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Wednesday 21 January

Statistics Theory · Cross-listed from cs.LG

Statistical Learning Theory for Distributional Classification

Christian Fiedler

In supervised learning with distributional inputs in the two-stage sampling setup, relevant to applications like learning-based medical screening or causal learning, the inputs (which are probability distributions) are not accessible in the learning phase, but only samples thereof. This problem is particularly amenable to kernel-based learning methods, where the distributions or samples are first embedded into a Hilbert space, often using kernel mean embeddings (KMEs), and then a standard kernel method like Support Vector Machines (SVMs) is applied, using a kernel defined on the embedding Hilbert space. In this work, we contribute to the theoretical analysis of this latter approach, with a particular focus on classification with distributional inputs using SVMs. We establish a new oracle inequality and derive consistency and learning rate results. Furthermore, for SVMs using the hinge loss and Gaussian kernels, we formulate a novel variant of an established noise assumption from the binary classification literature, under which we can establish learning rates. Finally, some of our technical tools like a new feature space for Gaussian kernels on Hilbert spaces are of independent interest.
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Statistics Applications

Zero-inflated binary Tree Pólya splitting regression for multivariate count data

Fabrice Moudjieu, Jean Peyhardi, Maxime Réjou-Méchain et al. (+2 more)

Species distribution models (SDMs) are widely used to assess the effects of environmental factors on species distributions. However, classical SDMs ignore inter-species dependencies. Multivariate SDMs (MSDMs), especially those based on latent Gaussian fields such as the multivariate Poisson log-normal (MPLN), address this limitation but face challenges related to computation, dimensionality, and interpretability. Pólya-splitting (PS) distributions offer an alternative, combining a model for total abundance with a multivariate allocation structure, and have natural interpretations from ecological process models. Yet, they lack flexibility in modeling correlation structures. Tree Pólya-splitting (TPS) distributions overcome this by introducing hierarchical structure such as a phylogenetic tree. In this paper, we extend TPS to account for zero-inflation, leading to the zero-inflated tree Pólya-splitting (Z-TPS) family. We detail its statistical properties, show how standard software enables efficient inference, and illustrate its ecological relevance using tree abundance data from over 180 genera across the Congo Basin tropical rainforest.
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All authors Fabrice Moudjieu, Jean Peyhardi, Maxime Réjou-Méchain, Patrice Soh Takam, Frédéric Mortier

Statistical Methodology

Global-local shrinkage priors for modeling random effects in multivariate spatial small area estimation

Shushi Nishina, Takahiro Onizuka and Shintaro Hashimoto

Small area estimation (SAE) plays a central role in survey statistics and epidemiology, providing reliable estimates for domains with limited sample sizes. The multivariate Fay-Herriot model has been extensively used for this purpose, because it enhances estimation accuracy by borrowing strength across multiple correlated variables. In this paper, we develop a Bayesian extension of the multivariate Fay-Herriot model that enables flexible, component-specific shrinkage of the random effects. The proposed approach employs global-local priors formulated through a sandwich mixture representation, allowing adaptive regularization of each element of the random-effect vectors. This construction yields greater robustness and prevents excessive shrinkage in areas exhibiting strong underlying signals. In addition, we incorporate spatial dependence into the model to account for geographical correlation across small areas. The resulting spatial multivariate framework simultaneously exploits cross-variable relationships and spatial structure, yielding improved estimation efficiency. The utility of the proposed method is demonstrated through simulation studies and an empirical application to real survey data.
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Statistical Methodology

Recent advances in the Bradley–Terry Model: theory, algorithms, and applications

Shuxing Fang, Ruijian Han, Yuanhang Luo et al. (+1 more)

This article surveys recent advances in the Bradley-Terry (BT) model and its extensions. We focus on statistical and computational aspects, with particular emphasis on the regime in which both the number of objects and the volume of comparisons tend to infinity-a setting relevant to large-scale applications. The main topics include asymptotic theory for statistical estimation and inference, together with the corresponding computational algorithms. We also review applications of these models in sports analytics, social choice, psychometrics, and machine learning. Finally, we discuss several key challenges and outline directions for future research.
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All authors Shuxing Fang, Ruijian Han, Yuanhang Luo, Yiming Xu

Statistics Applications

Regulatory Expectations for Bayesian Methods in Drug and Biologic Clinical Trials: A Practical Perspective on FDA's 2026 Draft Guidance

Yuan Ji and Ph.D

The U.S. Food and Drug Administration (FDA) released a landmark draft guidance in January 2026 on the use of Bayesian methodology to support primary inference in clinical trials of drugs and biological products. For sponsors, the central message is not merely that “Bayes is allowed,” but that Bayesian designs should be justified through explicit success criteria, thoughtful priors (especially when borrowing external information), prospective operating-characteristic evaluation (often via simulation when simulation is used), and computational transparency suitable for regulatory review. This paper provides a practical, regulatory-oriented synthesis of the draft guidance, highlighting where Bayesian designs can be calibrated to traditional frequentist error-rate targets and where, with sponsor–FDA agreement, alternative Bayesian operating metrics may be appropriate. We illustrate expectations through examples discussed in the guidance (e.g., platform trials, external/nonconcurrent controls, pediatric extrapolation) and conclude with an actionable checklist for planning documents and submission packages.
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Machine Learning (Statistics) · Cross-listed from math.OC

TRSVR: An Adaptive Stochastic Trust-Region Method with Variance Reduction

Yuchen Fang, Xinshou Zheng and Javad Lavaei

We propose a stochastic trust-region method for unconstrained nonconvex optimization that incorporates stochastic variance-reduced gradients (SVRG) to accelerate convergence. Unlike classical trust-region methods, the proposed algorithm relies solely on stochastic gradient information and does not require function value evaluations. The trust-region radius is adaptively adjusted based on a radius-control parameter and the stochastic gradient estimate. Under mild assumptions, we establish that the algorithm converges in expectation to a first-order stationary point. Moreover, the method achieves iteration and sample complexity bounds that match those of SVRG-based first-order methods, while allowing stochastic and potentially gradient-dependent second-order information. Extensive numerical experiments demonstrate that incorporating SVRG accelerates convergence, and that the use of trust-region methods and Hessian information further improves performance. We also highlight the impact of batch size and inner-loop length on efficiency, and show that the proposed method outperforms SGD and Adam on several machine learning tasks.
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Machine Learning (Statistics)

Semi-Supervised Mixture Models under the Concept of Missing at Radom with Margin Confidence and Aranda Ordaz Function

Jinyang Liao and Ziyang Lyu

This paper presents a semi-supervised learning framework for Gaussian mixture modelling under a Missing at Random (MAR) mechanism. The method explicitly parameterizes the missingness mechanism by modelling the probability of missingness as a function of classification uncertainty. To quantify classification uncertainty, we introduce margin confidence and incorporate the Aranda Ordaz (AO) link function to flexibly capture the asymmetric relationships between uncertainty and missing probability. Based on this formulation, we develop an efficient Expectation Conditional Maximization (ECM) algorithm that jointly estimates all parameters appearing in both the Gaussian mixture model (GMM) and the missingness mechanism, and subsequently imputes the missing labels by a Bayesian classifier derived from the fitted mixture model. This method effectively alleviates the bias induced by ignoring the missingness mechanism while enhancing the robustness of semi-supervised learning. The resulting uncertainty-aware framework delivers reliable classification performance in realistic MAR scenarios with substantial proportions of missing labels.
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Machine Learning (Statistics) · Cross-listed from cs.CV

Diffusion Epistemic Uncertainty with Asymmetric Learning for Diffusion-Generated Image Detection

Yingsong Huang, Hui Guo, Jing Huang et al. (+2 more)

The rapid progress of diffusion models highlights the growing need for detecting generated images. Previous research demonstrates that incorporating diffusion-based measurements, such as reconstruction error, can enhance the generalizability of detectors. However, ignoring the differing impacts of aleatoric and epistemic uncertainty on reconstruction error can undermine detection performance. Aleatoric uncertainty, arising from inherent data noise, creates ambiguity that impedes accurate detection of generated images. As it reflects random variations within the data (e.g., noise in natural textures), it does not help distinguish generated images. In contrast, epistemic uncertainty, which represents the model's lack of knowledge about unfamiliar patterns, supports detection. In this paper, we propose a novel framework, Diffusion Epistemic Uncertainty with Asymmetric Learning~(DEUA), for detecting diffusion-generated images. We introduce Diffusion Epistemic Uncertainty~(DEU) estimation via the Laplace approximation to assess the proximity of data to the manifold of diffusion-generated samples. Additionally, an asymmetric loss function is introduced to train a balanced classifier with larger margins, further enhancing generalizability. Extensive experiments on large-scale benchmarks validate the state-of-the-art performance of our method.
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All authors Yingsong Huang, Hui Guo, Jing Huang, Bing Bai, Qi Xiong

Statistics Applications

Implementing Substance Over Form: A Novel Metric for Taxing E-commerce to Address Deterritorialization

Li Tuobang

Against the backdrop of e-commerce restructuring consumption patterns, last-mile delivery stations have substantially fulfilled the function of community retail distribution. However, the current tax system only levies a low labor service tax on delivery fees, resulting in a tax contribution from the massive circulating goods value that is significantly lower than that of retail supermarkets of equivalent scale. This disparity not only triggers local tax base erosion but also fosters unfair competition. Based on the "substance over form" principle, this paper proposes a tax rate calculation method using "delivery fee plus insurance premium" as the base, corrected through "goods value conversion." This method aims to align the substantive tax burden of e-commerce with that of community retail at the terminal stage, effectively internalizing the high negative externalities of delivery stations through fiscal instruments, addressing E-commerce Deterritorialization.
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Machine Learning (Statistics)

Communication-efficient distributed hazard difference estimation for heterogeneous multi-site survival data

Ziwen Wang, Siqi Li, Marcus Eng Hock Ong et al. (+1 more)

Multi-site collaboration can power survival models that no single hospital could fit alone, but privacy rules and protected computing environments block patient-level data sharing and the persistent server connections required by iterative federated methods. We present DiSAH (\underline{Di}stributed \underline{S}urvival via \underline{A}dditive \underline{H}azards), a federated algorithm for time-to-event analysis whose closed-form, non-iterative structure removes the need for a dedicated central server. Coordination requires only aggregation of summary statistics, which any site can perform, with no patient-level data leaving the site. DiSAH is the first federated method to estimate hazard differences, the absolute change in event rate attributable to each risk factor, providing an actionable scale for triage, resource allocation, and health-economic evaluation. Across simulations and 47,778 emergency-department patients from the United States and Singapore, DiSAH matches centralized analysis in accuracy and discrimination, recovers mortality risk factors no individual site was powered to detect, and outperforms meta-analysis and local models.
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All authors Ziwen Wang, Siqi Li, Marcus Eng Hock Ong, Nan Liu

Machine Learning (Statistics) · Cross-listed from cs.IT

Optimality of Staircase Mechanisms for Vector Queries under Differential Privacy

James Melbourne, Mario Diaz and Shahab Asoodeh

We study the optimal design of additive mechanisms for vector-valued queries under $\epsilon$-differential privacy (DP). Given only the sensitivity of a query and a norm-monotone cost function measuring utility loss, we ask which noise distribution minimizes expected cost among all additive $\epsilon$-DP mechanisms. Using convex rearrangement theory, we show that this infinite-dimensional optimization problem admits a reduction to a one-dimensional compact and convex family of radially symmetric distributions whose extreme points are the staircase distributions. As a consequence, we prove that for any dimension, any norm, and any norm-monotone cost function, there exists an $\epsilon$-DP staircase mechanism that is optimal among all additive mechanisms. This result resolves a conjecture of Geng, Kairouz, Oh, and Viswanath, and provides a geometric explanation for the emergence of staircase mechanisms as extremal solutions in differential privacy.
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Statistics Theory

Cluster size distributions of discrete random fields

Dan Cheng and John Ginos

We study size distributions of finite excursion clusters of discrete random fields on the integer lattice $\mathbb Z^d$. For stationary fields, we assign a unique root to each finite cluster and derive an exact representation of the root Palm size law through joint exceedance and exterior nonexceedance probabilities for complete connected shapes. Root sampling gives each finite cluster equal weight and remains well defined even when infinite components are present. We also study the cluster size law conditional on a specified site being a local maximum above the threshold $u$, providing a local formulation for nonstationary fields. Under stationarity and almost sure cluster finiteness, an exact change of measure shows that peak sampling reweights the root law by the number of local maxima in each cluster. For stationary Gaussian fields satisfying suitable conditions, the total variation distance between these laws decreases exponentially in $u^2$. Guarded spatial Monte Carlo yields unbiased estimators of cluster intensities, estimates of sampling uncertainty from independent realizations, and a finite sample certificate for root truncation error. We further establish sufficient exponential cluster size tail bounds at a fixed threshold and exact logarithmic Gaussian decay rates at a fixed cluster size as $u\to \infty$. The latter rates are characterized by quadratic programs retaining the exterior constraints needed to identify complete components. Numerical illustrations compare direct probability evaluations with Monte Carlo estimates and assess sampling uncertainty and truncation error. The general representations and estimators apply to both Gaussian and non-Gaussian fields, providing a probabilistic foundation for quantifying spatial extent in discretely sampled data.
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Tuesday 20 January

Statistics Theory · Cross-listed from math.FA

The Shift Operator Calculus for Stationary Time Series Analysis

Anand Ganesh, Babhrubahan Bose and Anand Rajagopalan

The article establishes a rigorous shift operator calculus for stationary time series modeling, addressing a certain gap in the literature. It provides proofs of existence and isometry for the transfer function operators $f(B)$ and $f(T)$ where $B$ is the bilateral shift operator and $T$ is the unilateral shift operator for different families of functions $f$. The article establishes convergence of the power series of $f(B)$ and $f(T)$ under the operator norm for the Wiener algebra $\mathbb{W}_+$, and convergence under strong operator topology for $f$ in $H^{\infty}$, based on the use of Abel sums. Based on this calculus, it unifies the notion of stationary process invertibility with the operator invertibility of the transfer function $f(T)$.
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Machine Learning (Statistics) · Cross-listed from q-fin.ST

Test-Time Adaptation for Non-stationary Time Series: From Synthetic Regime Shifts to Financial Markets

Yurui Wu, Qingying Deng, Wonou Chung et al. (+1 more)

Time series encountered in practice are rarely stationary. When the data distribution changes, a forecasting model trained on past observations can lose accuracy. We study a small-footprint test-time adaptation (TTA) framework for causal timeseries forecasting and direction classification. The backbone is frozen, and only normalization affine parameters are updated using recent unlabeled windows. For classification we minimize entropy and enforce temporal consistency; for regression we minimize prediction variance across weak time-preserving augmentations and optionally distill from an EMA teacher. A quadratic drift penalty and an uncertainty triggered fallback keep updates stable. We evaluate this framework in two stages: synthetic regime shifts on ETT benchmarks, and daily equity and FX series (SPY, QQQ, EUR/USD) across pandemic, high-inflation, and recovery regimes. On synthetic gradual drift, normalization-based TTA improves forecasting error, while in financial markets a simple batch-normalization statistics update is a robust default and more aggressive norm-only adaptation can even hurt. Our results provide practical guidance for deploying TTA on non-stationary time series.
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All authors Yurui Wu, Qingying Deng, Wonou Chung, Mairui Li

Machine Learning (Statistics) · Cross-listed from cs.LG

Generative AI-enhanced Probabilistic Multi-Fidelity Surrogate Modeling Via Transfer Learning

Jice Zeng, David Barajas-Solano and Hui Chen

The performance of machine learning surrogates is critically dependent on data quality and quantity. This presents a major challenge, as high-fidelity (HF) data is often scarce and computationally expensive to acquire, while low-fidelity (LF) data is abundant but less accurate. To address this data-scarcity problem, we propose a probabilistic multi-fidelity surrogate modeling framework that integrates transfer learning with generative modeling. We employ a normalizing flow (NF) generative model as the backbone, which is trained in two phases: (i) the NF is first pretrained on a large LF dataset to learn a probabilistic forward model; (ii) the pretrained model is then fine-tuned on a small HF dataset, allowing it to correct for LF–HF discrepancies via knowledge transfer. To relax the dimension-preserving constraint of standard bijective NFs, we integrate surjective (dimension-reducing) layers with standard coupling blocks. This architecture enables learned dimension reduction while preserving the ability to train with exact likelihoods. The resulting surrogate provides fast probabilistic predictions with quantified uncertainty and significantly outperforms LF-only baselines while using fewer HF evaluations. We validate the approach for two benchmark systems: a rail-sleeper-ballast and a reinforced concrete slab. For both applications, we combine many coarse-mesh (LF) simulations with a limited set of fine-mesh (HF) simulations. The proposed model achieves probabilistic predictions with HF accuracy, demonstrating a practical path toward data-efficient, generative AI-driven surrogates for complex engineering systems.
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Statistics Applications · Cross-listed from astro-ph.GA

New techniques to investigate the AGN-SF connection with integral field spectroscopy

Aman Chopra, Henry R. M. Zovaro and Rebecca L. Davies

Understanding the connection between active galactic nuclei and star-formation (the AGN-SF connection) is one of the longest standing problems in modern astrophysics. In the age of large Integral Field Unit (IFU) surveys, studies of the AGN-SF connection greatly benefit from spatially resolving AGN and SF contributions to study the two processes independently. Using IFU data for 54 local active galaxies from the S7 sample, we present a new method to separate emission from AGN activity and SF using mixing sequences observed in the [NII]$\lambda 6584$/H$\alpha$ vs. [OIII]$\lambda 5007$/H$\beta$ Baldwin-Phillips-Terlevich (BPT) diagram. We use the new decomposition method to calculate the H$\alpha$ star-formation rate and AGN [OIII] luminosity for the galaxies. Our new method is robust to outliers in the line-ratio distribution and can be applied to large galaxy samples with little manual intervention. We infer star-formation histories (SFHs) using pPXF, conducting detailed recovery tests to determine the quantities that can be considered robust. We test the correlation between the AGN Eddington ratio, using the proxy L[OIII]/$\sigma_*^4$, and star-formation properties. We find a moderately strong correlation between the Eddington ratio and the star-formation rate (SFR). We also observe marginally significant correlations between the AGN Eddington ratio and the light-weighted stellar age under 100 Myr. Our results point to higher AGN accretion being associated with young nuclear star formation under 100 Myr, consistent with timelines presented in previous studies. The correlations found in this paper are relatively weak; extending our methods to larger samples, including radio-quiet galaxies, will help better constrain the physical mechanisms and timescales of the AGN-SF connection.
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Machine Learning (Statistics) · Cross-listed from cs.LG

engGNN: A Dual-Graph Neural Network for Omics-Based Disease Classification and Feature Selection

Tiantian Yang, Yuxuan Wang, Zhenwei Zhou et al. (+1 more)

Omics data, such as transcriptomics, proteomics, and metabolomics, provide critical insights into disease mechanisms and clinical outcomes. However, their high dimensionality, small sample sizes, and intricate biological networks pose major challenges for reliable prediction and meaningful interpretation. Graph Neural Networks (GNNs) offer a promising way to integrate prior knowledge by encoding feature relationships as graphs. Yet, existing methods typically rely solely on either an externally curated feature graph or a data-driven generated one, which limits their ability to capture complementary information. To address this, we propose the external and generated Graph Neural Network (engGNN), a dual-graph framework that jointly leverages both external known biological networks and data-driven generated graphs. Specifically, engGNN constructs a biologically informed undirected feature graph from established network databases and complements it with a directed feature graph derived from tree-ensemble models. This dual-graph design produces more comprehensive embeddings, thereby improving predictive performance and interpretability. Through extensive simulations and real-world applications to gene expression data, engGNN consistently outperforms state-of-the-art baselines. Beyond classification, engGNN provides interpretable feature importance scores that facilitate biologically meaningful discoveries, such as pathway enrichment analysis. Taken together, these results highlight engGNN as a robust, flexible, and interpretable framework for disease classification and biomarker discovery in high-dimensional omics contexts.
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All authors Tiantian Yang, Yuxuan Wang, Zhenwei Zhou, Ching-Ti Liu

Machine Learning (Statistics)

Large Data Limits of Laplace Learning for Gaussian Measure Data in Infinite Dimensions

Zhengang Zhong, Yury Korolev and Matthew Thorpe

Laplace learning is a semi-supervised method, a solution for finding missing labels from a partially labeled dataset utilizing the geometry given by the unlabeled data points. The method minimizes a Dirichlet energy defined on a (discrete) graph constructed from the full dataset. In finite dimensions the asymptotics in the large (unlabeled) data limit are well understood with convergence from the graph setting to a continuum Sobolev semi-norm weighted by the Lebesgue density of the data-generating measure. The lack of the Lebesgue measure on infinite-dimensional spaces requires rethinking the analysis if the data aren't finite-dimensional. In this paper we make a first step in this direction by analyzing the setting when the data are generated by a Gaussian measure on a Hilbert space and proving pointwise convergence of the graph Dirichlet energy.
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Statistical Methodology

The RobinCar Family: R Tools for Robust Covariate Adjustment in Randomized Clinical Trials

Marlena Bannick, Yuanyuan Bian, Gregory Chen et al. (+6 more)

Purpose: Covariate adjustment is a powerful statistical technique that can increase efficiency in clinical trials. Recent guidance from the U.S. FDA provided recommendations and best practices for using covariate adjustment. However, there has existed a gap between the extensive statistical literature on covariate adjustment and software that is easy to use and abides by these best practices. Methods: We have developed the RobinCar Family, which is comprised of RobinCar and RobinCar2. These two R packages enable covariate-adjusted analyses for continuous, discrete, and time-to-event outcomes that follow best practices. For continuous and discrete outcomes, the functions in the RobinCar Family facilitate traditional forms of covariate adjustment such as ANCOVA as well as more recent approaches like ANHECOVA, G-computation with generalized linear models and machine learning models, and adjustment for a super-covariate (as in PROCOVA(TM)). Functions for time-to-event outcomes implement the covariate-adjusted log-rank test, the stratified covariate-adjusted log-rank test, and the marginal covariate-adjusted hazard ratio. The RobinCar Family is supported by the ASA Biopharmaceutical Section Covariate Adjustment Scientific Working Group. Results: We provide an accessible overview of the covariate-adjusted statistical methods, and describe how they are implemented in RobinCar and RobinCar2. We highlight important usage notes for clinical trial practitioners. Conclusion: We apply RobinCar and RobinCar2 functions by analyzing data from the AIDS Clinical Trials Group Study 175, demonstrating that they are straightforward and user-friendly.
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All authors Marlena Bannick, Yuanyuan Bian, Gregory Chen, Liming Li, Yuhan Qian, Daniel Sabanés Bové, Dong Xi, Ting Ye, Yanyao Yi

Statistical Methodology

Doubly robust estimators of the restricted mean time in favor estimands in individual- and cluster-randomized trials

Xi Fang, Bingkai Wang, Guangyu Tong et al. (+3 more)

Progressive multi-state survival outcomes are common in trials with recurrent or sequential events and require treatment effect estimands that remain interpretable without proportional intensity or Markov assumptions. The restricted mean time in favor of treatment (RMT-IF) extends the restricted mean survival time to ordered multi-state processes and provides such an interpretable estimand. However, existing RMT-IF methods are nonparametric, assume covariate-independent censoring for independent observations, and do not accommodate cluster-randomized trials (CRTs), limiting both efficiency and applicability. We develop a class of doubly robust estimators for RMT-IF under right censoring using an augmented inverse-probability weighting framework that combines stage-specific outcome regression with arm-specific censoring models, yielding consistency when either nuisance model is correctly specified. We further extend the framework to CRTs by formalizing both cluster-level and individual-level average RMT-IF estimands to address informative cluster size and by constructing corresponding doubly robust estimators that account for within-cluster correlation. For inference, we employ model-agnostic jackknife variance estimators in both individually randomized and cluster-randomized settings. Extensive simulation studies demonstrate finite-sample performance, and the methods are illustrated using two randomized trial examples.
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All authors Xi Fang, Bingkai Wang, Guangyu Tong, Liangyuan Hu, Shuangge Ma, Fan Li

Machine Learning (Statistics)

Meta Flow Maps enable scalable reward alignment

Peter Potaptchik, Adhi Saravanan, Abbas Mammadov et al. (+3 more)

Controlling generative models is computationally expensive. This is because optimal alignment with a reward function–whether via inference-time steering or fine-tuning–requires estimating the value function. This task demands access to the conditional posterior $p_{1|t}(x_1|x_t)$, the distribution of clean data $x_1$ consistent with an intermediate state $x_t$, a requirement that typically compels methods to resort to costly trajectory simulations. To address this bottleneck, we introduce Meta Flow Maps (MFMs), a framework extending consistency models and flow maps into the stochastic regime. MFMs are trained to perform stochastic one-step posterior sampling, generating arbitrarily many i.i.d. draws of clean data $x_1$ from any intermediate state. Crucially, these samples provide a differentiable reparametrization that unlocks efficient value function estimation. We leverage this capability to solve bottlenecks in both paradigms: enabling inference-time steering without inner rollouts, and facilitating unbiased, off-policy fine-tuning to general rewards. Empirically, our single-particle steered-MFM sampler outperforms a Best-of-1000 baseline on ImageNet across multiple rewards at a fraction of the compute.
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All authors Peter Potaptchik, Adhi Saravanan, Abbas Mammadov, Alvaro Prat, Michael S. Albergo, Yee Whye Teh

Machine Learning (Statistics) · Cross-listed from astro-ph.IM

Opportunities in AI/ML for the Rubin LSST Dark Energy Science Collaboration

LSST Dark Energy Science Collaboration, Eric Aubourg, Camille Avestruz et al. (+63 more)

The Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) will produce unprecedented volumes of heterogeneous astronomical data (images, catalogs, and alerts) that challenge traditional analysis pipelines. The LSST Dark Energy Science Collaboration (DESC) aims to derive robust constraints on dark energy and dark matter from these data, requiring methods that are statistically powerful, scalable, and operationally reliable. Artificial intelligence and machine learning (AI/ML) are already embedded across DESC science workflows, from photometric redshifts and transient classification to weak lensing inference and cosmological simulations. Yet their utility for precision cosmology hinges on trustworthy uncertainty quantification, robustness to covariate shift and model misspecification, and reproducible integration within scientific pipelines. This white paper surveys the current landscape of AI/ML across DESC's primary cosmological probes and cross-cutting analyses, revealing that the same core methodologies and fundamental challenges recur across disparate science cases. Since progress on these cross-cutting challenges would benefit multiple probes simultaneously, we identify key methodological research priorities, including Bayesian inference at scale, physics-informed methods, validation frameworks, and active learning for discovery. With an eye on emerging techniques, we also explore the potential of the latest foundation model methodologies and LLM-driven agentic AI systems to reshape DESC workflows, provided their deployment is coupled with rigorous evaluation and governance. Finally, we discuss critical software, computing, data infrastructure, and human capital requirements for the successful deployment of these new methodologies, and consider associated risks and opportunities for broader coordination with external actors.
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All authors LSST Dark Energy Science Collaboration, Eric Aubourg, Camille Avestruz, Matthew R. Becker, Biswajit Biswas, Rahul Biswas, Boris Bolliet, Adam S. Bolton, Clecio R. Bom, Raphaël Bonnet-Guerrini, Alexandre Boucaud, Jean-Eric Campagne, Chihway Chang, Aleksandra Ćiprijanović, Johann Cohen-Tanugi, Michael W. Coughlin, John Franklin Crenshaw, Juan C. Cuevas-Tello, Juan de Vicente, Seth W. Digel, Steven Dillmann, Mariano Javier de León Dominguez Romero, Alex Drlica-Wagner, Sydney Erickson, Alexander T. Gagliano, Christos Georgiou, Aritra Ghosh, Matthew Grayling, Kirill A. Grishin, Alan Heavens, Lindsay R. House, Mustapha Ishak, Wassim Kabalan, Arun Kannawadi, François Lanusse, C. Danielle Leonard, Pierre-François Léget, Michelle Lochner, Yao-Yuan Mao, Peter Melchior, Grant Merz, Martin Millon, Anais Möller, Gautham Narayan, Yuuki Omori, Hiranya Peiris, Laurence Perreault-Levasseur, Andrés A. Plazas Malagón, Nesar Ramachandra, Benjamin Remy, Cécile Roucelle, Jaime Ruiz-Zapatero, Stefan Schuldt, Ignacio Sevilla-Noarbe, Ved G. Shah, Tjitske Starkenburg, Stephen Thorp, Laura Toribio San Cipriano, Tilman Tröster, Roberto Trotta, Padma Venkatraman, Amanda Wasserman, Tim White, Justine Zeghal, Tianqing Zhang, Yuanyuan Zhang

Machine Learning (Statistics) · Cross-listed from cs.LG

Q-learning with Adjoint Matching

Qiyang Li and Sergey Levine

We propose Q-learning with Adjoint Matching (QAM), a novel TD-based reinforcement learning (RL) algorithm that tackles a long-standing challenge in continuous-action RL: efficient optimization of an expressive diffusion or flow-matching policy with respect to a parameterized Q-function. Effective optimization requires exploiting the first-order information of the critic, but it is challenging to do so for flow or diffusion policies because direct gradient-based optimization via backpropagation through their multi-step denoising process is numerically unstable. Existing methods work around this either by only using the value and discarding the gradient information, or by relying on approximations that sacrifice policy expressivity or bias the learned policy. QAM sidesteps both of these challenges by leveraging adjoint matching, a recently proposed technique in generative modeling, which transforms the critic's action gradient to form a step-wise objective function that is free from unstable backpropagation, while providing an unbiased, expressive policy at the optimum. Combined with temporal-difference backup for critic learning, QAM consistently outperforms prior approaches on hard, sparse reward tasks in both offline and offline-to-online RL.
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Statistics Theory

Symmetry Testing in Time Series using Ordinal Patterns: A U-Statistic Approach

Annika Betken, Giorgio Micali and Manuel Ruiz Marín

We introduce a general framework for testing temporal symmetries in time series based on the distribution of ordinal patterns. While previous approaches have focused on specific forms of asymmetry, such as time reversal, our method provides a unified framework applicable to arbitrary symmetry tests. We establish asymptotic results for the resulting test statistics under a broad class of stationary processes. Comprehensive experiments on both synthetic and real data demonstrate that the proposed test achieves high sensitivity to structural asymmetries while remaining fully data-driven and computationally efficient.
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Statistical Methodology

Factor Analysis of Multivariate Stochastic Volatility Model

Taehee Lee and Jun S. Liu

Modeling the time-varying covariance structures of high-dimensional variables is critical across diverse scientific and industrial applications; however, existing approaches exhibit notable limitations in either modeling flexibility or inferential efficiency. For instance, change-point modeling fails to account for the continuous time-varying nature of covariance structures, while GARCH and stochastic volatility models suffer from over-parameterization and the risk of overfitting. To address these challenges, we propose a Bayesian factor modeling framework designed to enable simultaneous inference of both the covariance structure of a high-dimensional time series and its time-varying dynamics. The associated Expectation-Maximization (EM) algorithm not only features an exact, closed-form update for the M-step but also is easily generalizable to more complex settings, such as spatiotemporal multivariate factor analysis. We validate our method through simulation studies and real-data experiments using climate and financial datasets.
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Machine Learning (Statistics) · Cross-listed from cs.LG

Penalizing Localized Dirichlet Energies in Low Rank Tensor Products

Paris A. Karakasis and Nicholas D. Sidiropoulos

We study low-rank tensor-product B-spline (TPBS) models for regression tasks and investigate Dirichlet energy as a measure of smoothness. We show that TPBS models admit a closed-form expression for the Dirichlet energy, and reveal scenarios where perfect interpolation is possible with exponentially small Dirichlet energy. This renders global Dirichlet energy-based regularization ineffective. To address this limitation, we propose a novel regularization strategy based on local Dirichlet energies defined on small hypercubes centered at the training points. Leveraging pretrained TPBS models, we also introduce two estimators for inference from incomplete samples. Comparative experiments with neural networks demonstrate that TPBS models outperform neural networks in the overfitting regime for most datasets, and maintain competitive performance otherwise. Overall, TPBS models exhibit greater robustness to overfitting and consistently benefit from regularization, while neural networks are more sensitive to overfitting and less effective in leveraging regularization.
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Statistics Theory · Cross-listed from math.PR

Wasserstein distances between ERGMs and Erdős-Rényi models

Vilas Winstein

Ferromagnetic exponential random graph models (ERGMs) are random graph models under which the presence of certain small structures (such as triangles) is encouraged; they can be constructed by tilting an Erdős–Rényi model by the exponential of a particular nonlinear Hamiltonian. These models are mixtures of metastable wells which each behave macroscopically like an Erdős–Rényi model, exhibiting the same laws of large numbers for subgraph counts [CD13]. However, on the microscopic scale these metastable wells are very different from Erdős–Rényi models, with the total variation distance between the two measures tending to 1 [MX23]. In this article we clarify this situation by providing a sharp (up to constants) bound on the Hamming-Wasserstein distance between the two models, which is the average number of edges at which they differ, under the coupling which minimizes this average. In particular, we show that this distance is $\Theta(n^{3/2})$, quantifying exactly how these models differ. An upper bound of this form has appeared in the past [RR19], but this was restricted to the subcritical (high-temperature) regime of parameters. We extend this bound, using a new proof technique, to the supercritical (low-temperature) regime, and prove a matching lower bound which has only previously appeared in the subcritical regime of special cases of ERGMs satisfying a "triangle-free" condition [DF25]. To prove the lower bound in the presence of triangles, we introduce an approximation of the discrete derivative of the Hamiltonian, which controls the dynamical properties of the ERGM, in terms of local counts of triangles and wedges (two-stars) near an edge. This approximation is the main technical and conceptual contribution of the article, and we expect it will be useful in a variety of other contexts as well. Along the way, we also prove a bound on the marginal edge probability under the ERGM via a new bootstrapping argument. Such a bound has already appeared [FLSW25], but again only in the subcritical regime and using a different proof strategy.
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Statistical Computation · Cross-listed from math.OC

Gradient flow for finding E-optimal designs

Jieling Shi, Kim-Chuan Toh, Xin T. Tong et al. (+1 more)

The $E$-optimality criterion for a regression model maximizes the smallest eigenvalue of the information matrix and becomes non-differentiable when this eigenvalue has multiplicity greater than one. Working in the $2$-Wasserstein space, we show that the Wasserstein gradient at an empirical measure coincides, up to a constant factor, with the Euclidean particle gradient for smooth criteria such as $D$- and $L$-optimality, and that the approximation gap for equal-weight $N$-particle designs vanishes at an explicit rate. The main challenge is the nonsmooth $E$-criterion, for which the Wasserstein gradient does not exist. We replace it with a constrained Wasserstein steepest-ascent field obtained by maximizing feasible directional derivatives over the tangent cone of the design space, and prove that the resulting flow satisfies an exact energy identity and that every limit point is first-order stationary. The particle ascent computation reduces to a convex semidefinite programme whose dimension equals the multiplicity of the smallest eigenvalue. In numerical comparisons on second-order response surface models and a seven-dimensional logistic regression model, the constrained Wasserstein steepest-ascent method attains near-optimal $E$-criterion values and is markedly more reliable than particle swarm optimization in higher-dimensional settings. The framework applies more broadly to other nonsmooth minimax criteria in optimal design, and a numerical experiment on the minimax-single-parameter criterion confirms that the method attains the theoretical optimum.
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All authors Jieling Shi, Kim-Chuan Toh, Xin T. Tong, Weng Kee Wong

Statistics Applications · Cross-listed from q-fin.ST

Demystifying the trend of the healthcare index: Is historical price a key driver?

Payel Sadhukhan, Samrat Gupta, Subhasis Ghosh et al. (+1 more)

Healthcare sector indices consolidate the economic health of pharmaceutical, biotechnology, and healthcare service firms. The short-term movements in these indices are closely intertwined with capital allocation decisions affecting research and development investment, drug availability, and long-term health outcomes. This research investigates whether historical open-high-low-close (OHLC) index data contain sufficient information for predicting the directional movement of the opening index on the subsequent trading day. The problem is formulated as a supervised classification task involving a one-step-ahead rolling window. A diverse feature set is constructed, comprising original prices, volatility-based technical indicators, and a novel class of nowcasting features derived from mutual OHLC ratios. The framework is evaluated on data from healthcare indices in the U.S. and Indian markets over a five-year period spanning multiple economic phases, including the COVID-19 pandemic. The results demonstrate robust predictive performance, with accuracy exceeding 0.8 and Matthews correlation coefficients above 0.6. Notably, the proposed nowcasting features have emerged as a key determinant of the market movement. We have employed the Shapley-based explainability paradigm to further elucidate the contribution of the features: outcomes reveal the dominant role of the nowcasting features, followed by a more moderate contribution of original prices. This research offers a societal utility: the proposed features and model for short-term forecasting of healthcare indices can reduce information asymmetry and support a more stable and equitable health economy.
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All authors Payel Sadhukhan, Samrat Gupta, Subhasis Ghosh, Tanujit Chakraborty