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To construct a multivariate response data structure, we include three symptom related response variables from the dataset (\saychest ache, \saydyspnoea, \saypatient’s ability to perform normal tasks) along with the main response of interest, \saydiagnosis of mesothelioma. Thus, we have M=4,p=9,n=324M=4,\leavevmode\nobr... | Table 2: The coefficient values relating the explanatory variables to the main response variable (diagnosis of mesothelioma) obtained with naive mle and G-hive in the lung cancer dataset. | We apply our data driven G-hive procedure to a dataset from Chicco and Rovelli (2019) regarding mesothelioma, a type of lung cancer. Specifically, this dataset consists of real electronic health records on 324 patients in Turkey of which 96 are diagnosed with mesothelioma and 228 are not. The dataset includes 33 explan... | Next we evaluate the estimation error of Θ^\hat{\Theta} in three scenarios: (1) when we vary the level of influence of the hidden variables through the magnitude of η\eta, (2) when we increase the sample size nn, and (3) when we increase the dimension of the response MM. For (1) we vary η\eta to take values in {1,2,…,8... | To construct a multivariate response data structure, we include three symptom related response variables from the dataset (\saychest ache, \saydyspnoea, \saypatient’s ability to perform normal tasks) along with the main response of interest, \saydiagnosis of mesothelioma. Thus, we have M=4,p=9,n=324M=4,\leavevmode\nobr... | A |
Note: If the diversified projection is used for factor estimation, we randomly take out a tiny subset of the training set to estimate the diversified projection weight matrix and the number of factors. | Five statistical machining learn methods are considered as examples to verify if factor augmentation can improve the accuracy of learning algorithms. | Moreover, the right-hand side of Figure 7 displays the relative classification errors of different factor augmenting models with and without LR. If the point is below the zero horizon line, it indicates that further adding LR improves the performance in addition to the corresponding factor augmentation. It is shown tha... | We emphasize that the proposed feature augmentation framework is broadly applicable across diverse problem domains and learning algorithms. To demonstrate its general effectiveness in improving estimation performance, we complement the main study on Chinese news text data with a series of extensive experiments spanning... | Our goal is to verify the claim that simple feature augmentations can boost the performance of various learning methods across a wide range of datasets. | D |
This value can be elicited in several ways. One option is to define SlikelyS_{\text{likely}} as the mean of the truncated Gamma prior for SS, or as a simple midpoint of the elicited interval [L,U][L,U], i.e., Slikely=(L+U)/2S_{\text{likely}}=(L+U)/2. Alternatively, when historical survival data are available, SlikelyS_... | Under the pragmatic method, boundary optimization is performed only once, based on an initial estimate of the sample size. As the sample size is adjusted iteratively to achieve the desired statistical power, the originally estimated decision boundaries are retained throughout. Only after the sample size satisfies the p... | From Algorithm 2, two optimization strategies are considered for determining the final sample size and decision boundaries: optimal and suboptimal. | The sample size for a two-stage design is determined by minimizing the following weighted expected sample size function, while ensuring that the power is at least 1−β1-\beta when S∈[L,U]S\in[L,U]. This design aims to balance the need to minimize patient exposure to futile treatments and to maximize access to effective ... | While the original BOP2 framework provides practical decision rules, they do not include procedures for determining the necessary sample size to achieve desired operating characteristics, even in the two-stage setting. In this subsection, we introduce a novel method for determining both the interim and final sample siz... | D |
Maximum likelihood estimates of σ2\sigma^{2}, computed with the lme4 package (Bates et al.,, 2015), are in Table 1. The table also includes the corresponding estimates of h2h^{2} and τ2\tau^{2} (“total variance”). The estimate of σ12\sigma_{1}^{2}, the variance of the resistor random effect, is zero. The estimate of th... | Our focus is hypothesis tests, or inferences more generally, for the variance components and the proportions | Table 1: Maximum likelihood estimates of variance components and proportions of variability for the resistor data. Standard errors based on observed information are in parentheses. | Maximum likelihood estimates of σ2\sigma^{2}, computed with the lme4 package (Bates et al.,, 2015), are in Table 1. The table also includes the corresponding estimates of h2h^{2} and τ2\tau^{2} (“total variance”). The estimate of σ12\sigma_{1}^{2}, the variance of the resistor random effect, is zero. The estimate of th... | Figure 7: Densities for the distributions of widths of randomized split LRT confidence intervals for σ1\sigma_{1} (left) and σ2\sigma_{2} (right) with the resistor data. Based on drawing 1,000 random thresholds U(0,1)/α\mathrm{U}(0,1)/\alpha and computing the width for each threshold. | B |
Following the general pattern of the probit BART components from the gbart function in the BART R package (Sparapani et al.,, 2021), we add normal latent variables to the main function from monotone BART package (Chipman et al.,, 2022), following the ideas of Albert and Chib, (1993) and Chipman et al., (2010). These ad... | Before we proposal our model in Section 3, we first define original BART as well as the two variants of BART that our model proposal uses as cornerstones. | Our proposed probit monotone BART function, probit_monbart, is available as part of our modified version of the (Chipman et al.,, 2022)’s R package, mBARTprobit, available on Github (Fisher,, 2025). | Following the general pattern of the probit BART components from the gbart function in the BART R package (Sparapani et al.,, 2021), we add normal latent variables to the main function from monotone BART package (Chipman et al.,, 2022), following the ideas of Albert and Chib, (1993) and Chipman et al., (2010). These ad... | We present probit monotone BART, an important addition to the suite of BART tools that now allows monotone BART to estimate conditional expectations for binary outcome variables. An early version of the posterior sampler is available on Github (Fisher,, 2025). | B |
This serves as a computationally convenient conditional classification procedure for capturing nuances of individual mobility. Returns to activity regions must be defined explicitly since, although individuals do exhibit nonrandom routines, GPS spatial data measurements are on a continuous scale and unlikely to be repe... | To address these gaps, we introduce the Lévy flight cluster model (LFCM) — a generative Bayesian model for human mobility trajectories. Using the Lévy Itô decomposition, we model individuals’ movement as a Lévy flight exploration process that may exhibit a mixture of repetitive “activity clusters” represented by local ... | For a stochastic process {X¯(t):t≥0}\{\underline{X}(t):t\geq 0\}, the Lévy Flight Cluster Model (LFCM) is given by the mixture | Let x¯(t0)\underline{x}(t_{0}) denote the initial point observed in the spatio-temporal process {X¯(t):t≥0}\{\underline{X}(t):t\geq 0\}. The Mean-squared displacement of the process up to time tnt_{n} is defined by | Figure 6 illustrates the approximation using three instances of random walks in ℝ2\mathbb{R}^{2}, each run for 7,000 steps. Brownian motion steps are shown in black and Lévy flight jumps are shown in red; the left process is a Brownian motion, the middle process is a Lévy flight, and the right process is a Lévy flight ... | B |
The results show that the performance of signal-lasso-type methods depends on the variance of noise and the density of network connectivity, but are robust against distribution of the data. | (1) In cases of n>pn>p and the signal is sparse (first panel), we find that the SL_prod and SL_m outperform SigL and ASigL for different variance. In such cases, the SigL is not performs well, especially in case of large variance. When signal is non-sparse or dense, the results are the same (no show here). | We also discuss the performance of signal-lasso-type method in cases of non-sparse or dense signal, which usually appear in world trade web (WTW) (see Squartini, Fagiolo, and Garlaschelli (2011); Shi et al. (2023)). | Although CS and the lasso method are effective at shrinking parameter estimates toward zero, especially in sparse complex networks, they often fail to shrink existing links to their true value of 1, which can reduce estimation accuracy. To address this limitation, Shi et al. (2021) introduced the signal lasso (SigL) me... | We first consider the Case I and the results are listed in Table 2, where upper panel is for sparse signal with n>pn>p, middle panel is for sparse signal with n<pn<p, while bottom panel is about non-sparse signal with n<pn<p. The three column in each pane give the results of different variance with σ=0.4,1,2\sigma=0.4,... | B |
– a direct proof of a two-sided fixed point iteration under less restrictive assumptions than the ones in [6, Section 2.2], | The first and the second contribution seem to be new in the literature; in particular, we could not find a general convergence proof for the fixed point iteration used in [6] and also already in the software package [10]. One may note that the computation of univariate expectiles is also important for the computation o... | A fixed point iteration for ψα\psi_{\alpha} is the underlying idea of the Repeated Weighted Averaging (RWA) algorithm used in [10] for computing sample expectiles. In fact, the recursive formula in [6, p. 7] | (a version of the fixed point iteration for ψα\psi_{\alpha}) is also used by the codes in [10] to compute the empirical expectiles. This was probably not realized in [6] since it was not stated in the description/manual of [10]. On the other hand, [6] gives an interpretation of the fixed point iteration for ψα\psi_{\al... | The computation of expectiles is a non-trivial task. We refer the reader to the recent paper by Daouia, Stupfler and Usseglio-Carleve [6] which not only contains some exact computation formulas for the discrete case and numerical procedures such as a Newton type algorithm but also many examples illustrating several fea... | A |
H0∗:F=G=U(0,1)H_{0}^{*}:F=G=U(0,1) against H1a:F=U(0,1),G=U(a,1)H_{1}^{a}:F=U(0,1),G=U(a,1), for a fixed a∈(0,1)a\in(0,1), Vinzce [12, 13] uses the pair | With a view to Vincze’s idea, our approach is to use a transform Tnm=h(Rnm,Dnm)T_{nm}=h(R_{nm},D_{nm}) of the Vincze-statistic (Rnm,Dnm)(R_{nm},D_{nm}) as follows: | Tnm∗:={Dnm∗Rnm∗(n+m−Rnm∗) if Rnm∗∈{1,…,n+m−1},0 if Rnm∗=n+m.T_{nm}^{*}:=\begin{cases}\frac{D_{nm}^{*}}{\sqrt{R_{nm}^{*}(n+m-R_{nm}^{*})}}&\text{ if }R_{nm}^{*}\in\{1,\ldots,n+m-1\},\\ | Tnm:={DnmRnm(n+m−Rnm) if Rnm∈{1,…,n+m−1},0 if Rnm=n+m.T_{nm}:=\begin{cases}\frac{D_{nm}}{\sqrt{R_{nm}(n+m-R_{nm})}}&\text{ if }R_{nm}\in\{1,\ldots,n+m-1\},\\ | (Rnm,Dnm)(R_{nm},D_{nm}) instead of the single DnmD_{nm}. More precisely, in the case m=nm=n he determines the likelihood ratio of | D |
However, since the complexity of the true model is not know, RECI may compare residuals of arbitrarily underfit or overfit models. | is called an Identifiable Regression-based Scoring Function (IRSF), if both γ:ℝ≥0→ℝ\gamma:\mathbb{R}_{\geq 0}\to\mathbb{R} and λ:ℕ→ℝ\lambda:\mathbb{N}\to\mathbb{R} are strictly increasing. | The so-called Identifiable Regression-based Scoring Function (= IRSF) is proposed and a general framework for the identifiability of these functions is presented, including an instantiation by method SLOPPY, using splines and AIC and BIC as scoring function. | the cause and effect. Similarly, method RESIT from Peters et al. [35] executes the mean estimation, but an additional step of independence testing is done subsequently. | Paper [30] builds on the results of [31], and formulates an additional condition under which cause and effect are identifiable via so-called regularized regression. | D |
Next, observe that the functions log(t)\log(t) and log(1−t)\log(1-t) are both well defined over [τ,1−τ][\tau,1-\tau] for a small threshold τ>0\tau>0 , but not the entire ℝ\mathbb{R}. | With these modifications of log(t)\log(t) and log(1−t)\log(1-t), we then define the local extended surrogate log-likelihood (ESL) function for the latent position of a single vertex 𝐱i\mathbf{x}_{i} for GRDPG as | The global ESL function for the entire graph is defined as ℓ^n(𝐗)=∑i=1nℓ^in(𝐱i)\widehat{\ell}_{n}(\mathbf{X})=\sum_{i=1}^{n}\widehat{\ell}_{in}(\mathbf{x}_{i}). Here, the term “extended” means that the domain of the target function (2.3) is extended to the entire ℝd\mathbb{R}^{d} without constraint, and the term “... | It is desirable that these functions can be extended beyond this interval while certain regularities, such as differentiability and smoothness, are preserved. | The sums of squared errors of the four estimates are summarized in Table 1. While OSE is numerically unstable and has sums of squared errors larger than all other estimates due to the latent position 𝐯3=[0.7, 0.7]\mathbf{v}_{3}=[0.7,\,0.7] being close to the unit circle (two vertices in this block have an edge probabi... | C |
The rest of this paper is organized as follows. In Sections 2, we introduce the weighted functional principal component analysis and weighted functional linear model. The data-adaptive measure selections are established in Section 3. Simulations are shown in Section 4. Applications for COVID-19 data and the National He... | The rest of this paper is organized as follows. In Sections 2, we introduce the weighted functional principal component analysis and weighted functional linear model. The data-adaptive measure selections are established in Section 3. Simulations are shown in Section 4. Applications for COVID-19 data and the National He... | Through simulation studies and real data applications, we demonstrated that the approach consistently outperforms the standard functional linear model, offering a more flexible and powerful framework for functional linear regression. We also provide basic representations and relationships of eigen-systems for weighted ... | Table 1: Average mean squared prediction errors and standard deviations (in parentheses) for bounded domain 𝒯=[0,1]\mathcal{T}=[0,1], based on 1000 Monte Carlo simulations, comparing FLM (functional linear model with Lebesgue measure) and wFLM (weighted functional linear model with step function weights). | In this section, we introduce weighted functional principal component analysis (wFPCA) and then proceed to the wFPCA-based weighted functional linear model (wFLM). | D |
Let J(α)=12‖α−α0‖22−η∑iαilogαiJ(\alpha)=\tfrac{1}{2}\|\alpha-\alpha^{0}\|_{2}^{2}-\eta\sum_{i}\alpha_{i}\log\alpha_{i}. Then the KKT conditions yield | Let d(𝒟,𝒟′)d(\mathcal{D},\mathcal{D}^{\prime}) be a metric that dominates per-topic/section metrics. Under Assumption 1, | :=1|𝒮|∑s∈𝒮ps(𝒟s),V:=v(𝒟),E:=e(𝒟).\displaystyle:=\frac{1}{|\mathcal{S}|}\sum_{s\in\mathcal{S}}p_{s}(\mathcal{D}_{s}),\quad V:=v(\mathcal{D}),\quad E:=e(\mathcal{D}). | |mt(𝒟t)−mt(𝒟t′)|≤Lmdt(𝒟t,𝒟t′),etc.|m_{t}(\mathcal{D}_{t})-m_{t}(\mathcal{D}^{\prime}_{t})|\leq L_{m}\,d_{t}(\mathcal{D}_{t},\mathcal{D}^{\prime}_{t}),\quad\text{etc.} | Let 𝒮\mathcal{S} denote sections and 𝒯\mathcal{T} topics. A blueprint BB provides nonnegative weights {wt}t∈𝒯\{w_{t}\}_{t\in\mathcal{T}} with ∑twt=1\sum_{t}w_{t}=1, a duration TexamT_{\mathrm{exam}}, marking rules, and section-level pace targets {τs}s∈𝒮\{\tau_{s}\}_{s\in\mathcal{S}} (seconds per item). Interaction ... | A |
To address these limitations, we introduce Procause, a generative approach designed to estimate performance of PresPM methods in a realistic setting. ProCause enables evaluation using either non-sequential or sequential models, such as LSTMs, as the base model for three key learner architectures from the CI field: S-Le... | The paper is structured as follows. Section II provides background, and Section III outlines the motivation for ProCause. Section IV describes the methodology, followed by Sections V and VI, which cover the experimental setup and results. Section VII offers a discussion, and Section VIII concludes the paper. | This section presents the results. We start with the simulator to assess evaluation accuracy, discussing the impacts of learner type, model type, and providing general remarks. We conclude with real datasets to validate the realism of the generated variables. | We begin by generating a fixed training set using SimBank, which we split into two parts. One subset of 10,000 cases is used to train evaluators. Each evaluator is defined by a choice of learner (including an ensemble, which involves training 3 separate learners) and an underlying model (either an MLP or an LSTM). Each... | Second, it only implements the TARNet architecture, which may not yield reliable counterfactual estimates across all datasets, as described in Section II. More critically, selecting the most appropriate learner depends on identifying certain data characteristics (e.g., effect heterogeneity, see Section II), which is in... | A |
We compared Causal SHAP against five baseline methods using the insertion test [15], which sequentially adds features from most to least important based on each method’s attributions, measuring AUROC, Cross Entropy and Brier scores at each step. High AUROC, lower Cross Entropy and Brier scores indicate better performan... | On IBS dataset: Best AUROC (0.8594) and second-best Cross Entropy (0.4645) and Brier scores (0.1464) | Bold values indicate the best performance and underline values indicate second best for each dataset and metric. | We compared Causal SHAP against five baseline methods using the insertion test [15], which sequentially adds features from most to least important based on each method’s attributions, measuring AUROC, Cross Entropy and Brier scores at each step. High AUROC, lower Cross Entropy and Brier scores indicate better performan... | On Colorectal Cancer dataset: Best performance across all metrics (AUROC: 0.6271, Cross Entropy: 0.6735, Brier: 0.2397) | A |
Our combinatorial symmetries offer a complementary form of regularity that neural networks can exploit—distinct from the strong smoothness assumptions commonly used in scientific computing inspired deep learning [4, 19, 27], and more amenable to practical verification than compositional assumptions on the target functi... | Leveraging these results, we show that a sample complexity of 𝒪(1/Nr)≪𝒪(1/N)\mathcal{O}(1/N^{r})\ll\mathcal{O}(1/N) is achievable for any OOD regression task that shares the same combinatorial symmetries as the pre-training task (Corollary 5.1). This yields strictly faster rates than those obtainable via classical ... | . We exhibit a neural network architecture and propose a concrete, architecture-specific, randomized end-to-end training algorithm that learns network parameters implementing a uniform approximator of the ground truth function; even when trained on noisy data. Unlike RFN and NTK approaches, our training procedure (Algo... | We now specify the initialization scheme used for the weights and biases of our 33-layer MLP encoder. Our procedure largely follows standard random initialization protocols, with a mild but deliberate modification: we adjust the variance of the random weight matrices and choose non-random biases, following insights fro... | We note that when provided with noiseless training data our algorithm implies a randomized polynomial-time procedure for constructing a three-layer MLP capable of memorizing any finite regression dataset. Unlike the result of [34], our approach is not restricted to binary classification. Moreover, unlike [78, 110], thi... | D |
UMAP is a state-of-the-art non-linear dimensionality reduction technique adept at preserving both local and global data structures (McInnes et al., 2018). A KMeans clustering on these combined embeddings then produces tight, well‐separated topic groups without requiring supervision or predetermined labels (MacQueen, 19... | The integration of Top2Vec for automatic topic discovery and dense vector representation, followed by the construction of a document-topic bipartite graph and subsequent refinement of embeddings using Node2Vec, forms the cornerstone of our approach. This unique combination allows the model to capture not only the seman... | Figure 1 illustrates the overall pipeline: legal documents are first converted into semantic embeddings via Top2Vec, while a relational graph is embedded via Node2Vec; these embeddings are then concatenated and clustered using KMeans. To evaluate the effectiveness of our hybrid ‘Top2Vec+Node2Vec’ approach, we compare i... | To verify that the complexity of our hybrid model is justified, we conducted an ablation study to isolate the contribution of each component. We compared the full hybrid model against a semantic-only model (Top2Vec + KMeans) and a traditional baseline (TF-IDF + KMeans). The results, presented in Table 3, provide unequi... | In conclusion, the ‘Top2Vec+Node2Vec’ hybrid pipeline represents a compelling advancement for legal tech: it enables unsupervised discovery of themes in legal document collections with a high degree of analytical rigor and clarity. The methodology scales to large corpora and requires no labeled data, making it attracti... | B |
MEMs are commonly used to model complex systems that give rise to structured data, e.g., in network science [16, 17, 18] and time-series analysis [19, 20], where they capture structural properties such as (heterogeneous) node degrees in networks or empirical trends in (non-stationary) temporal data, respectively. | In particular, the hypothesis tests for contingency tables developed here have a direct correspondence with hypothesis tests between common network models. | For instance, when applied to networks, maximum entropy models in their canonical formulations are known as exponential random graph models [43, 44, 18]. Examples of commonly used maximum entropy network models are the Erdős–Rényi model, Configuration Models, and Stochastic Block Models [18, 16]. The framework presente... | The aim of this work is to develop optimal e-variables for hypothesis testing between maximum entropy models (MEMs). These models are derived by considering each possible realization 𝐱∈𝒳\mathbf{x}\in\mathcal{X} of the data (where 𝒳\mathcal{X} is the set of allowed realizations) and looking for the probability distri... | However, while statistical tests for exponential family models are well established, testing procedures specifically tailored to maximum entropy models remain far less developed, especially when applied in the microcanonical setting. | D |
Low Robustness: Existing evaluation metrics are sensitive to minor perturbations in anomaly scores, leading to unstable evaluation results. F1, F1-PA, and UAff-F1 all depend on anomaly score thresholds for calculation, making them highly sensitive to minor changes in anomaly scores and resulting in unstable evaluation ... | Property 5 (Scalability): The computational complexity of CCE is 𝒪(n)\mathcal{O}(n), where nn is the length of the time series data. CCE can be efficiently computed for large datasets, making it suitable for large-scale anomaly detection tasks. | High Computational Cost: VUS-ROC and PATE metrics have high computational costs, limiting their application and evaluation on large-scale datasets. Typically, excessive complexity is not conducive to rapid validation of new model development. | Hyperparameter Dependency: F1-PA, Aff-F1, and UAff-F1 rely on anomaly threshold selection during evaluation, resulting in slow evaluation speed and limiting their use for model selection. VUS-ROC and PATE do not require anomaly thresholds but need event buffer size settings, which affects the stability and reproducibil... | Property 1 (Intuition): CCE quantifies the model’s ability to distinguish between normal and anomalous events by evaluating both confidence and consistency. High confidence and high consistency indicate that the model’s predictions for normal and anomalous events are more reliable. | B |
Performative prediction, introduced by [1], describes a scenario where the deployment of a prediction model causes a shift in the data distribution it aims to predict. This concept has been extensively investigated across various domains involving decision-making or human interaction, such as recommendation system [2, ... | PerfGD [16] calculates the gradient of performative loss ℓ(θ)\ell(\theta) by combining the gradient of logistic regression loss function ℓ(θ)\ell(\theta) and the gradient induced by data distribution map 𝒟(θ)\mathcal{D}(\theta). PerfGD converges to performative optimality when its assumptions (e.g., the convexity o... | In performative prediction, the so-called performative loss (risk) is defined as the expected loss ℓ(𝐗,𝐲,θ)\ell(\mathbf{X},\mathbf{y},\theta) over the model-induced data distribution: | Performative Loss (Risk)=ℓ(𝐗,𝐲,θ){𝐗,𝐲}∼𝒟(θ),\text{Performative Loss (Risk)}=\underset{\{\mathbf{X},\mathbf{y}\}\sim\mathcal{D}(\theta)}{\operatorname*{\ell(\mathbf{X},\mathbf{y},\theta)}}, | DFO(λ\lambda) [18] estimates the gradient of performative loss with derivative-free optimization. The performative optimality can be achieved when the performative loss is convex. For non-convex performative loss, the resulting model leads to stationary points of performative loss when the loss value is bounded, and 𝒟... | B |
A plethora of structured data comes in the form of graphs (Bornholdt and Schuster, 2001; Malliaros and Vazirgiannis, 2013; Cao et al., 2020). This has driven the need to develop neural network models, known as Graph Neural Networks (GNNs), that can effectively process and analyze graph-structured data. GNNs have garner... | This need for per-node customization naturally aligns with the concept of Dynamic Neural Networks, also referred to as Adaptive Neural Networks (Bolukbasi et al., 2017). Dynamic Neural Networks represent a class of models that can adjust their architecture or parameters depending on the input. Dynamic Neural Networks h... | Determining the optimal number of message passing layers for each node in a GNN presents a significant challenge due to the intricate and diverse nature of graph structures, node features, and learning tasks. While deeper GNNs can capture long-range dependencies (Liu et al., 2021), they can also encounter issues like o... | In Graph Machine Learning, dynamic adaptations have been proposed for GNN message passing. These methods include dynamically determining which neighbors to consider at each layer, enabling more flexible and adaptive message passing (Finkelshtein et al., 2024), or allowing nodes to react to individual messages at varyin... | A plethora of structured data comes in the form of graphs (Bornholdt and Schuster, 2001; Malliaros and Vazirgiannis, 2013; Cao et al., 2020). This has driven the need to develop neural network models, known as Graph Neural Networks (GNNs), that can effectively process and analyze graph-structured data. GNNs have garner... | B |
H0:P(Extension|W1)=P(Extension|W2)=⋯=P(Extension|W7+).H_{0}:P(\text{Extension}|W_{1})=P(\text{Extension}|W_{2})=\cdots=P(\text{Extension}|W_{7+}). | It is noteworthy that among the aforementioned studies, the primary focus has been on confirming the presence of momentum in tennis competitions. However, a systematic framework for examining the influence mechanisms of the momentum effect has yet to be established. For instance, there has been a notable absence of in-... | When all expected frequencies satisfy n^ij≥5\hat{n}_{ij}\geq 5 and the total number of winning streaks n≥50n\geq 50, we apply Pearson’s Chi-squared test. | The statistical analysis meets all necessary assumptions for Pearson’s Chi-squared test, with each expected frequency n^ij>5\hat{n}_{ij}>5 and a sufficiently large sample size (n=3595≫50n=3595\gg 50). The calculated test statistic yields χ2=111.497\chi^{2}=111.497 with an extremely significant pp-value of 9.51×10−189.... | Under the null hypothesis, χ2\chi^{2} asymptotically follows a χ2\chi^{2}-distribution with k−1k-1 degrees of freedom. Let χ02\chi_{0}^{2} denote the observed test statistic. If the pp-value P(χ2>χ02)P(\chi^{2}>\chi_{0}^{2}) falls below the significance level α\alpha, we reject the null hypothesis, providing statistic... | C |
𝐫k+1=𝐲−𝚽Λk+1𝐱Λk+1\mathbf{r}^{k+1}=\mathbf{y}-\mathbf{\Phi}_{\Lambda^{k+1}}\mathbf{x}_{\Lambda^{k+1}} | In each iteration, the OMP sequentially employs four steps: (i) sweep or identification, (ii) update support or augmentation, (iii) update provisional solution or estimation, and (iv) update residual steps [21, 1, 8, 9]. In each iteration kk, in sweep stage, the algorithm chooses the most correlated column with the res... | Although OMP presented an exciting method for solving the ℓ0\ell_{0} norm problem effectively, the computational burden is quite extensive because in each iteration only one new non-zero element is added to the solution vector 𝐱\mathbf{x} and every time the vector 𝐱\mathbf{x} has to be newly solved, computing a new r... | to obtain the updated sparse solution vector 𝐱Λk+1\mathbf{x}_{\Lambda^{k+1}}. This is followed by the update residual step, where the new residual 𝐫k+1\mathbf{r}^{k+1} is calculated as: | In the generalized orthogonal matching pursuit (gOMP) algorithm[21], Wang et.al. attempted to reduce the computational complexity of the original OMP algorithm, modifying the sweep or identification step in each iteration. The main spirit of this algorithm is to choose multiple numbers of atoms (𝚽i\mathbf{\Phi}_{i}) i... | B |
These observations have received relatively less attention than the efficiency properties of PML estimators, but they raise some important questions on PML estimators, including Poisson regression. Although their behaviors with respect to heteroskedasticity and sparsity have been studied separately before, they are les... | When modeling data with non-negative outcomes, understanding the interactions between these features can help empirical researchers decide which regression approach to use that best handles the sparse non-negative data at hand. | However, as is well-known to empirical researchers and also illustrated by our examples in Section˜5, non-negative data in many finance and economics applications frequently exhibit both sparsity and heteroskedasticity. Yet, few studies address these characteristics simultaneously, and it remains unclear whether Poisso... | It may appear that under heteroskedasticity, one should always use the estimator that best captures the conditional variance as a function of the conditional mean, by determining the value of α\alpha. Previous works have proposed these types of methods to determine the dispersion using regression-based tests (Park, 196... | In this paper, we provide a systematic study of the interplays between these two prominent features of non-negative data. We use the model (2) to capture heteroskedasticity indexed by α\alpha. To capture excess levels of sparsity, we use the following censoring model: | A |
The malaria data consist of monthly counts of laboratory-confirmed malaria diagnoses from all health facilities across Niassa, a province in Mozambique, aggregated at the level of its 16 administrative districts, from 2017 to 2024. Access to these data was granted through a Data Transfer Agreement with the National Mal... | While these models offer a principled approach to capture spatio-temporal dependencies, they come with notable limitations. A major drawback is that they often struggle to represent localized temporal trends while preserving appropriate smoothing across space and time (Rushworth et al., 2017). This issue often stems fr... | Areal data represent observations linked to non-overlapping spatial units such as districts, counties, or municipalities. These data frequently arise in public health and environmental contexts, and are often collected at multiple time points. For instance, in disease mapping, the incidence of an infectious disease, re... | To overcome these limitations, spatio-temporal (ST) models have been developed to explicitly account for both spatial and temporal dependencies (Wang et al., 2024; Nazia et al., 2022). These models exploit the correlation structure in the data to improve efficiency and predictive accuracy while preventing overestimatio... | A crucial challenge in this context lies in accurately predicting when and where malaria outbreaks will occur, especially given the high spatial and temporal heterogeneity observed in the data. Standard approaches to modeling reported malaria counts often rely on spatio-temporal hierarchical models with global spatial ... | D |
We consider categorical random variables X1X_{1}, X2X_{2}, with KK categories each, respectively, defined by probability vectors 𝝅1∼Dirichlet(K,𝜶1)\bm{\pi}_{1}~\sim~\mathrm{Dirichlet}(K,\bm{\alpha}_{1}), 𝝅2X1=x1∼Dirichlet(K,𝜶2)\bm{\pi}_{2}^{X_{1}=x_{1}}~\sim~\mathrm{Dirichlet}(K,\bm{\alpha}_{2}), which are random... | An intervention on X1X_{1} means sampling a new 𝝅1\bm{\pi}_{1} for P(X1)P(X_{1}), while leaving the conditional P(X2|X1)P(X_{2}|X_{1}) unchanged. The marginal P(X2)P(X_{2}) thus also changes. An intervention on X2X_{2} means that X2X_{2} is fixed to a new distribution and made independent of X1X_{1}. In practice, w... | That is, we use Dirichlet priors to generate categorical distributions for both variables. The Dirichlet distributions, in turn, are specified by parameter vectors 𝜶1\bm{\alpha}_{1} and 𝜶2\bm{\alpha}_{2} that determine their shape. We set these parameters to | To achieve symmetry of marginal distributions in our generated synthetic data, at least for an observational case, we borrow the Bayesian Dirichlet equivalence (BDe) prior from the classical literature of structure learning (Koller & Friedman, 2009, Section 18.3.6.3). This allows us to control the extent of Bias 1: Mar... | We consider categorical random variables X1X_{1}, X2X_{2}, with KK categories each, respectively, defined by probability vectors 𝝅1∼Dirichlet(K,𝜶1)\bm{\pi}_{1}~\sim~\mathrm{Dirichlet}(K,\bm{\alpha}_{1}), 𝝅2X1=x1∼Dirichlet(K,𝜶2)\bm{\pi}_{2}^{X_{1}=x_{1}}~\sim~\mathrm{Dirichlet}(K,\bm{\alpha}_{2}), which are random... | B |
In [34], an improved architecture called the “modified DeepONet” was proposed, as illustrated in Figure˜2. This architecture retains the “vanilla” DeepONet as a backbone but incorporates two additional encoders and modifies the forward pass. While these changes reportedly lead to more accurate predictions, they also in... | We proposed a series of Transformer-inspired variants of DeepONet that balance the trade-off between predictive accuracy and computational efficiency observed in the “vanilla” DeepONet and the modified DeepONet models. | The trade-off between predictive accuracy and computational cost inherent in the existing “vanilla” DeepONet and the modified DeepONet frameworks motivates our work. The modified DeepONet, as introduced in [34], exhibits superior predictive accuracy in solving PDEs. However, compared to the “vanilla” DeepONet, it impos... | Specifically, to improve the predictive accuracy of the “vanilla” DeepONet, a modified DeepONet architecture with increased structural complexity was proposed in prior work [34]. While this design demonstrates improved predictive accuracy across a range of PDE benchmarks, it typically requires two to three times longer... | This section introduces the architectures of the operator learning models investigated in this study. We first describe the foundational “vanilla” DeepONet [20, 33] and modified DeepONet [34] frameworks in Section˜2.1. Building upon these concepts, Section˜2.2 then details the structure of our proposed Transformer-insp... | B |
This is from a direct computation. The boundary condition arises from a change of variables with the standard heat kernel. The derivation can be found in A.1. | We now define the preconditioned regularized Wasserstein proximal operator as the terminal time solution to a particular set of PDEs. Then, we show that it is equivalently a convolution involving another inhomogeneous kernel, with the kernel itself defined as a convolution with the anisotropic heat kernel. | We have seen that the regularized Wasserstein proximal is a particular Laplacian regularization of the Benamou–Brenier formulation, corresponding to coupled heat equations and computable using a kernel formula [29]. In this section, we define a geometry-aware elliptic regularization to the Benamou–Brenier formulation, ... | In particular, plugging in t=Tt=T, we have the following kernel formula for the PRWPO which is defined as the terminal solution. | Compared to Eq. 10, the preconditioned kernel replaces the Euclidean norm ‖x−y‖2\|x-y\|^{2} with the scaled norm ‖x−y‖M2\|x-y\|_{M}^{2}, which is by construction. We show that the terminal density and the kernel formula are equivalent in the following section. | A |
Luckily, the bootstrap is valid by Theorem 2 and corresponding confidence intervals may behave better in small samples. | Because the number of independent trials NN tends to be small in practice, the multinomial bootstrap will lead to a very discrete bootstrap distribution. We expect this to negatively influence finite-sample performance. Therefore, we opt for the Bayesian bootstrap instead [91], which is a multiplier bootstrap with the ... | For the multinomial bootstrap, the bootstrap weights are obtained by sampling from a multinomial distribution with NN trials and NN categories, where the probability of each category is 1/N1/N. | EWh(X˘N)E_{W}h(\breve{X}_{N}) is the expectation of h(X˘N)h(\breve{X}_{N}) with respect to the bootstrap weights WW given the remaining data | For both the multiplier and multinomial bootstrap, the bootstrap weights are independent of the observed data O1,…,ONO_{1},\dots,O_{N}. | A |
There are two natural approaches. (A) We might fit a highly flexible classifier — e.g., a transformer (Vaswani et al.,, 2017), or gradient-boosted tree (Chen and Guestrin,, 2016) — and then apply a post hoc interpretability method (e.g. Lundberg and Lee,, 2017; Ribeiro et al.,, 2016). But data in these applications are... | Therefore, we need both a new estimator, as well as a new confidence interval, for the binary- and count-valued response setting. We provide these in the present work. Along the way, we also provide an estimator and asymptotically valid confidence intervals for continuous responses with spatially varying noise. In part... | In each experiment, we draw 1000010000 training locations uniformly from [−1,1]2[-1,1]^{2}. The target locations are then constructed differently across the two designs. In the first experiment, targets are concentrated within a subset of the square, determined by a scale parameter, so that the infill property holds. I... | Limitations when Extrapolating. In cases where extrapolation is needed because the training data are not available near the target locations (either because of finite data or because the distribution of training locations is not supported near the target locations), we cannot hope to estimate βMLE\beta^{\text{MLE}} arb... | Additional challenges arise in the applications described, though. Namely, the spatial locations where we want to draw inferences need not align well with the locations where we have data. E.g., in example (c) above, scientists have access to sensors across the state but are interested in associations in major Texas ci... | D |
Instead, the price of sparsification is due to a bias in the observations that we explain by the fact that the sparsified observations Y~\tilde{Y} were not obtained as noisy projections of the true signal as in the original model (4), but rather via a naïve rescaling of the original observations (11). By simply rescali... | Given dense data and a fixed large enough sample size nn, by up to how much could we sparsify the data and still get recovery? We call this the sparsification budget. According to our result (14), its expression in the strong-sparsification regime is given by: | In the second part of this paper, we have studied the problem of recovering the signal based on sparsified – but originally dense – measurements and accordingly-rescaled observations. Our main result is that, in the linear sparsity and linear sparsification regime where s=αps=\alpha p and d=ψpd=\psi p for constant α,... | We call the amount of additional observations in the sparsification setting compared to the dense one price of sparsification. Unlike the price of sparsity, it is not due to the sparsity of the measurements but rather to a bias in the observations. We also interpret our result as providing an expression of the sparsifi... | Nevertheless, we believe that the sparsification problem is infeasible for strong enough regimes of sparsification. In particular, we conjecture that the recovery is information-theoretically impossible no matter the sample size in the sub-linear sparsification regime where d=o(p)d=o\left({p}\right). We leave the expl... | A |
The model we propose focuses on the disease transmission process and ultimately specifies the likelihood P(𝒟|𝒯)P(\mathcal{D}|\mathcal{T}) of observing the data 𝒟\mathcal{D} for a given tree 𝒯\mathcal{T}. We consider the observations in each host ii conditionally independent of each other (i.e., given 𝒯\mathcal{T}... | Figure 4: Convergence of the MCMC sampler to the theoretical results in the synthetic data. Each plot shows the ratio of the frequency of two networks 𝒯\mathcal{T} (see legend and networks 𝒯1,𝒯2\mathcal{T}_{1},\mathcal{T}_{2}, and 𝒯3\mathcal{T}_{3} on the right) as a function of the number of Markov steps performed... | While we assume that tisamplingt^{\textrm{sampling}}_{i} is available for all NSN_{S} sampled hosts, we consider that the location and genetic sequencing may be available only for some of them. Our main interest is to investigate how the properties of the inferred 𝒯\mathcal{T} depends on each of the three datasets, i.... | The model for each of the nodes ii considers that Pi(𝒟|𝒯)P_{i}(\mathcal{D}|\mathcal{T}) results from processes modelled through the following five models. Our general approach, and the first three models below, follow Ref. [28]. | We considered the problem of quantifying the dependence of inferred transmission trees 𝒯\mathcal{T} of a disease outbreak on different types of datasets 𝒟\mathcal{D} of sampled hosts: sampling time, location, and pairwise genetic distance of the virus. Our main methodological contribution is the proposal of a combine... | C |
Suppose ℳ=(𝐕,𝐔,𝐅,P(𝐔))\mathcal{M}=(\mathbf{V},\mathbf{U},\mathbf{F},P(\mathbf{U})) is a simple SCM with observational distribution Pℳ(𝐕)P^{\mathcal{M}}(\mathbf{V}) and causal graph 𝒢\mathcal{G}. For convenience, we usually drop the superscript ℳ\mathcal{M} when it is clear from the context. | It has been shown that PP always satisfies σ\sigma-Markov property with respect to 𝒢\mathcal{G}. However, the dd-Markov property holds in specific settings, e.g., acyclic SCMs, SCMs with continuous variables and linear relations, or SCMs with discrete variables (Bongers et al., 2021). | An SCM is called acyclic if the corresponding causal graph does not contain a cycle. According to Bongers et al. (2021), an acyclic SCM always induces unique observational, interventional, and counterfactual distributions, while this does not hold for an SCM with cycles. To solve this issue, Bongers et al. (2021) intro... | Scenarios 2: PℳP^{\mathcal{M}} satisfies σ\sigma-Markov property and σ\sigma-faithfulness w.r.t. 𝒢\mathcal{G}. In this case, CI relations are equivalent to dd-separations. That is,(X⟂⟂Y|𝐙)P⟺(X⟂⟂σY|𝐙)𝒢(X\perp\!\!\!\perp Y|\mathbf{Z})_{P}\Longleftrightarrow(X\perp\!\!\!\perp_{\sigma}Y|\mathbf{Z})_{\mathcal{G}}. | (X⟂⟂Y|𝐙)P(X\perp\!\!\!\perp Y|\mathbf{Z})_{P} holds in PP. Similarly, a distribution PP satisfies rr-faithfulness with respect to | A |
Patient dropout may occur between the start of the transplant referral stage and the final transplant listing decision. The likelihood of patient dropout in this process is nonrandom and evidence suggests that this may be linked to social determinants of health. Specifically, patients from underrepresented race/ethnici... | In practice, estimating mediation effects from available clinical data may be affected by sample selection bias. The population of interest is comprised of all patients referred to the transplantation clinic (and thus “at risk” of being listed for transplant). But the sample available for analysis typically only contai... | We analyze data from a retrospective cohort of liver transplant candidates at Johns Hopkins Hospital. The target population consists of patients referred for liver transplantation from 1/1/2016-12/31/2017. The data includes patient information across five categories: baseline SDOH, SEP, disease-related variables, the o... | We aim to estimate the target NIE and NDE parameters while accounting for any potential bias from sample selection. For patients who do not complete the evaluation process, there is no information on psychosocial review or listing outcomes, so our estimates of the NIE and NDE can only be based on the 361361 out of 4974... | Organ transplantation, in particular liver transplantation, is one domain where gender, racial, and socioeconomic position (SEP) disparities have been recognized (Mathur et al., 2010; Nephew and Serper, 2021; Warren et al., 2021) and interest in using machine learning for patient prioritization has been growing (Khorsa... | B |
The influence of spatio-temporal dependence was assessed on the posterior estimates of the coefficients for the weed control covariates, 𝜷C:p\bm{\beta}_{C:p}, including the association with species-specific control events and duration since a control event. For St. John’s wort, the 95% central CIs spanned zero for bot... | The sparseness of the ordinal data for each species in space and time (Section 2) was accommodated by the separable spatio-temporal model formulation described above. The posterior estimates for parameters are summarised in Table 2. Maps of the predictive posterior median probability of each ordinal category on 1 July ... | Serrated tussock also suggested the possibility that estimated positive associations between control events and increased weed coverage could arise due to higher probabilities of targeting high abundance sites. Posterior estimates (Table 2) suggested a positive association between population size and a control event th... | In addition to the spatio-temporal model, an ordinal GLM without random effects (M1M_{1}) and a model with only spatial dependence (M2M_{2}) were also fit for each of the four species (Supplementary Information); the full separable spatio-temporal model is M3M_{3}. These models were evaluated to assess the influence of... | The influence of spatio-temporal dependence was assessed on the posterior estimates of the coefficients for the weed control covariates, 𝜷C:p\bm{\beta}_{C:p}, including the association with species-specific control events and duration since a control event. For St. John’s wort, the 95% central CIs spanned zero for bot... | B |
Since BPS-PT evaluates the event rate for all of the permutations in the subset, the computation time of BPS-PT was approximately 4!+4!+2=504!+4!+2=50 times longer than BPS, which is a reason for the difference in computation time. | Fig. 1 shows the change in the maximum KS value with respect to the components of the continuous variable as a function of the number of samples. | Since the BPS failed to estimate the cluster probabilities, KS value for the BPS does not decrease as the number of samples increases. In contrast, KS value for the BPS-PT decreases with the number of samples. | Tab. 1 shows the cluster probability estimates, that is, the number of samples with each cluster index divided by the number of samples, by BPS and BPS-PT. | Table 1: Comparison of cluster probability estimates using BPS and BPS-PT samples. For BPS-PT, we only shows the cluster probability estimates for β=1\beta=1. We can find that the PT improves the estimation accuracy. | C |
The generalRSS provides six statistical inference functions for estimating and testing the population means, medians, proportions, and AUCs using RSS data. These functions include both parametric and nonparametric methods, as summarized in Table 2. | Both rss.z.test() and rss.t.test() functions handle one-sample and two-sample problems using the same pivotal statistics but differ in their approximation methods. The following example demonstrates the rss.t.test() function for a two-sample problem, testing the hypothesis that the population mean difference is 0: | The rss.sign.test() function performs a nonparametric one-sample sign test, providing median estimation, CIs, and hypothesis testing. For BRSS, the function follows the method of [17] whereas it implements the approach of [7] for URSS. Under the null hypothesis H0:M=M0H_{0}:M=M_{0}, the test statistic for BRSS is: | The rss.z.test() function provides point estimation, confidence intervals (CIs), and hypothesis testing for the population mean using a normal approximation for RSS data [13, 2]. | rss.AUC.test() returns the RSS AUC point estimate, CI, the ELR test statistics, and the pp value for the test. | C |
Prevalence of identity slippage was highest in political science (n = 42, 69%), followed by economics (n = 60, 68%), epidemiology (n = 61, 56%) and medicine (n = 22, 46%). Table 3 illustrates the prevalence of identity slippage stratified by discipline, approach (pragmatic vs. strict), and whether the estimand was expl... | Prevalence of identity slippage was highest in political science (n = 42, 69%), followed by economics (n = 60, 68%), epidemiology (n = 61, 56%) and medicine (n = 22, 46%). Table 3 illustrates the prevalence of identity slippage stratified by discipline, approach (pragmatic vs. strict), and whether the estimand was expl... | Figure 5: Prevalence of identity slippage across article section by discipline. Letter in parentheses denotes claim type. | All studies that targeted ΨLATE\Psi_{LATE} were evaluated for identity slippage (n = 299, 97%). Of these, 183 (61%) exhibited instances of identity slippage in at least one article section, and 145 (48%) omitted any explicit reference to the local nature of the estimand, leaving it to readers to infer. Prevalence of... | Table 3: Prevalence of identity slippage by discipline, framework and whether estimand was explicitly specified | D |
Given a real-valued random variable YY, suppose that YY and −Y-Y has the common distribution; that is, Y=𝑑−YY\overset{d}{=}-Y. Then, ℙ(Y≥0)≥1/2\mathbb{P}(Y\geq 0)\geq 1/2. | It directly follows that ∑i=1nℙ(d(Xi,μ)>n)=nℙ(d(X1,μ)>n)→n→∞0\sum_{i=1}^{n}\mathbb{P}(d(X_{i},\mu)>n)=n\mathbb{P}(d(X_{1},\mu)>n)\underset{n\to\infty}{\to}0. An application of Lemma 3 for p=2p=2 leads that for any real-valued random variable YY, 𝔼Y2=∫0∞2t⋅ℙ(|Y|>t)𝑑t\mathbb{E}Y^{2}=\int_{0}^{\infty}2t\cdot\... | The notion of geodesic symmetry of a probability distribution ℙX\mathbb{P}_{X} is defined as follows. | Since YY and −Y-Y have the same distribution, an application of countable sub-additivity of probability measures leads that | Given a real-valued random variable YY, suppose that YY and −Y-Y has the common distribution; that is, Y=𝑑−YY\overset{d}{=}-Y. Then, ℙ(Y≥0)≥1/2\mathbb{P}(Y\geq 0)\geq 1/2. | C |
More recently, Salaroli and del Carmen Pardo (2023) introduced a penalized Youden index-based method that incorporates various penalty terms. While innovative, this approach lacks theoretical guarantees and employs a generic optimization algorithm (MAPG) that is not specifically tailored for biomarker selection tasks, ... | Existing approaches for biomarker selection and combination frequently utilize logistic regression or support vector machines (SVM) (Li et al., 2022; Becker et al., 2011), valued for their simplicity and robustness. However, these methods are limited by their inability to directly optimize receiver operating characteri... | Despite their utility, metrics like AUC and pAUC lack granularity for clinical decision-making because they do not provide explicit cutoff points. The Youden index, by identifying an optimal cutoff, addresses this limitation but assumes equal importance for sensitivity and specificity, which may not align with clinical... | Approaches targeting ROC-related metrics can be broadly categorized into two main types. The first category comprises empirical performance-based methods, which typically follow a two-step framework: biomarkers are first selected based on their contributions to metrics like AUC or pAUC, and then combined. For example, ... | To address these limitations, we introduce a novel approach that combines practical applicability, theoretical rigor, and computational innovation. By adopting the weighted Youden index as the optimization objective, our method allows for greater flexibility in aligning with clinical priorities, such as balancing sensi... | B |
For the beta prior with parameters aa and bb, choosing values below 1 (i.e. a<1a<1 or b<1b<1) can lead to extreme behavior in the posterior, such as a mode at the boundary (0 or 1) when the observed counts are very small. | To ensure well-behaved posterior estimates and avoid such issues, we recommend using a,b≥1a,b\geq 1, which corresponds to a non-informative or weakly informative prior that provides shrinkage without producing extreme modes. | For the beta prior with parameters aa and bb, choosing values below 1 (i.e. a<1a<1 or b<1b<1) can lead to extreme behavior in the posterior, such as a mode at the boundary (0 or 1) when the observed counts are very small. | We can say that the concept of “non-informative” prior is quite misleading, because the non-informative estimates π~BL\tilde{\pi}_{BL} and π~J\tilde{\pi}_{J} do not correspond to the MLE. | naturally, X=nX=n represents an analogous complication. The conclusion was to avoid a<1a<1 and b<1b<1 for beta priors and thus to avoid Jeffreys prior. Among informative priors for the situation with some prior knowledge about π\pi, the beta prior represents a very flexible and highly recommendable choice. The estimate... | A |
Let (ℙm,P)(\mathbb{P}^{m},P) be a full-dimensional simplex-like positive geometry. If P^\widehat{P} is a minimal spectrahedral cone, then PP a completely monotone positive geometry. | Note that (ℙm,P)(\mathbb{P}^{m},P) is simplex-like if and only if ∂aP\partial_{a}P is cut out by a homogeneous polynomial of degree m+1m+1. | By simplex-like we mean the algebraic boundary of P⊂ℙmP\subset\mathbb{P}^{m} has degree m+1m+1, and by minimal spectrahedral we mean the algebraic boundary is cut out by a polynomial admitting a symmetric determinantal representation, for which P^\widehat{P} is a hyperbolicity cone. An example is the half-pizza, a posi... | Its algebraic boundary consists of two components, one of degree four, cut out by the dual variety to V(p)V(p) and given by the vanishing locus of | If (ℙm,P)(\mathbb{P}^{m},P) is a completely monotone positive geometry, then its algebraic boundary, the Zariski closure of its topological boundary, is cut out by a hyperbolic polynomial with hyperbolicity region equal to PP. | B |
Table 1: Datasets and their original publication. Two of them have not been published yet. Donate A Cry can be found on Github. We give the total number of cry, their mean duration and standard deviation, in seconds, the number of baby recorded and the range of cries per baby. For Donate A Cry dataset, we do not have t... | Although our results might suggest that these latent representations could be used to predict the cause of cries, we must remain very cautious with this possibility. The results obtained from the Donate A Cry dataset are unreliable, particularly due to the lack of information about the identity of the crying child. | The EnesBabyCries2 dataset, from [3] and freely accessible111https://osf.io/ru7na/?view_only=, contains longitudinal recordings of cries from 24 children. It includes information about the child's age at the time of recording (15 days, 1.5 months, 2.5 months or 3.5 months), the sex, identity and the cause (discomfort, ... | As an unexpected result, we were able to predict the cause of cries with accuracy better than chance. As noted in Section 2.1, it is challenging to draw definitive conclusions from the results on the Donate A Cry dataset, as the lack of information about the babies’ identities introduces a huge bias. On the other hand,... | The Donate A Cry dataset222https://github.com/gveres/donateacry-corpus/ includes information on the cause of cry, age, and sex. CryCeleb [15] provides labels associated with the child's identity and age (birth or discharge). | B |
CFDL𝒯(p,𝒟)=𝔼(𝐱,𝐲)∼𝒟[u(σ𝒯(p^(𝐱)),𝐲)]−𝔼(𝐱,𝐲)∼𝒟[u(σ𝒯(p(𝐱)),𝐲)].\mathrm{CFDL}_{{\mathcal{T}}}(p,{\mathcal{D}})=\operatorname*{\mathbb{E}}_{(\mathbf{x},\mathbf{y})\sim{\mathcal{D}}}[u(\sigma_{\mathcal{T}}(\widehat{p}(\mathbf{x})),\mathbf{y})]-\operatorname*{\mathbb{E}}_{(\mathbf{x},\mathbf{y})\sim{\ma... | This expression allows us to easily calculate the CFDL for specific decision tasks. For example, consider the task 𝒯2=(A,u){\mathcal{T}}_{2}=(A,u) where the action space AA is the unit interval A=[0,1]A=[0,1], and the payoff function is quadratic: | For the reverse direction, if (4.2) holds for any decision task, then in particular, it holds for the task 𝒯2{\mathcal{T}}_{2} above, implying CFDL𝒯2(p,𝒟)=0\mathrm{CFDL}_{{\mathcal{T}}_{2}}(p,{\mathcal{D}})=0. By (4.6), we have ECE2(p,𝒟)=0\mathrm{ECE}_{2}(p,{\mathcal{D}})=0, so pp is perfectly calibrated, as desi... | A decision task 𝒯{\mathcal{T}} has two components: an action space AA and a payoff function u:A×{0,1}→ℝu:A\times\{0,1\}\to{\mathbb{R}}. Given a decision task 𝒯=(A,u){\mathcal{T}}=(A,u), the decision maker must pick an action a∈Aa\in A in order to maximize the payoff u(a,y)∈ℝu(a,y)\in{\mathbb{R}}. Here, the payoff de... | We define the Calibration Decision Loss (CDL) of the predictor pp as the supremum of the CFDL over all decision tasks (A,u)(A,u) where the payoff function u:A→[0,1]u:A\to[0,1] has its range bounded in [0,1][0,1]: | A |
In the preparatory phase, the raw spectra extracted with MALDI underwent routine pre-processing steps to account for physiological, instrumental, and analytical variability. Specifically, the spectra followed the biological five-step protocol described in Capitoli et al. (2025), summarized in Section S.1 of the Supplem... | In line with the data structure outlined in Section 1.1, we consider a collection of TT datasets 𝓨={𝒀(t)}t=1T\bm{\mathcal{Y}}=\{\bm{Y}^{(t)}\}_{t=1}^{T}, one for each analyzed molecular level. Then, 𝒀(t)\bm{Y}^{(t)} denotes the MALDI-MSI abundance matrix of the tt-th molecular class, which is characterized by N(t)N^... | Figure 6: Spatial and spectral characterization of three representative regions of interest identified within the tissue. The left panels show the spatial distribution of each CC, highlighting the localization patterns across the sample. Right panels display the corresponding posterior averages of the analytes’ rescale... | Figure 2 provides a visual overview of the data. Panels (B), (C), and (D) show the normalized median abundance of each molecular class across the tissue section. These images highlight molecular heterogeneity that is not always apparent from histology alone. Panels (F), (G), and (H) illustrate spectral profiles for a s... | More specifically, the region captured in Cluster A was annotated by the pathologist as a mixed-grade tumor, representing an intermediate stage between grade 2 and grade 3. The region in Cluster C, instead, contains hemorrhagic tissue, where tumor cells were classified as grade 2. Finally, the central panel (Cluster B)... | C |
XXZZYYSSTTRRWWU1U_{1}U2U_{2}U3U_{3}U4U_{4}U5U_{5}U6U_{6}XXZZYYSSTTXX=1X_{X=1}ZX=1Z_{X=1}YX=1Y_{X=1}U1U_{1}U2U_{2}U5U_{5}U6U_{6}XXZZYYSSXX=1X_{X=1}ZX=1Z_{X=1}YX=1Y_{X=1}U1U_{1}U2U_{2} | In looking for causes of a particular observation in this SCM, we can use three quantities based on counterfactual reasoning [7]. The first is the probability of necessity (PN) of a cause XX for an effect YY, defined as: | A twin network might be built and, based on it, a multilinear objective function for minimization of PN for cause XX and effect YY would have degree 6. | U5U_{5} and U6U_{6} have been removed. Bounds on PN or on PS can be obtained minimizing/maximizing appropriate multilinear objective functions of degree 2 (instead of degree 4 using the counterfactual graph), as shown in Example 3. | Previous work has shown that the computation of lower and upper values for interventional quantities, given a canonicalized SCM an an input distribution, leads to minimization/maximization of a multilinear objective function subject to linear constraints [14]. For a quasi-Markovian SCM, the degree of the multilinear ob... | B |
Our implementation is different; the regridding and “LHS in LHS” operations we propose are arguably closer to the original procedure for distributing points via LHS and, by relaxing the requirement of a perfect Latin hypercube, we allow for expansions of any size. | In this paper, we presented a new algorithm for expanding an existing LHS while optimally preserving its space-filling properties. Our procedure leverages the flexibility of LHS by embedding a new LHS within the initial one. Loss of optimality arises from the potential occurrence of overlapping samples in the regridded... | Compared to other proposed LHS expansion strategies [15, 16, 17, 18, 19, 20], our approach allocates new samples by rebinning the original hypercube to preserve the projection property. Building on this idea, we can further leverage the versatility of Latin hypercubes by essentially designing an LHS within the existing... | Figure 1: The “LHS in LHS” expansion algorithm. The left panel shows an initial LHS with N=7N=7 points in P=2P=2 dimensions. | LHS plays a major role in simulation design, as evidenced by the vast literature on the topic (for a review see Ref. [4]). The additional flexibility provided by our expansion algorithms broadens the use cases of this powerful tool. One interesting application is in training machine learning models. A model initially t... | A |
The regularised ZVCV methods show little benefit from increasing the polynomial order beyond Q=2Q=2 or from increasing the sample size. Even when sampling is costly, they remain noticeably slower than the other methods. CF yields the worst results, which are improved upon by SECF. SECF outperforms ZV at the same polyno... | We propose using ensemble learning for constructing control variates. This technique consists of combining multiple weak learners to construct a stronger learner and is commonly used in many machine learning applications (Mienye & Sun, 2022). An example of ensemble learning in control variates is SECF, which can be vie... | Alternatively, J∗J^{*} can grow linearly in SS as in LeJeune et al. (2020). Under standard linear regression assumptions with Gaussian predictors and asymptotic subsampling conditions, a properly tuned large ensemble of bagged OLS predictors with feature randomness may exhibit an implicit regularisation equivalent to t... | Ensemble OLS estimators can address over‑parameterised linear approximation problems. Under standard regression assumptions and asymptotic sub-sampling conditions, a large ensemble of bagged OLS predictors with feature randomness may exhibit an implicit regularisation equivalent to that of the optimally tuned ridge reg... | This work has explored the use of averaging-based ensemble learning approaches to construct Stein-based control variates, with a particular focus on ZVCV, which may become over-parameterised in medium- and high-dimensional settings. While regularised ZVCV techniques based on penalised regression techniques help to miti... | D |
represent key demographic, socioeconomic, resource accessibility, mobility and geographic attributes of area ii, respectively. Table | represent key demographic, socioeconomic, resource accessibility, mobility and geographic attributes of area ii, respectively. Table | 2 also describes the expected relationship with population bias. Here it is relevant to highlight that representative subnational data on digital resource accessibility and engagement is not available in the UK. We proxied this via our census-derived measures of resource accessibility. The model iteratively | resident population count and so deviation from it indicates greater bias. We thus compare population | population counts. This dataset is openly-available on GitHub333https://t.ly/dzlzB, and was processed to | B |
Heterogeneity driving behavior data. Many studies inconsistently adjust for exposure intensity, such as mileage, and for contextual data, such as road condition or weather condition. Integration of ADAS warning systems with GNSS contextual data within unified frameworks remains limited. | Data sparsity and data availability. Privacy often leads to having only short observation windows for drivers; also, drivers may be unwilling to cooperate or may share short-period data. The lack of time stream data makes it a significant challenge in the development of a reliable risk prediction model for each individ... | Furthermore, accurately characterizing driver behavior is essential in driving risk analysis. Different types of vehicles and drivers show distinct patterns: sports car drivers often perform high-risk maneuvers such as rapid acceleration and sharp turns, while conservative drivers favor gentle acceleration and gradual ... | Given the weekly driver NME dataset, it is not straightforward to predict a driver’s future risk by simply applying the ZIP model due to data sparsity and inconsistency. To address the issue of heterogeneity, we improved the ZIP model and proposed a group-based ZIP model. Drivers’ entire driving behavior can be regarde... | In driving behavior studies, certain data features pose persistent challenges. Most automobile insurance databases record a large number of policyholders with zero claims, and zero inflation may be exacerbated by reporting incentives (e.g., deductibles or bonus-malus penalties) [4, 5]. In contrast, when NMEs are captur... | A |
The three approaches differ substantially in terms of computational burden. The EM algorithm converges rapidly, even for n=500n=500, and typically completes in seconds. Parametric AFT estimation requires maximum likelihood optimization, scaling approximately as O(np2)O(np^{2}), and is completed in minutes. Bayesian A... | The EM estimator closely tracks the truth, while the Weibull AFT may deviate under misspecification. | This study has some limitations must be acknowledged. First, the EM estimator yields step functions that, while faithful, may appear jagged and require smoothing for better visualization. Second, parametric AFT models depend critically on the adequacy of the assumed distribution; when misspecified, effect estimates and... | Ovarian analysis confirmed the key lessons of our simulation study. First, the EM estimator remains indispensable as a design-respecting baseline that reveals an interval-driven shape. Second, parametric AFT models yield interpretable time ratios but rely on the adequacy of distributional assumptions. Third, the Bayesi... | Parametric approaches, such as accelerated failure time (AFT) models with Weibull or log-normal distributions, yield smooth curves, admit covariates, and provide interpretable regression effects [9, 10]. In particular, the coefficients in the AFT models correspond to multiplicative shifts in the median or mean survival... | B |
Given its desirable properties and superior performance, the proposed model is expected to gain traction in analyzing count data across diverse domains, particularly in health sciences. The results suggest that these models could provide better insights into health science data, and practitioners are advised to conside... | Finding new probability models to handle over-dispersed data is crucial in addressing challenges posed by over-dispersion. Appropriately selecting such models for various scenarios leads to better data fits and more reliable interpretations. In this context, we introduced a novel count data model, the Poisson-Copoun di... | (Orooji et al., 2021) studied the factors affected LOS among elderly patients using count regression models. (Fernandez and Vatcheva, 2022) compared different statistical methods for modelling count data with application to hospital LOS. | Additionally, a three-inflated version of the PCD was developed and applied to analyze the length of stay (LOS) data of patients with pancreatic disorders. The results highlighted the effectiveness of the three-inflated models in hospital LOS data analysis. | Future research could explore its application to other fields and extend its functionality by incorporating covariates or developing multivariate versions. For instance, an immediate avenue for future work is to study the LOS of tourists and the factors influencing it using three-inflated count distributions. | D |
A direct result of D1 and the application of product kernel is that KK and K~\widetilde{K} are Lipschitz continuous. This property will be utilized in the proof later. | We justify the asymptotic validity of the cPI with DNN and kernel estimators. Moreover, we explore the effects of the equal distance DD between grid points on the coverage rate. We show the possibility that a cPI guarantees at least 1−α1-\alpha coverage rate even in the finite sample situations if all involved DNNs can... | We verify the asymptotic validity of cPI with kernel estimators by developing a non-asymptotic error bound on density estimation as follows: | We can also combine the calibration approach with kernel-based estimators. The main idea is that we first estimate fY|Xf_{Y|X} which is the conditional density of YY given XX by f^Y|X\widehat{f}_{Y|X} and then the cPI is built based on some specific calibration approach and the CDF estimation which is obtained by takin... | With the conditional density estimator f^(y|x)\hat{f}(y|x) defined by expressions in Eq. 6, we first show a non-asymptotic error bound of f^(y|x)\hat{f}(y|x) on estimating the true conditional density f(y|x)f(y|x) under standard assumptions in 5.1. The asymptotic validity of cPIs with kernel estimators, e.g., PIaa... | B |
Multiscale and hierarchical architectures have enhanced image diffusion models through progressive refinement strategies [13, 26, 45, 23, 44, 25]. Complementary approaches leverage wavelet decompositions to exploit natural multiscale structures [59, 39, 16, 42, 32]. These methods connect to renormalization group (RG) t... | Scale-adaptive schedules for unknown structure (Section 5): For complex non-Gaussian distributions such as the invariant measure of the stochastically forced Navier-Stokes equation where fine-scale structure cannot be prescribed easily a priori, we develop scale-adaptive interpolation schedules that maintain numerical ... | We address these competing requirements through two complementary strategies tailored to the available prior knowledge on the data. For distributions whose fine-scale structure is analytically tractable—such as Gaussian random fields and stochastic Allen–Cahn invariant measures that are absolutely continuous with respe... | Building on similar principles, we demonstrate that scale-adaptive design of noise distributions and interpolation schedules can substantially improve numerical performance while maintaining accurate reproduction across all scales with modest computational overhead. | In this section, we show that when using rougher noise, we can design a specialized scale-dependent interpolation schedule that addresses the numerical ill-conditioning and leads to substantially better estimation with the same number of discretization steps. | C |
Convergence rate in a nonlinear two-time-scale stochastic approximation with state (time)-dependence. | In Po-Ling Loh and Maxim Raginsky, editors, Proceedings of Thirty Fifth Conference on Learning Theory, volume 178 of Proceedings of Machine Learning Research, pages 2984–3014. PMLR, 02–05 Jul 2022. | In Sanjoy Dasgupta, Stephan Mandt, and Yingzhen Li, editors, Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, volume 238 of Proceedings of Machine Learning Research, pages 2251–2259. PMLR, 02–04 May 2024. | In Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesvari, Gang Niu, and Sivan Sabato, editors, Proceedings of the 39th International Conference on Machine Learning, volume 162 of Proceedings of Machine Learning Research, pages 18250–18280. PMLR, 17–23 Jul 2022. | In Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesvari, Gang Niu, and Sivan Sabato, editors, Proceedings of the 39th International Conference on Machine Learning, volume 162 of Proceedings of Machine Learning Research, pages 639–668. PMLR, 17–23 Jul 2022. | B |
This section formulates and proves Theorem 4.5, on near optimal sampling for the resampling method, with finite number of nodes KK, in the four steps: | The variance (2.1) establishes the generalization error in the case with infinite amount of data J=∞J=\infty | In the case with finite KK and infinite amount of data, J=∞J=\infty, the training error and the testing error become the same | In the case with infinite amount of data, J=∞J=\infty, and yj=f(xj)y_{j}=f(x_{j}) the generalization error (i.e., the testing error) and training error become equal and satisfy | In the case of infinite amount of data, J=∞J=\infty, the random Fourier feature method has the generalization error | B |
BNs significantly improve the precision and reliability of Average Treatment Effect (ATE) estimation, as well as the power in testing statistical hypotheses. This advancement not only enhances the validity of causal inferences drawn from observational studies but also provides a more robust framework for policy-making ... | In very recent literature Vicard et al. (2025), BNPS method has been proposed leveraging BNs for estimating propensity scores, which are crucial for causal inference in observational studies with binary outcomes and discrete covariates. As already said, traditional methods such as logistic regression are criticized for... | This would potentially lead, in its turn, to more accurate estimates of the Average Treatment Effect (ATE). The theoretical advantages of BNs can be identified in avoiding misspecification errors, which are common in logistic models, and in making efficient the use of inverse probability weighting for ATE estimation, p... | BNPS framework can be extended also to accommodate more complex scenarios, such as those involving multiple treatments and non-binary outcomes. | Once the treatment variable and the other covariates were generated, the binary potential outcomes Y(0)Y_{(0)} and Y(1)Y_{(1)}, as specified below, | C |
Point Event - Window Prediction: F1w gives partial credit for predictions near the event, but penalizes excess window; others score near zero. | Point Event - Window Prediction: F1w gives partial credit for predictions near the event, but penalizes excess window; others score near zero. | We compare TimesFM to two baseline models: a random baseline, which assigns event probabilities uniformly at random, and a null baseline, which is set to yield an F-score of 0. Note that this is not the same as assigning 0 probability to all events. These baselines provide reference points for evaluating the predictive... | For the in-the-wild datasets ADARP and Wrist Angel, F1w was uniquely able to capture meaningful model performance, whereas conventional metrics yielded near-zero scores due to point-based annotations. In contrast, the ROAD dataset, with its long continuous stress segments, naturally resulted in high scores for all metr... | Point Event - Random Prediction: All metrics are zero except F1w, which is slightly elevated due to the event density in the random predictions. | D |
More recently, there has been a class of methods for nonlinear dimensionality reduction that seek to preserve local neighborhoods. Examples include Laplacian eigenmaps [2], as well as the highly popular t-SNE [35] and UMAP [23]. | Compared to t-SNE, which uses attractive and repulsive forces to produce a global embedding that effectively align the clusters (this is done simultaneously in t-SNE), here too the C+E approach is more transparent and more modular, as the analyst is free to align the clusters as they wish. Our choice is based on strict... | Laplacian eigenmaps is presented as an algorithm that both clusters and embeds the data at the same time [2], as is clear through the strong connection between the method and spectral clustering. However, force-directed methods such as t-SNE and UMAP which aim to balance attractive and repulsive forces between points, ... | In this paper, we propose a general framework that aims to strike a compromise between a faithful embedding at the cluster-level and a faithful global embedding of all the data that preserves distances. As explained in [5], t-SNE can be viewed as a method that first clusters the data while embedding it and then aligns ... | Ma [5] provide some theoretical explanation, establishing that during the early exaggeration stage, t-SNE is approximately performing spectral clustering to both create an embedding and cluster the data. More specifically, during the early exaggeration stage, t-SNE converges to the projection of the initial state onto ... | B |
Panel (a) of Figure 7 illustrates how the estimated graph evolves as the threshold increases. As expected, larger thresholds produce sparser graphs, with several connections disappearing at higher values. Panel (b) shows the resulting logistic regression coefficient estimates and 95% confidence intervals. Across thresh... | Overall, these findings suggest that MMG delivers robust inference across a wide range of reasonable threshold values. Importantly, this stability reinforces our main conclusion: MMG improves efficiency and interpretability over complete-case analysis and alternative imputation methods, while remaining relatively insen... | While the NP-MMG offers a flexible and model-free approach, it suffers from the curse of dimensionality and can be computationally infeasible. This limitation motivates our consideration of a statistical learning approaches that preserve the principles of MMG while being computationally tractable. In this section, we d... | and the missingness is MCAR, the same graph can be used in the MMG. In MCAR, a complete case analysis yields an unbiased estimate of the model. This result suggests that we may use complete data to find a graph quantifying the dependency and use it for MMG. | Although the graph in MMG influences the results of downstream analysis, our sensitivity analysis in Section 6.4 shows that MMG-based inferences remain stable under mild perturbations of the graph, suggesting that the method is robust to reasonable choices of GG. | A |
Otherwise said: a policy is applied to a large population and only the distribution of the aggregated result matters. | The approach developed in (betlei2024maximizing, 2) is closely related to our method. (betlei2024maximizing, 2) introduce an optimization problem to directly maximize the probability of success of a test by assigning buckets of user populations to policies. At the difference to our work, (betlei2024maximizing, 2) only ... | Typically, the DM is interested in the policy performance overall, and might want to trade-off robustness and performance at this aggregated level. Our work is motivated by the observation that instead of optimizing directly for the true objective, most methods rely on proxy goals such as maximizing the expected reward... | In this experiment, we evaluate the performance of the threshold-based selection criterion, defined as j(x)=1[x>x¯]j(x)=1[x>\bar{x}], and compare it against standard IPS and LS baselines. We consider three thresholds x¯1,x¯2,x¯3\bar{x}_{1},\bar{x}_{2},\bar{x}_{3}, corresponding to relative improvements I=Hn(πθ)/Hn(... | Offline contextual bandit (dudik2011doubly, 5) is a widely used framework that leverages logged data from past interactions to improve future decision-making (bottou2013counterfactual, 3). In classical off-policy optimization, the performance of any new policy π\pi is measured by its value V(π)V(\pi), which is the exp... | B |
U^ng(π)=1n∑i=1ng(ri,π0(ai∣xi))logπ(ai∣xi),\displaystyle\hat{U}^{\texttt{g}}_{n}(\pi)=\frac{1}{n}\sum_{i=1}^{n}g(r_{i},\pi_{0}(a_{i}\mid x_{i}))\log\pi(a_{i}\mid x_{i})\,, | Our work provides strong evidence supporting this perspective and advocates an alternative approach based on policy-weighted log-likelihood (PWLL) objectives. Unlike traditional estimators, PWLL optimizes an objective U^n(π)\hat{U}_{n}(\pi) designed for ease of optimization rather than accuracy in estimating V(π)V(\p... | This robustness leads to better final policies: PWLL-based methods outperform OPE-based methods on all datasets. Even POTEC, a state-of-the-art method designed for large action spaces, is surpassed by the much simpler and easier-to-optimize cLPI. This supports our central claim: optimization stability is key to effecti... | Unlike OPE-based objectives, this form is logarithmic in the policy π\pi. This small change has a profound impact on optimization. | We demonstrated that simpler PWLL-based objectives offer a compelling alternative. By design, they are strongly concave for common policy classes, eliminating optimization issues like local maxima and plateaus. Our experiments confirm that this focus on optimization pays off: these simpler methods are more robust, easi... | C |
These hypotheses formed the foundation of a causal model that not only reflects data-based dependencies but also structures and reveals the implicit knowledge embedded in clinical practice. The model was developed iteratively and validated in collaboration with clinical staff, with the goal of creating a realistic and ... | The data we received contained up to 26 distinct events for each procedure. In collaboration with the clinic and Sqior we focused on three key sub-processes: induction, preparation and procedure. The duration of these steps was calculated using the time difference between the following events: anesthesia_start, anesthe... | Figure 1: The perioperative process is divided in the preoperative steps, commonly subsumed as induction, a surgical procedure, and recovery. Induction comprises the administration of anesthesia, positioning of the patient to facilitate access to body regions relevant to the surgical procedure, and further preparatory ... | We identified four relevant process variables: the durations of induction, preparation, the surgical procedure proper, and recovery. In our study, we focus on induction and procedure duration, which are measured as follows: | During the Induction, the patient is being moved to the operating room, their identity is verified, monitoring devices for heart rate and respiration are attached, and catheters are emplaced. Most importantly, anesthesia is being administered. The duration of the induction phase is the time between start and completion... | C |
This study demonstrates the feasibility of using simple 3D convolutional autoencoders to extract clinically and anatomically meaningful features from brain MRI data. The autoencoder achieved consistently low reconstruction errors, with MSE values below 0.01 across all clinical groups, indicating high fidelity in preser... | Table 6 presents the counts of significant and non-significant regions identified by t-SNE and UMAP across different clinical groups and latent/dimension pairs. For t-SNE, in the NOR_AD group, the number of significant regions varied notably by latent layer and dimension, ranging roughly from 53 to 74 significant regio... | DR techniques revealed clear class separation, particularly with PLS, where 100% of AAL regions (116/116116/116) were statistically significant in the NOR–AD comparison across multiple latent layers and dimensions. In contrast, PCA showed reduced sensitivity in intermediate groups like NOR–MCIc, with significance in on... | Table 4 summarizes the number of significant and non-significant brain regions identified using PCA and PLS across different clinical groups and latent/dimension combinations. For PCA, the results show a strong pattern of significance in the NOR-AD group, especially in all the Layers at dimensions 0 and 1, where all re... | Figure 16 shows the number of significant regions as a function of latent for different groups and methods. It can be observed that the NOR-AD group exhibits the highest number of significant regions, while the NOR-MCIc and NOR-MCI groups show fewer regions in comparison. Interestingly, for UMAP in the NOR-MCIc group, ... | B |
∑r=0k(m+1)zrar−k(m−1)2m,k=(1+z+⋯+zm−1)k\sum_{r=0}^{k(m+1)}z^{r}\,a_{\,r-\tfrac{k(m-1)}{2}}^{m,k}=(1+z+\cdots+z^{m-1})^{k} | To isolate a single PC component in each KZFT bandpass filter, the filter window length (mm) must be set to avoid overlap with adjacent frequencies to be rejected. Previous simulation studies have shown that increasing mm narrows the filter’s bandwidth, effectively suppressing frequencies outside a narrow range centere... | The KZ filter is an iterated moving average (MA) filter defined by two arguments: mm, a positive integer representing the window length, and kk, the number of iterations applied [23]. As a low-pass filter, the KZ filter effectively attenuates signals with frequencies at or above 1m\frac{1}{m}, while preserving lower-fr... | Figure 2 presents the periodogram of the detrended IHD hospitalization series. The periodogram revealed distinct peaks at weekly frequency and its harmonic frequencies. Peaks at annual frequency and its harmonic frequencies were also observed (Supplementary Figure S1 – S3). The top ten additional high-amplitude frequen... | The KZFT is a symmetric band pass filter around frequency vv and its energy transfer function at a frequency λ\lambda is shown below: | D |
We perform a full grid search over our four retrieval hyperparameters—KK, kknowk_{know}, ksafek_{safe}, and kfetchk_{fetch}—subject to 1≤kknow<K1\leq k_{know}<K, 1≤ksafe≤K−kknow1\leq k_{safe}\leq K-k_{know}, and K∈{1,⋯,10}K\in\{1,\cdots,10\}, kfetch∈{25,50,75,100,125,150,175,200}k_{fetch}\in\{25,... | If NN is the number of distinct KK values and FF the number of kfetchk_{fetch} options, the total number of valid 4-tuples (K,kknow,Ksafe,kfetchK,k_{know},K_{safe},k_{fetch}) we test is: | Finally, SafetyClamp guarantees exactly kknowk_{know} knowledge passages, ksafek_{safe} safety passages, and fills the remaining (K−(kknow+ksafe)K-(k_{know}+k_{safe})) slots from RR: | We perform a full grid search over our four retrieval hyperparameters—KK, kknowk_{know}, ksafek_{safe}, and kfetchk_{fetch}—subject to 1≤kknow<K1\leq k_{know}<K, 1≤ksafe≤K−kknow1\leq k_{safe}\leq K-k_{know}, and K∈{1,⋯,10}K\in\{1,\cdots,10\}, kfetch∈{25,50,75,100,125,150,175,200}k_{fetch}\in\{25,... | RAGuard introduces three new retrieval hyperparameters; knowledge-k (denoted kknowk_{know}), safety-k (denoted ksafek_{safe}), and fetch-k (denoted kfetchk_{fetch}). These control the balance between technical depth and safety oversight in the dual index setup. The aforementioned top−ktop-k remains in use a... | A |
To deal with high-dimensional node features, we consider using either ridge regression or LASSO, which we discuss in detail below in Sections 3.1.1 and 3.1.2, respectively. | Of course, since we do not have access to the latent positions XX directly, we must plug in estimates X^\hat{X} for them. | We collect the estimates b^r(1),b^r(2),…,b^r(d)\hat{b}_{r}^{(1)},\hat{b}_{r}^{(2)},\dots,\hat{b}_{r}^{(d)} in the columns of a matrix B^r\hat{B}_{r}, that is, B^r,ik=b^r,i(k)\hat{B}_{r,ik}=\hat{b}_{r,i}^{(k)}. | The following result shows that the estimates b^(k)\hat{b}^{(k)} based on the estimated latent positions X^\hat{X} are close to the oracle estimates b~Q(k)\tilde{b}^{(k)}_{Q}, once we choose QQ so as to account for the orthogonal non-identifiability in the latent space. | As discussed previously, in practice, we do not have access to the true latent positions XX, but rather must estimate them (up to some rotational non-identifiability) as X^\hat{X}. | A |
Closest in spirit to this work is the work by [5] which first proposed to use invertible neural networks for solving inverse problems. Translated to the notation of this paper, they treat the case m≤nm\leq n and use an invertible neural network to learn a mapping S:ℝn→ℝm+kS:\mathbb{R}^{n}\rightarrow\mathbb{R}^{m+k} wit... | We presented a generic framework for simulation and inference using invertible mappings. The proposed construction has the unique feature that simulation and inference can be performed with a single generative model, run in either forward or reverse mode. Possible advantages of the proposed construction include the imp... | This work proposes a novel framework for the use of generative models in inverse problems, which unifies the tasks of simulation (sampling from the likelihood) and inference (sampling from the posterior). Surprisingly, this yields a single invertible mapping S:ℝm+n→ℝm+nS:\mathbb{R}^{m+n}\to\mathbb{R}^{m+n}. This mappin... | This work can be seen as a bridge between these two approaches and provides a unified framework for using invertible mappings for simulation and inference. | Closest in spirit to this work is the work by [5] which first proposed to use invertible neural networks for solving inverse problems. Translated to the notation of this paper, they treat the case m≤nm\leq n and use an invertible neural network to learn a mapping S:ℝn→ℝm+kS:\mathbb{R}^{n}\rightarrow\mathbb{R}^{m+k} wit... | C |
Table 1: Evaluation of the Prob-GParareal probabilistic forecast across various DEs. The reported metrics are averaged over ten independent runs of the simulations (launched with a different random seed to account for algorithmic randomness), with standard deviation in parentheses. | TProb-GPara≈KconvTℱ+(nN∨1)(Kconv+1)NT𝒢+∑k=1KconvTfProb-GPara(k)+NKconvCdist,T_{\text{Prob-GPara}}\approx K_{\rm conv}T_{\mathscr{F}}+(\tfrac{n}{N}\vee 1)(K_{\rm conv}+1)NT_{\mathscr{G}}+\sum_{k=1}^{K_{\rm conv}}T^{\text{Prob-GPara}}_{f}(k)+NK_{\rm conv}C_{\rm dist}, | a connection between the Prob-GParareal solution (in particular, its mean) and its deterministic counterpart, the GParareal solution 𝒖i,kGPara\boldsymbol{u}_{i,k}^{\textrm{GPara}} obtained by sequential applications of 𝒢\mathscr{G} corrected by the GP posterior mean f^GPara(⋅)=𝝁𝒟k(⋅)\widehat{f}_{\rm GPara}(\cdot)... | T⋅T_{\cdot} and K⋅K_{\cdot} denote the runtime and iterations to converge, respectively, for Prob-GParareal (Prob-GPara) and GParareal (GPara). | where f^GPara(𝒖i−1,k)=(f^GPara(1)(𝒖i−1,k),…,f^GPara(d)(𝒖i−1,k))⊤∈ℝd\widehat{f}_{\rm GPara}(\boldsymbol{u}_{i-1,k})=\left(\widehat{f}^{(1)}_{\rm GPara}(\boldsymbol{u}_{i-1,k}),\ldots,\widehat{f}^{(d)}_{\rm GPara}(\boldsymbol{u}_{i-1,k})\right)^{\top}\in\mathbb{R}^{d} is the vector of posterior means, with f^GPara(... | C |
We denote by ℱn\mathcal{F}_{n} the filtration generated by the process (𝒆n)n∈[1,N](\boldsymbol{e}_{n})_{n\in[1,N]}. | and f:ℰ×{0,1}𝒞→ℝ+𝒞f:\mathcal{E}\times\{0,1\}^{\mathcal{C}}\to\mathbb{R}_{+}^{\mathcal{C}} is a map that, given the event e∈ℰe\in\mathcal{E} and the list of campaigns that are active (encoded by a binary vector from {0,1}𝒞\{0,1\}^{\mathcal{C}}), outputs the increment of spend of each campaign 111here we focus on the ... | The state ss of the platform is the level of spend of its campaigns, that is, if cc is the index of a campaign in the finite set of campaigns 𝒞\mathcal{C}, and n∈[1:N]n\in[1:N] is the index of an auction event, then sncs^{c}_{n} is the cumulated spend of the campaign cc after the resolution of the nnth auction. | Figure 5. Evolution of the predicted spend for a subset of campaigns over the iterations of the algorithm. The budget (same for all campaigns) is the red dotted horizontal line. | At initialization, the counters for each campaign are set to zero, and all campaigns are assumed to be active. At each iteration, the algorithm estimates the expected value Fi+1F_{i+1} of the auction function given the next event in sequence, conditioned on the history of previously observed events. Based on this estim... | B |
=exp(zi,t)∑aexp(zi,t);i∈{1,2}\displaystyle=\frac{\text{exp}(z_{i,t})}{\sum_{a}\text{exp}(z_{i,t})};\quad i\in\{1,2\} | Mathis et al., (2024); Github, (2024); McAndrew and Reich, (2021); Osthus and Moran, (2021); Osthus et al., (2019); Ulloa, (2019); Morgan et al., (2018); Farrow et al., (2017). To make scoring and ensemble construction straightforward, | superior to the individual forecasts Wang et al., (2023); Li et al., (2023); Gyamerah et al., (2020); Li et al., (2019); Reich et al., 2019b . For example, in the 2023-24 United States Centers | Mathis et al., (2024); Cramer et al., (2022); Hyndman, (2020); Makridakis et al., (2020); Reich et al., 2019a ; Biggerstaff et al., (2016); Hong et al., (2016). In these initiatives, multiple forecasters submit | pool Lavine et al., (2021); Li et al., (2019); Yao et al., (2018); Thorey et al., (2017); Geweke and Amisano, (2011). | A |
&\lesssim_{p,\alpha}C\kappa^{1/2p}t^{-1/2p}+A^{1/(2p\vee\alpha)}\begin{cases}C^{1-\alpha/2p}\kappa^{1/2p}t^{-1/2p}&\text{if }\alpha<2p,\\ | We further note that in case two processes Ξ\mathrm{\Xi} and H\mathrm{H} are observed over potentially different time frames, a bound for the statistical error of the plug-in estimator follows from Theorem 3.3 via the triangle inequality. | The lower bounds in Proposition 5.5(i)(i) match the three error terms achieved by the empirical plug-in estimator in Theorem 3.3 up to a logarithmic term for α=2p\alpha=2p. Consequently, no plug-in procedure, i.e., no estimator obtained by replacing the unknown measures by an estimator (based on observations of an ST ... | Throughout the remainder of this section, we assume that Ξ\mathrm{\Xi} is a weakly time-stationary L2L^{2} point process and analyze the relation between the time-reduced factorial covariance measure γ˘[2]\breve{\gamma}_{[2]} and our partitioned variance growth assumption 1.3. The latter serves as a crucial element for... | In the following, we describe two different settings for weights and the time points which will lead to different convergence behaviors for the empirical KRD than the Poisson point processes. | A |
One of the core themes of our work is that it is better to make assumptions explicit and falsifiable than to deploy methods which silently fail due to implicit or poorly understood assumptions. Causal diagrams provide a clear, mathematically principled way of making assumptions about dataset bias explicit, and we belie... | We thank our coauthors on the projects presented in this primer – as well as colleagues both within and outside Imperial College London – for support and input. C.J. is supported by Microsoft Research, EPSRC, and The Alan Turing Institute through a Microsoft PhD scholarship and a Turing PhD enrichment award. B.G. recei... | In this primer, we show how many of these issues stem from an inadequate understanding of the underlying causal and statistical structures present in data. We analyse implicit assumptions harming the validity of machine learning methods and applications, and we produce theoretical and empirical results that explain app... | Notably, our results follow from our causal setup in Section 2, showing how a causal approach helps to clarify complex issues in bias and fairness. We do not presuppose any architecture or implementation for the classifiers. Nor do we make assumptions about the functional mechanisms in the underlying scm. We scrutinise... | While the study of algorithmic bias is important and has gained significant interest in recent years, underlying dataset biases remain poorly understood. In Section 2, we introduced the no fair lunch principle, demonstrating how the causal nature of dataset bias has profound consequences for deep learning algorithms. I... | A |
Assume we have SS different uplift models M1M_{1}, M2M_{2}, …, MSM_{S} in consideration. When we select all NN candidates in the population, there will be no difference in the underlying cumulative gain FMs(N)F_{M_{s}}(N) on YY by using predictions from uplift model MsM_{s} for ranking, s=1,…,Ss=1,...,S. | For multiple models, we can split the selection universe randomly to sub-universes of size NsN_{s}, where N=∑s=1SNsN=\sum_{s=1}^{S}N_{s}. Then we select the top nNs/NnN_{s}/N candidates ranked by model scores of MsM_{s} in the sub-universe ss respectively to keep the same selection ratio n/Nn/N. The point estimates of... | In addition, in order to compare the cumulative gain performance of these 2 ranking models at different choices of the selection size, we need to estimate the uplift curves on the entire selection universe. It seems difficult or nearly impossible to come up with proper mean uplift estimates at selection sizes greater t... | When we only select a portion of the universe, choosing which model to rank the candidates becomes a relevant question to optimize for total uplift. In order to get a cumulative gain estimate fMs(n)f_{M_{s}}(n), technically we need to use model MsM_{s} to rank the universe and select the top nn candidates. | Assume we have SS different uplift models M1M_{1}, M2M_{2}, …, MSM_{S} in consideration. When we select all NN candidates in the population, there will be no difference in the underlying cumulative gain FMs(N)F_{M_{s}}(N) on YY by using predictions from uplift model MsM_{s} for ranking, s=1,…,Ss=1,...,S. | C |
In this short note, we discuss the intrinsic connections among the post-training techniques discussed above. Our findings are summarized below, tailored to both autoregressive and diffusion models. | Further, we point out that soft best-of-NN sampling can be applied to diffusion models to achieve the goal of classifier-free diffusion guidance, and the above resampling approach can be extended to tackle reward-directed diffusion models without resorting to RL-based techniques. | We demonstrate that, RLHF and RLIF can be formulated equivalently, assuming suitable parameter choices and faithfulness of reference policies. | recall from (• ‣ 2.2) and (4) that RLHF can be interpreted as a procedure that tilts the reference policy π𝗋𝖾𝖿(⋅|q)\pi_{\mathsf{ref}}(\cdot\,|\,q) to exp(r(q,⋅)/β𝗁𝖿)π𝗋𝖾𝖿(⋅|q)\exp(r(q,\cdot)/\beta_{\mathsf{hf}})\pi_{\mathsf{ref}}(\cdot\,|\,q) with suitable normalization, where rr is the reward function derived b... | We show that soft best-of-NN sampling for test-time scaling is asymptotically (as N→∞N\rightarrow\infty) equivalent to RLHF, and is also equivalent to RLIF under further assumptions on the reference policy. | B |
High data-to-model Ratio. In our previous experiments, Muon is outperformed by Soap in the 8×\times Chinchilla regime for the 130M and 520M models. To further test this, we train three 300M models to 16×\times Chinchilla and verify that Muon is no longer the optimal optimizer when the data-to-model ratio increases (Fig... | Re-evaluation Methodology. Our work is a rigorous evaluation of optimizers for pretraining. Rigorous evaluation has been an important part of deep learning research to clarify the current status of research and move the community forward. Jiang et al. (2019) critically examines metrics for predicting LLMs’ generalizati... | One exemplary hyperparameter optimization procedure for AdamW on a model with 300M parameters and 1× Chinchilla is shown in Table˜3. | Our systematic sweeps uncover both universal optimization principles and surprising optimization-specific nuances, which call for rigorous study when designing future optimizers. | Our study includes a wide range of eleven optimizers listed in Table˜1. Due to the page limit, we defer the exact algorithm descriptions of these optimizers to Appendix˜A. We selected these eleven optimizers according to three guiding principles: (i) include widely adopted baselines such as AdamW and Lion; (ii) cover r... | C |
Moreover, LLMs lack temporal consistency and exhibit high prompt sensitivity (Bodroža et al., 2024a). | Current approaches center around applying human psychological experiments – such as theory-of-mind tasks (Kosinski, 2024; van Duijn et al., 2023; Kim et al., 2023; Pi et al., 2024), reasoning biases (Lampinen et al., 2024; Han et al., 2024b; O’Leary, 2025; Yu et al., 2024), and moral judgment scenarios (Ji et al., 2025... | Over-anthropomorphism risks miscalibrating users’ trust (Mireshghallah et al., 2024; Cohn et al., 2024; Sun & Wang, 2025), fostering misconceptions about capabilities (Steyvers et al., 2025), or even encouraging emotional over-reliance on AI systems (Akbulut et al., 2025; Zhou et al., 2024; Shunsen et al., 2024). | Recent studies further show survey prompts often diverge from open-ended behavior (Röttger et al., 2024; Huang & Hadfi, 2025), and cultural alignment is unstable, formatting-dependent, and largely unsteerable (Khan et al., 2025; Dominguez-Olmedo et al., 2024). | This disconnect is further supported by recent findings that survey-based evaluations—though often linguistically coherent—fail to predict open-ended model behavior or reflect genuine psychological dispositions (Röttger et al., 2024; Dominguez-Olmedo et al., 2024). | D |
To decide on values of ν,n0′\nu,n_{0}^{\prime}, and n0′′n_{0}^{\prime\prime} to use in the remaining sections based on our experiments, we primarily focus on dℓ=0.5d_{\ell}=0.5 as it is more reflective of reality. We find that choosing a medium value ν=0.8\nu=0.8 works best in general. Moreover, (n0′,n0′′)=(15,5)(n_{0}... | In this section, we describe the choices for the implementation parameters n0′n_{0}^{\prime}, n0′′n_{0}^{\prime\prime}, and ν\nu for ℐ𝒵ℰ{\cal IZE} and n0n_{0} for ℱB{\cal F}_{B} and ℐ𝒵ℛ{\cal IZR}. | We adopt the same experimental configuration as in Section 5.3.2, with two key modifications. First, we focus on the SM configuration to better represent a practical setting. | To decide on values of ν,n0′\nu,n_{0}^{\prime}, and n0′′n_{0}^{\prime\prime} to use in the remaining sections based on our experiments, we primarily focus on dℓ=0.5d_{\ell}=0.5 as it is more reflective of reality. We find that choosing a medium value ν=0.8\nu=0.8 works best in general. Moreover, (n0′,n0′′)=(15,5)(n_{0}... | We adopt the configuration of ν=0.8\nu=0.8 and n0′=n0−5n_{0}^{\prime}=n_{0}-5 in the remainder of this section and also focus on the CV variance configuration. | D |
Quantum SafeML has demonstrated its ability to identify weaknesses in QML, particularly across both VQC and QCNN architectures, through application of quantum distance metrics. This section discusses the effectiveness, challenges, and implications of the approach. | No single metric emerged as universally optimal. Instead, using multiple metrics in parallel, analyzing their convergence or divergence, provided a more holistic understanding of classifier performance. | Quantum SafeML proved effective in identifying labelling errors in QML classification tasks. By applying distance metrics to density matrix representations, it reliably highlighted mislabelled instances and quantified their occurrence. For example, the Wine dataset exhibited lower accuracy and high divergence in metric... | This study evaluated the performance of different quantum distance metrics within the Quantum SafeML framework. The findings indicated that each metric has specific strengths and weaknesses depending on the classifier type and dataset. Trace distance emerged as the most stable, while Bures distance was most suited to n... | Quantum SafeML proved effective in delivering detailed performance assessments across multiple distance metrics, allowing for meaningful comparisons with classifier accuracy. | D |
“If a clinician says, ‘This one is different’ or ‘It’s not like the ones in your table,’ ‘This time I’m surer,’ the obvious question is, ‘Why should we care whether you think this one is different or whether you are surer?’ Again, there is only one rational reply to such a question. We have now to study the success fre... | Meehl highlights a dozen other studies in his book and continued to track examples throughout his career. No matter how much he looked, he kept finding the same thing: statistical rules were seldom worse and often much better than clinical predictions. In a reflection on his book, Meehl wrote in 1986, “There is no cont... | Given the dark and heated rhetoric of Meehl’s closing, it isn’t surprising his book has been met by the persistent, angry disbelief of clinicians. This contentiousness, unfortunately, meant the central results were often misunderstood. One of the more common misreadings of Meehl claims he was arguing to do away with cl... | To get after the merits between the clinical and statistical, Meehl strongly boxes in the scope of questions to be answered. One of the central aims was to determine the scope of utility of statistical judgment. There was a significant set of decisions where he deemed statistics superior. By being precise about this su... | The trick that Meehl plays is in the quantification of “better.” By better, we of course mean on average. This is a subtle point: Meehl discusses in Chapter 4 that a clinician may be able to detect a variety of exceptional cases that don’t appear in the original data seen by the statistical algorithm. His famous exampl... | B |
If the probability of the individual of having CRC is large enough (p(CRC|x)>th1p(CRC|x)>th1), then administer a stool-DNA (sDNA) test; if positive, administer a colonoscopy. | If the probability of the individual of having CRC is large enough (p(CRC|x)>th1p(CRC|x)>th1), then administer a stool-DNA (sDNA) test; if positive, administer a colonoscopy. | If the probability of the individual of having CRC is intermediate (th1≥p(CRC|x)>th2th1\geq p(CRC|x)>th2), then administer a fecal immunochemical test (FIT); if positive, administer a colonoscopy. | with the probabilities p(CRC|x)p(CRC|x) based on the BN model and the thresholds th1,th2th1,th2 depending on resources available. | If the probability of the individual of having CRC is low (th2>p(CRC|x)th2>p(CRC|x)), then do nothing, | B |
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