Papers

Coastal planners using probabilistic risk assessments to evaluate structural flood risk reduction projects may wish to simulate the hydrodynamics associated with large suites of tropical cyclones in large ensembles of landscapes: with and without projects' implementation; over decades of their useful lifetimes; and under multiple scenarios reflecting uncertainty about sea level rise, land subsidence, and other factors. Wave action can be a substantial contributor to flood losses and overtopping of structural features like levees and floodwalls, but numerical methods solving for wave dynamics are computationally expensive, potentially limiting budget-constrained planning efforts. In this study, we present and evaluate the performance of deep learning-based surrogate models for predicting peak significant wave heights under a variety of relevant use cases: predicting waves with or without modeled peak storm surge as a feature, predicting wave heights while simultaneously predicting peak storm surge, or using storm surge predicted by another surrogate model as an input feature. All models incorporate landscape morphological elements (e.g., elevation, roughness, canopy) and global boundary conditions (e.g., sea level) in addition to tropical cyclone characteristics as predictive features to improve accuracy as landscapes evolve over time. Using simulations from Louisiana's 2023 Coastal Master Plan as a case study, we demonstrate suitable accuracy of surrogate models for planning-level studies, with a two-sided Kolmogorov-Smirnov test indicating no significant difference between significant wave heights generated by the Simulating Waves Nearshore model and those predicted by our surrogate models in approximately 89% of grid cells and landscapes evaluated in the study, with performance varying by landscape and model. On average, the models produced a root mean squared error of 0.05-0.06 m.

Probabilistic graphical models (PGMs) are powerful tools for representing statistical dependencies through graphs in high-dimensional systems. However, they are limited to pairwise interactions. In this work, we propose the simplicial Gaussian model (SGM), which extends Gaussian PGM to simplicial complexes. SGM jointly models random variables supported on vertices, edges, and triangles, within a single parametrized Gaussian distribution. Our model builds upon discrete Hodge theory and incorporates uncertainty at every topological level through independent random components. Motivated by applications, we focus on the marginal edge-level distribution while treating node- and triangle-level variables as latent. We then develop a maximum-likelihood inference algorithm to recover the parameters of the full SGM and the induced conditional dependence structure. Numerical experiments on synthetic simplicial complexes with varying size and sparsity confirm the effectiveness of our algorithm.

The local intrinsic dimension (LID) of data is a fundamental quantity in signal processing and learning theory, but quantifying the LID of high-dimensional, complex data has been a historically challenging task. Recent works have discovered that diffusion models capture the LID of data through the spectra of their score estimates and through the rate of change of their density estimates under various noise perturbations. While these methods can accurately quantify LID, they require either many forward passes of the diffusion model or use of gradient computation, limiting their applicability in compute- and memory-constrained scenarios. We show that the LID is a lower bound on the denoising score matching loss, motivating use of the denoising score matching loss as a LID estimator. Moreover, we show that the equivalent implicit score matching loss also approximates LID via the normal dimension and is closely related to a recent LID estimator, FLIPD. Our experiments on a manifold benchmark and with Stable Diffusion 3.5 indicate that the denoising score matching loss is a highly competitive and scalable LID estimator, achieving superior accuracy and memory footprint under increasing problem size and quantization level.

This study develops a real-time framework for estimating pedestrian crash risk at signalized intersections under heterogeneous, non-lane-based traffic. Existing approaches often assume linear relationships between covariates and parameters, oversimplifying the complex, non-monotonic interactions among different road users. To overcome this, the framework introduces a non-linear link function within a Bayesian generalized extreme value (GEV) structure to capture traffic variability more accurately. The framework applies extreme value theory through the block maxima approach using post-encroachment time as a surrogate safety measure. A hierarchical Bayesian model incorporating both linear and non-linear link functions into GEV parameters is estimated using Markov Chain Monte Carlo simulation. It also introduces a behavior-normalized Modified Crash Risk (MRC) formula to account for pedestrians' habitual risk-taking behavior. Seven Bayesian hierarchical models were developed and compared using deviance information criterion. Models employing non-linear link functions for the location and scale parameters significantly outperformed their linear counterparts. The results revealed that pedestrian speed has a negative relationship with crash risk, while flow and speed of motorized vehicles, pedestrian flow, and non-motorized vehicles conflicting speed contribute positively. The MRC formulation reduced overestimation and provided crash predictions with 93% confidence. The integration of non-linear link functions enhances model flexibility, capturing the non-linear nature of traffic extremes. The proposed MRC metric aligns crash risk estimates with real-world pedestrian behavior in mixed-traffic environments. This framework offers a practical analytical tool for traffic engineers and planners to design adaptive signal control and pedestrian safety interventions before crashes occur.

We consider the modulation of data given by random vectors $X_n \in \mathbb{R}^{d_n}$, $n \in \mathbb{N}$. For each $X_n$, one chooses an independent modulating random vector $\Xi_n \in \mathbb{R}^{d_n}$ and forms the projection $Y_n = \Xi_n'X_n$. It is shown, under regularity conditions on $X_n$ and $\Xi_n$, that $Y_n|\Xi_n$ converges weakly in probability to a normal distribution. More broadly, the conditional joint distribution of a family of projections constructed from random samples from $X_n$ and $\Xi_n$ is shown to converge weakly to a matrix normal distribution. We derive, $via$ G. Pólya's characterization of the normal distribution, a necessary and sufficient condition on $Y_n$ for $\Xi_n$ to be normally distributed. When $\Xi_n$ has a spherically symmetric distribution we deduce, through I. J. Schoenberg's characterization of the spherically symmetric characteristic functions on Hilbert spaces, that the probability density function of $Y_n|\Xi_n$ converges pointwise in certain $p$th means to a mixture of normal densities and the rate of convergence is quantified, resulting in uniform convergence. The cumulative distribution function of $Y_n|\Xi_n$ is shown to converge uniformly in those $p$th means to the distribution function of the same mixture, and a Lipschitz property is obtained. Examples of distributions satisfying our results are provided; these include Bingham distributions on hyperspheres of random radii, uniform distributions on hyperspheres and hypercubes of random volumes, and multivariate normal distributions; and examples of such $\Xi_n$ include the multivariate $t$-, multivariate Laplace, and spherically symmetric stable distributions.

We introduce a novel framework for Federated Class Incremental Learning, called Federated Gaussian Task Embedding and Alignment (FedGTEA). FedGTEA is designed to capture task-specific knowledge and model uncertainty in a scalable and communication-efficient manner. At the client side, the Cardinality-Agnostic Task Encoder (CATE) produces Gaussian-distributed task embeddings that encode task knowledge, address statistical heterogeneity, and quantify data uncertainty. Importantly, CATE maintains a fixed parameter size regardless of the number of tasks, which ensures scalability across long task sequences. On the server side, FedGTEA utilizes the 2-Wasserstein distance to measure inter-task gaps between Gaussian embeddings. We formulate the Wasserstein loss to enforce inter-task separation. This probabilistic formulation not only enhances representation learning but also preserves task-level privacy by avoiding the direct transmission of latent embeddings, aligning with the privacy constraints in federated learning. Extensive empirical evaluations on popular datasets demonstrate that FedGTEA achieves superior classification performance and significantly mitigates forgetting, consistently outperforming strong existing baselines.

Neal's funnel refers to an exponential tapering in probability densities common to Bayesian hierarchical models. Usual sampling methods, such as Markov Chain Monte Carlo, struggle to efficiently sample the funnel. Reparameterizing the model or analytically marginalizing local parameters are common techniques to remedy sampling pathologies in distributions exhibiting Neal's funnel. In this paper, we show that the challenges of Neal's funnel can be avoided by performing the hierarchical analysis, well, hierarchically. That is, instead of sampling all parameters of the hierarchical model jointly, we break the sampling into multiple stages. The first stage samples a generalized (higher-dimensional) hierarchical model which is parameterized to lessen the sharpness of the funnel. The next stage samples from the estimated density of the first stage, but under a constraint which restricts the sampling to recover the marginal distributions on the hyper-parameters of the original (lower-dimensional) hierarchical model. A normalizing flow can be used to represent the distribution from the first stage, such that it can easily be sampled from for the second stage of the analysis. This technique is useful when effective reparameterizations are computationally expensive to calculate, or a generalized hierarchical model already exists from which it is easy to sample.

Systems of interacting continuous-time Markov chains are a powerful model class, but inference is typically intractable in high dimensional settings. Auxiliary information, such as noisy observations, is typically only available at discrete times, and incorporating it via a Doob's $h$-transform gives rise to an intractable posterior process that requires approximation. We introduce Latent Interacting Particle Systems, a model class parameterizing the generator of each Markov chain in the system. Our inference method involves estimating look-ahead functions (twist potentials) that anticipate future information, for which we introduce an efficient parameterization. We incorporate this approximation in a twisted Sequential Monte Carlo sampling scheme. We demonstrate the effectiveness of our approach on a challenging posterior inference task for a latent SIRS model on a graph, and on a neural model for wildfire spread dynamics trained on real data.

Betas from spot regressions are central to asset pricing and risk management, as measures of systematic risk. This paper develops a new estimation and inference framework for spot regressions by leveraging high-frequency candlesticks, extending conventional (open-to-close) returns with intra-period high/low prices. Specifically, I construct candlestick-based estimators of regression parameters, including spot beta, by minimizing a quadratic risk under a fixed-k asymptotic framework. I then develop a feasible hypothesis testing procedure for spot betas with correct asymptotic size. Simulation results show that the proposed estimator reduces estimation risk relative to return-based estimators, especially in small samples, and the test achieves notably higher power. I apply the framework to assess the market neutrality of Bitcoin using 1-minute data on IBIT and SPY, finding deviations from neutrality, particularly in high-volatility periods.

Multi-agent large language model (LLM) systems are increasingly adopted for complex language processing tasks that require communication and coordination among agents. However, these systems often suffer substantial overhead from repeated reprocessing of overlapping contexts across agents. In typical pipelines, once an agent receives a message from its predecessor, the full context-including prior turns-must be reprocessed from scratch, leading to inefficient processing. While key-value (KV) caching is an effective solution for avoiding redundant computation in single-agent settings where prefixes remain unchanged, it cannot be directly reused in multi-agent scenarios due to diverging prefixes introduced by agent-specific context extensions. We identify that the core challenge lies in the offset variance of KV-caches across agents. To address this, we propose KVCOMM, a training-free framework that enables efficient prefilling in multi-agent inference by reusing KV-caches and aligning cache offsets of overlapping contexts under diverse prefix contexts. KVCOMM estimates and adjusts KV-caches for shared content by referencing a pool of cached examples-termed anchors-that store observed cache deviations under varying prefixes. The anchor pool is maintained and updated online, allowing dynamic adaptation to distinct user requests and context structures. KVCOMM achieves over 70% reuse rate across diverse multi-agent workloads, including retrieval-augmented generation, math reasoning, and collaborative coding tasks, all without quality degradation. Particularly, when each fully-connected agent receives 1K input tokens with 512 prefix tokens and 512 output tokens under a five-agent setting, KVCOMM achieves up to 7.8x speedup compared to the standard prefill pipeline, reducing TTFT from ~430 ms to ~55 ms.

We present CuMPerLay, a novel differentiable vectorization layer that enables the integration of Cubical Multiparameter Persistence (CMP) into deep learning pipelines. While CMP presents a natural and powerful way to topologically work with images, its use is hindered by the complexity of multifiltration structures as well as the vectorization of CMP. In face of these challenges, we introduce a new algorithm for vectorizing MP homologies of cubical complexes. Our CuMPerLay decomposes the CMP into a combination of individual, learnable single-parameter persistence, where the bifiltration functions are jointly learned. Thanks to the differentiability, its robust topological feature vectors can be seamlessly used within state-of-the-art architectures such as Swin Transformers. We establish theoretical guarantees for the stability of our vectorization under generalized Wasserstein metrics. Our experiments on benchmark medical imaging and computer vision datasets show the benefit CuMPerLay on classification and segmentation performance, particularly in limited-data scenarios. Overall, CuMPerLay offers a promising direction for integrating global structural information into deep networks for structured image analysis.

We consider the problem of constructing probabilistic predictions that lead to accurate decisions when employed by downstream users to inform actions. For a single decision maker, designing an optimal predictor is equivalent to minimizing a proper loss function corresponding to the negative utility of that individual. For multiple decision makers, our problem can be viewed as a variant of omniprediction in which the goal is to design a single predictor that simultaneously minimizes multiple losses. Existing algorithms for achieving omniprediction broadly fall into two categories: 1) boosting methods that optimize other auxiliary targets such as multicalibration and obtain omniprediction as a corollary, and 2) adversarial two-player game based approaches that estimate and respond to the “worst-case" loss in an online fashion. We give lower bounds demonstrating that multicalibration is a strictly more difficult problem than omniprediction and thus the former approach must incur suboptimal sample complexity. For the latter approach, we discuss how these ideas can be used to obtain a sample-efficient algorithm through an online-to-batch conversion. This conversion has the downside of returning a complex, randomized predictor. We improve on this method by designing a more direct, unrandomized algorithm that exploits structural elements of the set of proper losses.

We develop a unified statistical framework for softmax-gated Gaussian mixture of experts (SGMoE) that addresses three long-standing obstacles in parameter estimation and model selection: (i) non-identifiability of gating parameters up to common translations, (ii) intrinsic gate-expert interactions that induce coupled differential relations in the likelihood, and (iii) the tight numerator-denominator coupling in the softmax-induced conditional density. Our approach introduces Voronoi-type loss functions aligned with the gate-partition geometry and establishes finite-sample convergence rates for the maximum likelihood estimator (MLE). In over-specified models, we reveal a link between the MLE's convergence rate and the solvability of an associated system of polynomial equations characterizing near-nonidentifiable directions. For model selection, we adapt dendrograms of mixing measures to SGMoE, yielding a consistent, sweep-free selector of the number of experts that attains pointwise-optimal parameter rates under overfitting while avoiding multi-size training. Simulations on synthetic data corroborate the theory, accurately recovering the expert count and achieving the predicted rates for parameter estimation while closely approximating the regression function. Under model misspecification (e.g., $\epsilon$-contamination), the dendrogram selection criterion is robust, recovering the true number of mixture components, while the Akaike information criterion, the Bayesian information criterion, and the integrated completed likelihood tend to overselect as sample size grows. On a maize proteomics dataset of drought-responsive traits, our dendrogram-guided SGMoE selects two experts, exposes a clear mixing-measure hierarchy, stabilizes the likelihood early, and yields interpretable genotype-phenotype maps, outperforming standard criteria without multi-size training.

This paper explores the topological signatures of ReLU neural network activation patterns. We consider feedforward neural networks with ReLU activation functions and analyze the polytope decomposition of the feature space induced by the network. Mainly, we investigate how the Fiedler partition of the dual graph and show that it appears to correlate with the decision boundary – in the case of binary classification. Additionally, we compute the homology of the cellular decomposition – in a regression task – to draw similar patterns in behavior between the training loss and polyhedral cell-count, as the model is trained.

We revisit the $\alpha$–regression framework for compositional data. We formulate $\alpha$–regression as a non–linear least squares problem, study its asymptotic properties, and provide efficient estimation via the Levenberg–Marquardt algorithm. We then propose a permutation–based hypothesis testing procedure, derive marginal effects for interpretation, and provide a visual inspection of the effect of each predictor. We further discuss robustified versions, the inclusion of natural splines, and the incorporation of compositional predictors, which further facilitate the formulation of a simple time series model. The framework is extended to spatial settings through four models. (a) The $\alpha$–spatially–lagged X regression model, which incorporates spatial spillover effects via spatially–lagged covariates, with decomposition into direct and indirect effects. (b) The $\alpha$–spatial autoregressive model that allows for spatial autocorrelation. (c) The geographically–weighted $\alpha$–regression, which allows coefficients to vary spatially for capturing local relationships. (d) The $\alpha$–eigenvector spatial filtering that is computationally efficient and captures spatial dependence via the eigenvectors of the kernelized distance matrix. Applications to four real datasets illustrate that the models perform on par with or outperform existing models in the literature. The examples showcase that $\alpha$–regression can outperform various competing regression models under different scenarios and its spatial extensions capture the dependence and improve the predictive performance. Overall, the examples provide evidence that the log–ratio methodology does not always lead to the optimal results.

Entropy-regularized optimal transport, which has strong links to the Schrödinger bridge problem in statistical mechanics, enjoys a variety of applications from trajectory inference to generative modeling. A major driver of renewed interest in this problem is the recent development of fast matrix-scaling algorithms\textemdash known as iterative proportional fitting or the Sinkhorn algorithm\textemdash for entropic optimal transport, which have favorable complexity over traditional approaches to the unregularized problem. Here, we take a perspective on this algorithm rooted in the thermodynamic origins of Schrödinger's problem and inspired by the modern geometric theory of diffusion: is the Sinkhorn flow (viewed in continuous-time as a mirror descent by recent results) the gradient flow of entropy in a formal Riemannian geometry? We answer this question affirmatively, finding a nonlocal Wasserstein gradient structure in the dynamics of its free marginal. This offers a physical interpretation of the Sinkhorn flow as the stochastic dynamics of a particle with law evolving by the nonlocal diffusion of a chemical potential. Simultaneously, it brings a standard suite of functional inequalities characterizing Markov diffusion processes to bear upon its geometry and convergence. We prove an entropy-energy (de Bruijn) identity, a Poincaré inequality, and a Bakry-Émery-type condition under which a logarithmic Sobolev inequality (LSI) holds and implies exponential convergence of the Sinkhorn flow in entropy. We lastly discuss computational applications such as stopping heuristics and latent-space design criteria leveraging the LSI and, returning to the physical interpretation, the possibility of natural systems whose relaxation to equilibrium inherently solves entropic optimal transport or Schrödinger bridge problems.

The default Gaussian latent in flow-based generative models poses challenges when learning certain distributions such as heavy-tailed ones. We introduce a general framework for learning data-adaptive parametric prior distributions (latent noise) using one-dimensional quantile functions, optimized via the Wasserstein distance between noise and data. The quantile-based prior parameterization naturally adapts to both heavy-tailed and compactly supported distributions and shortens transport paths. Numerical results on heavy-tailed weather and image datasets confirm the method's flexibility and effectiveness achieved with negligible computational overhead.

This paper develops a statistical framework for goodness-of-fit testing of volatility functions in i.i.d. McKean-Vlasov stochastic differential equations, which model large diffusion systems with distribution-dependent dynamics. Although integrated volatility estimation for classical SDEs is well established, formal model validation and goodness-of-fit testing for McKean-Vlasov systems remain largely unexplored, particularly in settings combining large particle limits with high-frequency observations. We propose a goodness-of-fit test based on discrete observations of a particle system and study its asymptotic properties in a joint regime where both the number of particles and the sampling frequency tend to infinity. We establish asymptotic normality for the relevant volatility estimators and derive a central limit theorem for the resulting test statistic. These results provide a rigorous basis for assessing volatility specifications in high-dimensional mean-field diffusion models.

An open problem in Machine Learning is how to avoid models to exploit spurious correlations in the data; a famous example is the background-label shortcut in the Waterbirds dataset. A common remedy is to train a model across multiple environments; in the Waterbirds dataset, this corresponds to training by randomizing the background. However, selecting the right environments is a challenging problem, given that these are rarely known a priori. We propose Universal Adaptive Environment Discovery (UAED), a unified framework that learns a distribution over data transformations that instantiate environments, and optimizes any robust objective averaged over this learned distribution. UAED yields adaptive variants of IRM, REx, GroupDRO, and CORAL without predefined groups or manual environment design. We provide a theoretical analysis by providing PAC-Bayes bounds and by showing robustness to test environment distributions under standard conditions. Empirically, UAED discovers interpretable environment distributions and improves worst-case accuracy on standard benchmarks, while remaining competitive on mean accuracy. Our results indicate that making environments adaptive is a practical route to out-of-distribution generalization.

We propose a novel framework for reconstructing the chronology of genetic regulation using causal inference based on Pearl's theory. The approach proceeds in three main stages: causal discovery, causal inference, and chronology construction. We apply it to the ndhB and ndhD genes of the chloroplast in Arabidopsis thaliana, generating four alternative maturation timeline models per gene, each derived from a different causal discovery algorithm (HC, PC, LiNGAM, or NOTEARS). Two methodological challenges are addressed: the presence of missing data, handled via an EM algorithm that jointly imputes missing values and estimates the Bayesian network, and the selection of the $\ell_1$-regularization parameter in NOTEARS, for which we introduce a stability selection strategy. The resulting causal models consistently outperform reference chronologies in terms of both reliability and model fit. Moreover, by combining causal reasoning with domain expertise, the framework enables the formulation of testable hypotheses and the design of targeted experimental interventions grounded in theoretical predictions.

Causal discovery aims to learn causal relationships between variables from targeted data, making it a fundamental task in machine learning. However, causal discovery algorithms often rely on unverifiable causal assumptions, which are usually difficult to satisfy in real-world data, thereby limiting the broad application of causal discovery in practical scenarios. Inspired by these considerations, this work extensively benchmarks the empirical performance of various mainstream causal discovery algorithms, which assume i.i.d. data, under eight model assumption violations. Our experimental results show that differentiable causal discovery methods exhibit robustness under the metrics of Structural Hamming Distance and Structural Intervention Distance of the inferred graphs in commonly used challenging scenarios, except for scale variation. We also provide the theoretical explanations for the performance of differentiable causal discovery methods. Finally, our work aims to comprehensively benchmark the performance of recent differentiable causal discovery methods under model assumption violations, and provide the standard for reasonable evaluation of causal discovery, as well as to further promote its application in real-world scenarios.

Time series anomaly detection plays a crucial role in a wide range of real-world applications. Given that time series data can exhibit different patterns at different sampling granularities, multi-scale modeling has proven beneficial for uncovering latent anomaly patterns that may not be apparent at a single scale. However, existing methods often model multi-scale information independently or rely on simple feature fusion strategies, neglecting the dynamic changes in cross-scale associations that occur during anomalies. Moreover, most approaches perform multi-scale modeling based on fixed sliding windows, which limits their ability to capture comprehensive contextual information. In this work, we propose CrossAD, a novel framework for time series Anomaly Detection that takes Cross-scale associations and Cross-window modeling into account. We propose a cross-scale reconstruction that reconstructs fine-grained series from coarser series, explicitly capturing cross-scale associations. Furthermore, we design a query library and incorporate global multi-scale context to overcome the limitations imposed by fixed window sizes. Extensive experiments conducted on multiple real-world datasets using nine evaluation metrics validate the effectiveness of CrossAD, demonstrating state-of-the-art performance in anomaly detection.

Recently, weighted cumulative residual Tsallis entropy has been introduced in the literature as a generalization of weighted cumulative residual entropy. We study some new properties of weighted cumulative residual Tsallis entropy measure. Next, we propose some non-parametric estimators of this measure. Asymptotic properties of these estimators are discussed. Performance of these estimators are compared by mean squared error. Non-parametric estimators for weighted cumulative residual entropy measure are also discussed. Estimator for weighted cumulative residual Tsallis entropy for progressive type-II censored data is proposed and its performance is investigated by Monte-Carlo simulations for various censoring schemes. Two uniformity tests for complete samples are proposed based on an estimator of these two measures and power of the tests are compared with some popular tests. The tests perform reasonably well. Uniformity test under progressively type-II censored data is also developed. Some real datasets are analysed for illustration.

Geopolitical and geoeconomic shocks reprice sovereign credit risk through different transmission channels. Using a daily panel of 42 advanced and emerging economies over 2018–2025, we show that geopolitical shocks raise sovereign CDS spreads primarily through direct sovereign repricing, while the Global Financial Cycle (GFC) channel moves in the opposite direction and partly offsets that increase – a “scissors pattern.” Geoeconomic shocks, by contrast, transmit mainly through financial conditions, policy uncertainty, and domestic amplification, with only a limited direct repricing component. A semistructural framework provides sign benchmarks for four transmission channels, and a Shapley–Taylor decomposition of nonlinear machine-learning predictions partitions each observation's spread into Direct, GFC, Uncertainty, and Local components. Narrative local projections around four dated crisis events recover the scissors pattern for Russia–Ukraine and support the broader channel taxonomy in the remaining episodes. Additional scorecard, placebo, and sign-restricted SVAR evidence corroborates the taxonomy beyond the baseline ML decomposition. Geopolitical direct effects decay with distance from the conflict zone in a gravity-style pattern (R2 = 0.35 for Russia–Ukraine), while policy-uncertainty shocks activate the Uncertainty channel more globally. The taxonomy implies that liquidity provision can mitigate GFC-driven spread widening, but not direct geopolitical sovereign repricing.

Weak convergence of joint distributions generally does not imply convergence of conditional distributions. In particular, conditional distributions need not converge when joint Gaussian distributions converge to a singular Gaussian limit. Algebraically, this is due to the fact that at singular covariance matrices, Schur complements are not continuous functions of the matrix entries. Our results lay out special conditions under which convergence of Gaussian conditional distributions nevertheless occurs, and we exemplify how this allows one to reason about conditional independence in a new class of graphical models.

We introduce Cautious Weight Decay (CWD), a one-line, optimizer-agnostic modification that applies weight decay only to parameter coordinates whose signs align with the optimizer update. Unlike standard decoupled decay, which implicitly optimizes a regularized or constrained objective, CWD preserves the original loss and admits a bilevel interpretation: it induces sliding-mode behavior upon reaching the stationary manifold, allowing it to search for locally Pareto-optimal stationary points of the unmodified objective. In practice, CWD is a drop-in change for optimizers such as AdamW, Lion, and Muon, requiring no new hyperparameters or additional tuning. For language model pre-training and ImageNet classification, CWD consistently improves final loss and accuracy at million- to billion-parameter scales.

Wind power producers can benefit from forming coalitions to participate cooperatively in electricity markets. To support such collaboration, various profit allocation rules rooted in cooperative game theory have been proposed. However, existing approaches overlook the lack of coherence among producers regarding forecast information, which may lead to ambiguity in offering and allocations. In this paper, we introduce a “reconcile-then-optimize” framework for cooperative market offerings. This framework first aligns the individual forecasts into a coherent joint forecast before determining market offers. With such forecasts, we formulate and solve a two-stage stochastic programming problem to derive both the aggregate offer and the corresponding scenario-based dual values for each trading hour. Based on these dual values, we construct a profit allocation rule that is budget-balanced and stable. Finally, we validate the proposed method through empirical case studies, demonstrating its practical effectiveness and theoretical soundness.

In this paper, we refine the Berry-Esseen bounds for the multivariate normal approximation of Polyak-Ruppert averaged iterates arising from the linear stochastic approximation (LSA) algorithm with decreasing step size. We consider the normal approximation by the Gaussian distribution with covariance matrix predicted by the Polyak-Juditsky central limit theorem and establish the rate up to order $n^{-1/3}$ in convex distance, where $n$ is the number of samples used in the algorithm. We also prove a non-asymptotic validity of the multiplier bootstrap procedure for approximating the distribution of the rescaled error of the averaged LSA estimator. We establish approximation rates of order up to $1/\sqrt{n}$ for the latter distribution, which significantly improves upon the previous results obtained by Samsonov et al. (2024).

We develop a version of variational inference for Bayesian count response regression-type models that possesses attractive attributes such as convexity and closed form updates. The convex solution aspect entails numerically stable fitting algorithms, whilst the closed form aspect makes the methodology fast and easy to implement. The essence of the approach is the use of Pólya-Gamma augmentation of a Negative Binomial likelihood, a finite-valued prior on the shape parameter and the structured mean field variational Bayes paradigm. The approach applies to general count response situations. For concreteness, we focus on generalized linear mixed models within the semiparametric regression class of models. Real-time fitting is also described.

The evolution of a time series is often influenced not only by its past values but also by external covariates, giving rise to forecasting with exogenous variables. Nonlinear and delayed effects between covariates and the target series make this task particularly challenging. We propose a forecasting framework based on Ridge regression with sliding-window signature features, combining the computational efficiency of (semi-)parametric models with the flexibility of nonparametric approaches. These features capture complex dependencies between the target and the exogenous variables without relying on prior assumptions about the form of these relationships or the influence of past observations. We establish theoretical guarantees in the discrete-time setting, including universality of approximation and stationarity for the sliding-window transform. To ease implementation, we introduce a novel sequential algorithm that exploits window overlap for efficient signature updates. The method is evaluated on both synthetic and real electricity demand data. Results show that signature features effectively encode temporal and nonlinear dependencies, yielding accurate forecasts competitive with those based on expert knowledge and recent neural network approaches.