathcal{B}_i\right\}.
\end{equation*}
\If{$|I(\mathbf{x})|=1$}
\State Assign $C(\mathbf{x})$ the unique element of $I(\mathbf{x})$.
\EndIf
\If{$|I(\mathbf{x})| = 0$}
\State $C(\mathbf{x}) = \arg\min_i d(\mathbf{x},\mathcal{B}_i)$.
\EndIf
\If{$|I(\mathbf{x})| > 1$}
\State $C(\mathbf{x}) = \arg\min_i \tilde{d}(\mathbf{x},\mathcal{B}_i)$.
\EndIf
\end{algorithmic} | "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"
} | "2024-03-15T05:24:48.442243" | {
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} | [] | "algorithm" | "be38228b-6714-4f2a-987e-5364b1359ad6" | 490 | easy |
|
\begin{algorithmic}
\State Initialize \(k=1, \mathbf{w}\sim Uniform(|\Phi|)\)
\While{\(k<k_{max}\)}
\State \(\hat{J}=-\infty\)
\For{\(\sigma_{\text{test}} \in [0,1]\)}
\If{\(J(\mathbf{w}, \sigma_{\text{test}}) > \hat{J}\)}
\State \(\sigma \gets \sigma_{\text{test}}\)
\State \(\hat{J} \gets J(\mathbf{w}, \sigma_{\text{test}})\)
\EndIf
\EndFor
\State Compute gradient \(\nabla_\mathbf{w} J(\mathbf{w},\sigma)\)
\State \(\mathbf{w} \gets \text{Proj}_{L_2}(\mathbf{w} - \alpha \nabla_\mathbf{w} J(\mathbf{w},\sigma))\)
\If{\(\left\|\nabla_\mathbf{w} J(\mathbf{w},\sigma) - \frac{\nabla_\mathbf{w} J(\mathbf{w},\sigma)^\top \mathbf{w}}{\|\mathbf{w}\|^2} \mathbf{w}\right\| < \beta\)}
\State terminate with \(\mathbf{w}\).
\EndIf
\State \(k\gets k+1\)
\EndWhile
\end{algorithmic}
| \begin{algorithmic}
\State Initialize \(k=1, \mathbf{w}\sim Uniform(|\Phi|)\)
\While{\(k<k_{max}\)}
\State \(\hat{J}=-\infty\)
\For{\(\sigma_{\text{test}} \in [0,1]\)}
\If{\(J(\mathbf{w}, \sigma_{\text{test}}) > \hat{J}\)}
\State \(\sigma \gets \sigma_{\text{test}}\)
\State \(\hat{J} \gets J(\mathbf{w}, \sigma_{\text{test}})\)
\EndIf
\EndFor
\State Compute gradient \(\nabla_\mathbf{w} J(\mathbf{w},\sigma)\)
\State \(\mathbf{w} \gets \text{Proj}_{L_2}(\mathbf{w} - \alpha \nabla_\mathbf{w} J(\mathbf{w},\sigma))\)
\If{\(\left\|\nabla_\mathbf{w} J(\mathbf{w},\sigma) - \frac{\nabla_\mathbf{w} J(\mathbf{w},\sigma)^\top \mathbf{w}}{\|\mathbf{w}\|^2} \mathbf{w}\right\| < \beta\)}
\State terminate with \(\mathbf{w}\).
\EndIf
\State \(k\gets k+1\)
\EndWhile
\end{algorithmic} | "https://arxiv.org/src/2207.06392" | "2207.06392.tar.gz" | "2024-01-25" | {
"title": "relationship design for socially-aware behavior in static games",
"id": "2207.06392",
"abstract": "autonomous agents can adopt socially-aware behaviors to reduce social costs, mimicking the way animals interact in nature and humans in society. we present a new approach to model socially-aware decision-making that includes two key elements: bounded rationality and inter-agent relationships. we capture the interagent relationships by introducing a novel model called a relationship game and encode agents' bounded rationality using quantal response equilibria. for each relationship game, we define a social cost function and formulate a mechanism design problem to optimize weights for relationships that minimize social cost at the equilibrium. we address the multiplicity of equilibria by presenting the problem in two forms: min-max and min-min, aimed respectively at minimization of the highest and lowest social costs in the equilibria. we compute the quantal response equilibrium by solving a least-squares problem defined with its karush-kuhn-tucker conditions, and propose two projected gradient descent algorithms to solve the mechanism design problems. numerical results, including two-lane congestion and congestion with an ambulance, confirm that these algorithms consistently reach the equilibrium with the intended social costs.",
"categories": "cs.ma cs.sy eess.sy",
"doi": "",
"created": "2022-07-13",
"updated": "2024-01-25",
"authors": [
"shenghui chen",
"yigit e. bayiz",
"david fridovich-keil",
"ufuk topcu"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2207.06392"
} | "2024-03-15T08:38:27.674079" | {
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|
\begin{algorithm}[!ht]\caption{LSH, private procedures}\label{alg:LSH_private_app}
\begin{algorithmic}[1]
\State {\bf data structure} \textsc{LSH}
\State
\State {\bf private}
\Procedure{\textsc{ChooseHashFunc}}{$k,L\in \mathbb{N}_+$}\label{lin:choose_hash_func}
\For{$l \in [L]$}
\State \Comment{Amplify hash functions by concatenating}
\State $\mathcal{H}_{l} \leftarrow$ sample $k$ hash functions $(f_{1,l},f_{2,l},\cdots,f_{k,l})$ from $\mathcal{H}$ \label{lin:LSH_sample_k_functions}
\EndFor
\EndProcedure
\State
\Procedure{\textsc{ConstructHashTable}}{$\{x_i\}_{i\in[n]}\subset \mathbb{R}^d$}\label{lin:construct_hash_table}
\For{$l\in [L]$}
\For{$i\in [n]$}
\State $\mathcal{H}_l(x_i)$.\textsc{Insert}($x_i$) \label{lin:find_bucket_insert_element}
\State $\mathcal{T}_l\leftarrow \mathcal{T}_l\cup \mathcal{H}_l(x_i)$ \Comment{Creat hashtable by aggregating buckets} \label{lin:aggregate_hash_table}
\EndFor
\EndFor
\EndProcedure
\State {\bf end data structure}
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}[!ht]
\caption{LSH, private procedures}\begin{algorithmic}
[1]
\State {\bf data structure} \textsc{LSH}
\State
\State {\bf private}
\Procedure{\textsc{ChooseHashFunc}}{$k,L\in \mathbb{N}_+$} \For{$l \in [L]$}
\State \Comment{Amplify hash functions by concatenating}
\State $\mathcal{H}_{l} \leftarrow$ sample $k$ hash functions $(f_{1,l},f_{2,l},\cdots,f_{k,l})$ from $\mathcal{H}$ \EndFor
\EndProcedure
\State
\Procedure{\textsc{ConstructHashTable}}{$\{x_i\}_{i\in[n]}\subset \mathbb{R}^d$} \For{$l\in [L]$}
\For{$i\in [n]$}
\State $\mathcal{H}_l(x_i)$.\textsc{Insert}($x_i$) \State $\mathcal{T}_l\leftarrow \mathcal{T}_l\cup \mathcal{H}_l(x_i)$ \Comment{Creat hashtable by aggregating buckets} \EndFor
\EndFor
\EndProcedure
\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"
} | "2024-03-15T05:43:39.046127" | {
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Image2Structure - Latex
Dataset description
We introduce Image2Structure, a dataset to evaluate the capabilities of multimodel models to learn the structure of a document. This subdataset focuses on Latex code. The model is given an image of the expected output with the prompt:
Prease provide the LaTex code used to generate this image. Only generate the code relevant to what you see. Your code will be surrounded by all the imports necessary as well as the begin and end document delimiters.
An additional message is added if assets are available:
The following assets can be used:
- assets/cs/1_log.png
- ...
The assets are provided under the assets folder for each subject. The subjects were collected on ArXiv and are: eess, cs, stat, math, physics, econ, q-bio, q-fin.
The dataset is divided in 5 categories:
- equations
- figures
- tables
- algorithms
- code
- Downloads last month
- 148