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新论文 · v1arXiv:2610.37353

Cost-based variable selection for prediction models

Lasai Barreñada, Andrew Vickers, Laure Wynants, Bieke Tack, Dirk Timmerman, Ewout Steyerberg, Ben Van Calster

原文摘要

Objective: Variable selection for clinical prediction models is commonly done on statistical grounds related to model fit. Statistical approaches ignore the cost of misclassifications and the harm of measuring a variable. We aim to develop a decision-analytic variable selection algorithm based on net benefit. Materials and Methods: The proposed algorithm selects the set of predictors by exhaustively comparing the net benefit of all combinations using cross validation, with an extension based on backward elimination for settings with many predictors. Variables are selected if the increased net benefit from better predictiveness exceeds the net benefit reduction from the harm of variable measurement. Harm includes financial expense, time, resource allocation, and patient burden. We illustrate the algorithm through a simulated example and three real case studies. We compare its performance to traditional backward elimination and LASSO. Results: Across the case studies, parsimonious models were generated that optimized clinical utility with minimal impact on discrimination and calibration. Penalizing predictors based on their cost ensured that expensive or burdensome variables were only selected if they offer sufficient clinical utility. The algorithm was implemented in the R package NBvarsel. Discussion: Decision-analytic variable selection allows prediction models to maximize patient benefit while minimizing unnecessary clinical burden and costs. Conclusion: Clinical utility should not be an afterthought reserved only for implementation. By integrating a harm-adjusted net benefit metric directly into the variable selection process, NBvarsel allows researchers to select only the variables that sufficiently improve clinical utility.

stat.ME · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37272

Low-degree polynomials lower bounds for clustering in small dimension

Alexandra Carpentier, Nicolas Verzelen

原文摘要

We study the computational limits of clustering $n$ observations drawn from a mixture of $K$ isotropic distributions in $\mathbb R^d$, in the regime where the number $K$ of groups is much larger than the dimension $d$. In this regime, tensor-based procedures recover the partition with a polylogarithmic separation between the centers, but they require a sample size that is a large and non-explicit polynomial of $dK$, whereas the existing low-degree lower bounds only show that $n$ must be larger than $dK^2$. We introduce a mixture of $2K$ product Bernoulli distributions on $\{0,1\}^d$, with $K=(d+1)^m$, whose centers are built from a dual BCH code. This construction ensures that the moment tensors of the observations coincide with those of the uniform distribution on $\{-1,1\}^d$ up to the order $2m+1$. For any fixed $m$, we establish a low-degree polynomial lower bound showing that clustering is hard as long as the separation $Δ$ satisfies $Δ^2\ll(K^2d^{3/2}/n)^{1/(2m+2)}\wedge\sqrt d$, up to polylogarithmic factors. In particular, with a polylogarithmic separation, low-degree polynomials require $n\gtrsim K^2d^{3/2}$ observations, up to polylogarithmic factors. Through a Gaussianization argument, this hardness carries over, in the sense of reductions, to isotropic Gaussian mixtures. Our proof relies on a family of polynomials of the observations, indexed by bipartite graphs, which is almost orthonormal. The moments of these polynomials are governed by the number of solutions of polynomial systems over the finite field $\mathbb F\_{d+1}$ that are induced by the BCH code, and the crux of our analysis is to connect the combinatorial structure of the bipartite graphs with the structure of the solution sets of these systems.

stat.ML · cs.LG

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2605.06993

Optimal Experiments for Partial Causal Effect Identification

Tobias Maringgele, Jalal Etesami

原文摘要

Causal queries are often only partially identifiable from observational data, and experiments that could tighten the resulting bounds are typically costly. We study the problem of selecting, prior to observing experimental outcomes, a cost-constrained subset of experiments that maximally tightens bounds on a target query. We formalize this as the max-potency problem, where epistemic potency measures the worst-case reduction in bound width guaranteed by an experiment, and show that this problem is NP-hard via a reduction from 0-1 knapsack. Building on the polynomial-programming framework of Duarte et al. (2023), we give a general procedure for evaluating epistemic potency in discrete settings. To control the super-exponential search space, we introduce two graphical pruning criteria that depend only on the causal graph and the query: a novel path-interception rule that exploits district structure to certify zero potency in linear time, and an identifiability check based on the ID algorithm. On Erdos-Renyi random graphs and 11 bnlearn benchmark networks, the two criteria together prune 50-88% of candidate experiments on average without solving a single polynomial program. For the general subset search, we show that ID-pruned experiments are combinatorially inert, yielding a super-exponential reduction in the number of subsets evaluated. We close with an end-to-end demonstration on observational NHANES data, selecting optimal experiments for estimating the effect of physical activity on diabetes.

cs.AI · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37227

Doubly Robust Deep Kernel Tests for Structured Outcomes

Robin Leman, Bariscan Bozkurt, Sofiane Tanji, Arthur Gretton, Houssam Zenati

原文摘要

We propose a test of whether two interventions induce the same outcome distribution when outcomes are structured and high-dimensional, such as images, text and graphs. We represent the interventional distributions as mean embeddings on learned deep features, such that the treatment effect is a doubly robust representation of the difference in mean embeddings. Our test, DR-KTE-Deep, optimises the learned features so as to maximise an estimated power criterion on this treatment effect representation. To motivate our learning objective, we show that the power criterion characterises the asymptotic signal-to-noise ratio of the test under fixed alternatives, and we derive a uniform finite-sample bound for its regularised estimate. We show that, with the learned kernel fixed, a held-out test is asymptotically valid under the null given suitable nuisance-estimation rates. Empirically, DR-KTE-Deep achieves substantially higher power than fixed and bandwidth-optimised kernel baselines across image, text and graph outcomes, while maintaining well-calibrated Type-I error.

stat.ML · cs.LG

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2605.30188

CalArena: A Large-Scale Post-Hoc Calibration Benchmark

Eugène Berta, David Holzmüller, Francis Bach, Michael I. Jordan

原文摘要

Reliable probability estimates are critical in many machine learning applications, yet modern classifiers are often poorly calibrated. Post-hoc calibration provides a simple and widely used solution, but the large number of proposed methods, combined with small-scale and inconsistent evaluations, makes it difficult to determine which approaches are truly effective in practice. We introduce a large-scale, standardized benchmark for post-hoc calibration, covering nearly 2000 experiments across tabular and computer vision tasks, including binary, multiclass, and large-scale classification settings. Our benchmark aggregates predictions from a diverse set of classical models, modern deep learning architectures, and foundation models, and provides unified, reproducible implementations of dozens of calibration methods within a common evaluation framework. We argue that Post-Hoc Improvement (PHI) in proper scoring rules offers a principled alternative to traditional calibration error estimators for comparing post-hoc methods, capturing both calibration quality and potential degradation to the model's predictive performance. Using this framework, we conduct the most comprehensive empirical study of post-hoc calibration to date. Our results reveal consistent patterns across domains: smooth calibration functions outperform binning-based approaches, dedicated multiclass methods are essential in high-dimensional settings, and generic machine learning models are not competitive without calibration-specific design. To facilitate future research, we release all data, code, and evaluation tools, providing a plug-and-play benchmark for developing and comparing calibration methods.

cs.LG · cs.AI · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37169

Rènyi-Regularized Flow-Based Variational Inference for Bayesian Calibration

Exaucè Luweh Adjim Ngarti, Élise Arnaud, Léo Nicoletti, Victor Trappler, Arthur Vidard

原文摘要

Variational inference with normalizing flows provides a flexible posterior approximation for Bayesian model calibration, but struggles when the posterior has several modes separated by regions of low probability mass. We study this behavior in a two-parameter twin experiment and regularize the variational objective. Under Gaussian observation errors and a Gaussian prior, the corresponding minimization objective is the expected Tikhonov calibration objective minus the differential entropy of the approximating distribution. However, the expected Tikhonov term favors concentration near one of the modes, while entropy maximization does not guarantee multimodality. We introduce a regularization term based on Rényi divergence that encourages the approximate posterior to cover the prior support. In the connected bimodal case, a flow approximation represents both modes; in the case with well-separated modes, the flow and Gaussian mixture frequently miss one mode. The introduced regularization reduces the near-collapse fraction from 50% to 25%. While the regularization improves mode coverage in this experiment, it changes the Bayesian variational objective, introduces a trade-off in approximation accuracy, and does not provide a general solution to mode collapse.

cs.AI · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37159

Physics-Guided Flow Matching: A Generative AI Framework for Global Total Electron Content Forecasting

Si-Tong Yang, Feng Ye, Xian Lu, Dong Lin, Benjamin C. Martinez

原文摘要

Accurate forecasting of global total electron content (TEC) is important for space weather monitoring and the reliable operation of satellite communication and navigation systems. We propose a physics-guided generative artificial intelligence (AI) framework for day-ahead global TEC forecasting. The framework builds on flow matching, which learns to gradually transform samples from an initial distribution into new samples that share the statistical characteristics of the target data. The proposed model incorporates ionospheric dynamics described by a partial differential equation (PDE) into this transformation process, guiding the changes between initial and target samples using physical knowledge. The model further combines the physical dynamics with statistical patterns captured from data to learn this transformation, adaptively adjusting their relative contributions at each location. The model is trained and evaluated using one year of global TEC data generated by the Thermosphere Ionosphere Electrodynamics General Circulation Model (TIEGCM). The results demonstrate that our model improves both spatial and temporal forecasting accuracy over representative benchmarks, including statistical, deep learning, and generative AI methods at all lead times and across latitudes. The average root mean square error (RMSE) is 39.2% lower than that of ConvLSTM and 23.8% lower than that of the same framework without physical guidance. The learned contribution weights vary systematically with latitude and across geographic locations, showing how the physical contribution changes across the forecast domain. These findings demonstrate that explicit physical guidance improves generative forecasts of global TEC and highlight the value of incorporating physical dynamics into generative AI modeling.

cs.LG · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37731

Amortized Localized Posterior Inference for Model Calibration with Application to an Ocean Turbulence Closure

Exaucé Luweh Adjim Ngarti, Élise Arnaud, Léo Nicoletti, Victor Trappler, Arthur Vidard

原文摘要

Model discrepancy may prevent a single calibration parameter from reproducing a physical response across the context domain. In addition, uncertainties in observations and contexts affect calibration and must be accounted for and quantified. We construct a family of localized posteriors by weighting observation likelihoods according to their proximity to a target context. Gaussian localization weights incorporate context uncertainty through covariance inflation, with reflection at domain boundaries and an optional correction for uneven context sampling. A conditional normalizing flow approximates the family of posteriors through amortized variational inference. Integrating the localized posteriors under a prescribed context measure gives the marginalized parameter distribution. In a twin experiment with the Branin-Hoo model, we compare global and localized inference under uniform and skewed context distributions. Localization reduces the reported aggregate predictive errors relative to the global posterior. An application to the k-$ε$ turbulence closure in a single-column ocean model, with atmospheric surface forcing as context, shows that localized posterior calibration reduces temperature and zonal-velocity errors relative to deterministic and global-posterior calibration. Both twin experiments are constructed to admit local compensation.

cs.AI · cs.LG · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37086

Is Your LLM Relay Serving What It Claims? A low-cost and high-power test for LLM Relay Auditing

Fangran Miao, Shengjie Niu, Jian Huang, Ting Li

原文摘要

Relay and reseller APIs have become a common way to access large language models (LLMs), yet users cannot directly verify whether they receive the models they request and pay for. This opacity motivates LLM relay auditing, but existing methods struggle to combine low cost, robustness to benign deployment changes, and statistically interpretable decisions under black-box access. To address these limitations, we propose distributional fingerprint auditing (DFA), a statistical method that requires only textual responses from suspect and trusted reference endpoints. DFA repeatedly queries semantically simple finite-choice probes and uses the resulting categorical response distributions to construct endpoint fingerprints. It compares the suspect and reference fingerprints probe by probe and aggregates the resulting evidence using the Cauchy combination test, yielding an approximate endpoint-level $p$-value for audit decisions at a prespecified nominal significance level. Using registered fingerprints of candidate models, a likelihood-based formulation further supports model attribution under full substitution and joint estimation of substitute identity and substitution ratio under constant-ratio mixed routing. Our benchmark includes 16 proprietary and open-weight LLMs from 10 model families. Across 240 ordered full-substitution pairs, DFA achieves high detection rates at a nominal significance level of $α=0.05$, using five probes and 250 relay requests per audit with stored reference fingerprints. Configuration overrides can lead to rejection even when the served model remains unchanged, with effects varying across models and configurations. Simulations based on stored empirical fingerprints demonstrate accurate model attribution and estimate substitution ratios, with estimation error decreasing as the audit budget increases.

stat.AP · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.36999

Online gas classification at the edge

Ton Juny Pina, Hugh Greatorex, Elisabetta Chicca

原文摘要

Field applications in chemical sensing, from portable safety monitors to mobile robots, require models that are lightweight, fast to respond, and can be recalibrated from limited labelled data. Current gas classification pipelines assume controlled sampling cycles and offline feature extraction, and rely on computationally expensive models. With a few thousand neurons and sub-milliwatt power consumption, insects reliably classify odours in open environments. Inspired by the insect olfactory system, we present a neural network architecture that classifies raw sensor array readings using a sparse, high-dimensional binary representation. We evaluate it on random sequences of single gases and binary mixtures, introducing new samples dynamically and classifying gas identity from the transient sensor response. In this setting, the architecture out-performs a linear \gls{svm} on gas mixtures and matches an optimised non-linear \gls{svm}, while maintaining online class-level frequency estimates that distinguish familiar from novel stimuli. It relies exclusively on binary weights and Hebbian-based local learning, remaining computationally lightweight and well suited to ultra-low-power neuromorphic processors. We demonstrated the network on-chip with a hazardous gas detection experiment running on the mixed-signal neuromorphic chip TEXEL. The on-chip classifier yielded an accuracy of 74.6\% while running at 482 $\unit{\nano\joule}$ per inference and 27 \unit{\micro\watt} of static-power.

cs.ET · cs.LG · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.36864

Intrinsic Information-Theoretic Analysis of ReLU Nets

Johan Mylius-Kroken, Elisabeth Wetzer, Ali Ramezani-Kebrya, Robert Jenssen, Kristoffer Knutsen Wickstrøm

原文摘要

Mutual information (MI) is fundamental to representation-learning analysis in deep networks, but in high dimensions MI estimators depend on hyperparameters whose bias often dominates the signal. We show that continuous piecewise-linear (CPWL) networks, including ReLU networks, admit an intrinsic information-theoretic analysis that avoids this pitfall: their inherent partition of the input space into convex linear regions assigns to every input a discrete region label $Π$ alongside the continuous representation $T$ and label $Y$. We introduce a decomposition of the mutual information $I(Y;T)$ into interpretable geometric terms. We show that the dominant term, the *routing information* $I(Y; Π)$, admits an estimable plug-in estimator, that in the well-sampled regime, approximates a population lower bound on the joint information $I(Y; Π, T)$. When the partition saturates, a functional-equivalence quotient collapses regions implementing the same linear operator and restores informativeness; this extension has a single bounded, dimensionless parameter, which is reported through the quotient's compression ratio. The routing estimator agrees strongly with three established MI baselines applied to the same networks and data. The functional quotient recovers informative estimates in the regime bordering the well-sampled and under-sampled regime. We provide a framework for analysing the internal information geometry of CPWL networks, grounded in their inherent piecewise-linear structure rather than in external discretisation.

stat.ML · cs.LG

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2502.08414

Non-asymptotic Estimation of Sparse Partial Correlation via Joint Partial Regression

Samuel Erickson, Tobias Rydén

原文摘要

Partial correlation analysis is widely used in modern multivariate analysis. However, prior methods lack non-asymptotic guarantees and have slow asymptotic estimation rates. We present a method for simultaneously estimating sparse high-dimensional partial correlation matrices and inverse covariance with non-asymptotic rates. The method is a two-stage estimation which exploits the connection between the inverse covariance matrix and linear regression estimation method while enforcing positive semi-definiteness simultaneously. An efficient proximal splitting algorithm for numerically computing the estimate is also derived, and we provide a fast implementation of the algorithm. The effectiveness of the proposed method is demonstrated on both synthetic and real-world data.

stat.ML · cs.LG

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.36854

Boundary Geometry Determines Optimal Shallow ReLU Approximation under Weighted Coefficient Constraints

Jia-Qi Yang, Lei Shi

原文摘要

We study how boundary geometry affects $L^q$ approximation by shallow ReLU neural networks on convex bodies $K\subset\mathbb R^d$. The target classes are unit balls of weighted variation spaces that can enlarge classical spaces by incorporating domain geometry into constraints on output coefficients. We establish upper and lower bounds for arbitrary convex bodies and determine the optimal polynomial approximation exponents for all planar convex bodies and their products with polytopes, including cubes and circular cylinders. For $C^2$ convex bodies, we determine the optimal exponents in a dimension-dependent range of $q$ extending beyond $2$. When all principal curvatures are positive, the result extends to every finite $q\ge2$. For these classes, the dependence of the optimal exponent on the domain is captured by a single geometric growth exponent associated with small boundary caps. We also identify sharp weight thresholds for retaining the classical approximation exponent and improve previous weights on Euclidean balls while preserving the classical $L^2$ approximation rate. When the target is given as a finite ReLU network, the upper bounds can be realized by a compressed network using only the original neurons, without increasing the weighted coefficient sum. These results show that boundary geometry can change the optimal exponent even when dimension, error norm, and weighting rule are fixed.

stat.ML · cs.LG · math.FA · math.MG

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2608.18643

ProxyGuard: Direct Reliability Inference for Randomized Data Release Mechanisms with Shared Targets

Dipesh Tharu Mahato, Pramod Dhungana

原文摘要

Researchers often choose a proxy dataset from many releases, transformations, or seeds. Search can make an invalid release appear adequate, while one adequate release does not establish that its generator is reliable. ProxyGuard controls both errors using prespecified bounded risks and a sealed target set. Named-release mode corrects for multiplicity and certifies specific releases. Direct shared-target mode evaluates independent mechanism draws on a common target, lower-bounds their favorable-score rate, and subtracts a bound on favorable scores contributed by invalid releases. Conditional on the target, release scores are independent, yielding a finite-sample mechanism-reliability guarantee without independent target batches or assumptions on release-level $p$-value dependence. We show that the mean-only penalty is sharp and derive a smooth-score certificate with additive target concentration. In a registered three-requirement study, direct mode raises power from $5.6\%$ to $64.2\%$ at reliability $0.95$, while named mode remains stronger under high-signal evidence. Prospective audits span full-pipeline Rice--TVAE, which retrains on every draw, and a non-tabular text mechanism.

cs.LG · stat.ME · stat.ML

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2506.01183

Doubly Robust Alignment for Large Language Models

Erhan Xu, Kai Ye, Hongyi Zhou, Luhan Zhu, Francesco Quinzan, Chengchun Shi

原文摘要

This paper studies reinforcement learning from human feedback (RLHF) for aligning large language models with human preferences. While RLHF has demonstrated promising results, many algorithms are highly sensitive to misspecifications in the underlying preference model (e.g., the Bradley-Terry model), the reference policy, or the reward function, resulting in undesirable fine-tuning. To address model misspecification, we propose a doubly robust preference optimization algorithm that remains consistent when either the preference model or the reference policy is correctly specified (without requiring both). Our proposal demonstrates superior and more robust performance than state-of-the-art algorithms, both in theory and in practice. The code is available at https://github.com/DRPO4LLM/DRPO4LLM

cs.LG · cs.AI · stat.ML

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arXiv ↗PDF ↗
版本更新 · v5arXiv:2508.03059

Two-sample comparison through additive tree models for density ratios

Naoki Awaya, Yuliang Xu, Li Ma

原文摘要

The ratio of two densities provides a direct characterization of their differences. We consider the two-sample comparison problem by estimating this ratio given i.i.d. observations from two distributions. To this end, we propose additive tree models for density ratio estimation along with efficient algorithms using a new loss function, the balancing loss. The loss allows tree-based models to be trained using several algorithms originally designed for supervised learning, such as forward-stagewise optimization and gradient boosting. Moreover, the balancing loss resembles an exponential family kernel, and it can serve as a pseudo-likelihood with conjugate priors. This property enables generalized Bayesian inference on the density ratio using backfitting samplers designed for Bayesian additive regression trees (BART). Our Bayesian strategy provides uncertainty quantification for the inferred density ratio, which is critical for applications involving high-dimensional and data-limited distributions with potentially substantial uncertainty. We further show connections of the balancing loss to the exponential loss in binary classification and to the variational form of f-divergence, particularly the squared Hellinger distance. Numerical experiments demonstrate that the proposed boosting algorithms achieve high accuracy at low computational cost, and that the Bayesian additive tree is competitive in accuracy while additionally providing uncertainty quantification, which the compared estimators do not offer. Finally, we demonstrate its application to assessing the quality of generative models for microbiome compositional data.

stat.ME · stat.CO · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.36806

LLM knowledge for improved Out-of-Distribution Tabular Prediction - A Cross-Validated Regularisation Approach

Sølve Langseth, Kristoffer Herland Hellton, Hugo L. Hammer

原文摘要

Prediction models degrade when the deployment population differs from the one used to train them, and training data cannot say which feature-response relationships will transfer. Expert elicitation is slow and unscalable. We ask whether coefficient priors elicited from large language models (LLMs) improve out-of-distribution (OOD) prediction as the shrinkage target of a regularised regression instead of zero, across five tabular datasets split on real covariates, selecting providers and prior structures by source-domain cross-validation alone. The priors help on four of five datasets, by up to 7.9% OOD mean squared error, and ten of twenty-four prior-informed results resolve the mean improvement at conventional confidence; single-deployment intervals are much wider. On classification the gain is in probabilistic accuracy, not ranking, and control tests with corrupted priors attribute the benefit to feature-specific content rather than scale. Two findings temper this. Variation across candidate priors exceeds the average benefit, yet cross-validation margins fall below their own noise, so selection avoids the worst prior rather than finding the best. On three datasets the prior improves in-domain accuracy as much as out-of-domain, making it better regularisation than shift correction. Only where the training data are large enough that the in-domain gain disappears does elicited knowledge demonstrably improve transfer. Code, priors and results: https://github.com/hugohammer/llm-priors-ood.

cs.LG · stat.ME · stat.ML

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2610.27030

Hilbert-Scale Stability of Posterior Diffusion Priors for Ill-Posed Signal Recovery

Bahman Moraffah, Raha Moraffah

原文摘要

Indirect and noisy observations are difficult to invert when the forward operator smooths out the unknown signal. In this case, the unstable modes are precisely the modes that the data reveals least, thus the success of any reconstruction method depends on how prior information interacts with the geometry of the operator across regularity scales. Diffusion priors have become ubiquitous for such problems; however, the current theory still does not determine when a learned score remains informative under ill-posed forward operators. In this paper, we study posterior diffusion for linear inverse problems on Hilbert scales and derive a stability theory under an explicit score-amplification condition. Under a smoothing condition on the forward map, a source condition on the truth, and weak-norm control of score error, we derive non-asymptotic recovery bounds in \(\Hs^s\) that separate observation noise, score approximation, and reverse-time discretization. These bounds give a recoverable regularity threshold determined jointly by operator smoothing, truth regularity, score regularity, and the posterior correction. The threshold specifies the Hilbert-scale norms \(\Hs^s\) in which weak-norm score error remains controlled after propagation through the posterior reverse dynamics. For larger regularity indices \(s\), the inverse geometry magnifies the same error, and the Hilbert-scale recovery estimate no longer gives uniform stability. We also prove that a posterior correction adapted to the forward operator improves stability relative to isotropic guidance in the regularity ranges where the smoothing action of the forward map matters most. The recovery estimates give a regularity-sensitive theory of posterior diffusion and show how learned score error, operator smoothing, and reconstruction norm jointly determine the stable range predicted by the analysis.

cs.LG · cs.IT · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.36751

Generative Refinement Learning for Temporal Interpolation in Scientific Machine Learning

Pu Ren, Michael W. Mahoney, N. Benjamin Erichson

原文摘要

Computationally expensive simulations and real-world observations often provide data at a lower temporal resolution than downstream tasks require. Averaging observations at fixed grid points can introduce errors, and motion estimates alone do not determine how the physical field values change. In this work, we study whether learning to correct a simple numerical interpolation improves the reconstruction of intermediate scientific fields. Our model, interpolative FLow EXpert (iFLEX), first estimates the missing field by taking a weighted average of the two observations at each grid point, giving more weight to the observation closer to the requested time. During training, subtracting this estimate from an observed intermediate field gives the residual that a conditional diffusion model learns to generate. Both observations condition the model, together with the target time, the interval between observations, and available physical parameters. To reconstruct an unobserved intermediate field, the generated residual is added to the weighted average. We evaluate iFLEX on Navier-Stokes Kraichnan turbulence, Shanghai radar precipitation, and sea surface temperature. Across these datasets, iFLEX achieves lower reconstruction error than the evaluated baselines, including optical-flow and diffusion models developed for video frame interpolation in computer vision. In a controlled turbulence comparison at a Reynolds number of 36,000, learning the residual reduces relative Frobenius norm error from about 13.7 for direct field generation to 10.5, with the diffusion backbone and training setup held fixed. Code is available at https://github.com/paulpuren/iflex.

cs.LG · cs.AI · math-ph · stat.ML

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2609.02728

Momentum in large-batch training: Polyak enlarges the critical batch size, Nesterov improves data efficiency

Jia-Nan Wang, Zixun Huang, Kairui Li, Zilin Wang, Lei Wu

原文摘要

We study when and how momentum improves large-batch training in the one-pass regime, using power-law kernel regression as a tractable setting. We first characterize stochastic stability through the \emph{critical learning rate}, defined as the largest learning rate for stable training, and obtain $η_{\mathrm{SGD}}^{\mathrm{crit}}\eqsim 1$, $η_{\mathrm{Polyak}}^{\mathrm{crit}}\eqsim \min\{1,B(1-β)\}$, and $η_{\mathrm{Nesterov}}^{\mathrm{crit}}\eqsim \min\{1,B^q(1-β)\}$, where $B$ is the batch size, $β\in[0,1)$ is the momentum factor, and \(q>1\) is the capacity exponent governing spectral decay. Within the stable region, we derive scaling laws for the full risk dynamics, capturing the progression from an early transient through power-law decay to a noise floor. We then optimize the final-step risk under a fixed data budget, obtaining a three-regime phase diagram that reveals how the benefits of momentum change with batch size. Notably, Polyak enlarges the critical batch size, the largest batch size preserving the optimal small-batch data-scaling exponent, thereby allowing fewer sequential updates without sacrificing data efficiency. In contrast, Nesterov improves the optimal data-scaling exponent in the large-batch regime through look-ahead-induced suppression of noise amplification. Experiments on PLK regression quantitatively support the theoretical scaling predictions, while neural-network experiments provide qualitative evidence for the predicted batch-size dependence and stability behavior.

stat.ML · cs.LG · math.OC

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.36708

Conservative Dueling Bandits: Preference Learning under Baseline Constraints

Rohan Deb, Mohammad Ghavamzadeh, Arindam Banerjee

原文摘要

Contextual dueling bandits learn from pairwise comparisons, the same feedback used to fine-tune language models from human preferences. Standard algorithms explore aggressively and can show users two poor options. We study conservative contextual dueling bandits, which require that, at every round, the cumulative score of the better displayed item stay above a $(1-α)$ fraction of a trusted baseline's. An item's score is its probability of beating the best available item, so the constraint depends only on utility differences and needs no absolute rewards. This also changes how safety can be certified: we show that transferring the safety test of the conservative bandit algorithm CLUCB unchanged can incur linear regret, even when the baseline's utilities are known exactly. For linear utilities, we develop MaxInP-BC, which certifies scores through utility gaps and, when it must fall back, pairs the baseline with an informative partner so that fallback rounds still drive learning. It is safe with high probability at all times, with regret $\tilde{O}(d\sqrt{T}/κ)$ plus an additive cost of conservatism that does not grow with the horizon. For general utility classes, we develop BTIGW-BC, which turns the guarantee of an online logistic-regression oracle into cumulative safety certificates. It is safe at all times, makes finitely many fallbacks, and has sublinear regret whenever the oracle's logistic regret is sublinear. In experiments, both satisfy the constraint, which their unconstrained counterparts often violate, at a moderate cost in regret.

cs.LG · cs.AI · stat.ML

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arXiv ↗PDF ↗
版本更新 · v4arXiv:2608.19584

Kähler landscapes for complex neural network descents and guarantees including a search and destroy of the Calabi-Yau manifold

Andrew Gracyk

原文摘要

We study landscapes for complex-parameterized networks. Our approach is motivated with an information-theoretic manifold perspective of the parameter and via classical optimization guarantees although of complex geometric variety such as through Dolbeault asymptotics. The descent path admits a Kähler information metric under a cross-entropy via the Wirtinger Hessian on the log-likelihood potential. We restrict attention to a descent update rule with natural gradient descent via a differentiated loss scaled by the inverse metric, so the descent path remains in the holomorphic tangent bundle. We emphasize Calabi-Yau information manifolds which profane theoretical guarantees via an ill-curvature-conditioned, or lack thereof, landscape. We focus on Calabi-Yau metrics specifically in a non-compact setting with a global potential, so defined geometrically rather than invoking the topological requirements of the Calabi conjecture. In non-compact settings, we can write the metric determinant with respect to a background in terms of a function, pluriharmonic or real. Using Yau's Liouville theorem, we get a partial eigenvalue blow-up effect. In an empirical setting, a Ricci-flat metric will not form, but a blow-up can be a local condition and can hold empirically on open sets even partially in generalized Kähler cases due to lower bounds on the Ricci potential. Moreover, it has been discovered that negative curvature subverts the loss landscape, specifically sectional curvature, so we expand on this and draw interconnections to negative-definite Ricci curvature. Our arguments primarily exist via geometric modality, although we establish roots in deep learning theory such as through asymptotics at initialization and connections through failure modes of neural network guarantees under vanishing and negative Ricci curvature.

cs.LG · math.DG · stat.ML

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2606.03217

An Asymptotic Theory of Chain-of-Thought in In-Context Learning

Kaito Takanami, Cengiz Pehlevan

原文摘要

Chain-of-thought (CoT) reasoning has become a widely used mechanism for eliciting multi-step reasoning in large language models by generating intermediate reasoning steps at inference time. Yet the scaling behavior of generalization with CoT depth remains poorly understood. To address this question, we study a theoretically solvable model of CoT for in-context weight prediction in linear regression, where test-time reasoning is represented as an iterative refinement of the weight-parameter estimate. Using tools from random matrix theory under high-dimensional asymptotics, we derive an exact formula for the generalization error as a function of reasoning depth, pretraining data amount, and context length. Our analysis reveals a sharp phase transition separating exponential and polynomial improvement, saturation, and overthinking, and characterizes how the optimal reasoning depth scales. We further show that deeper reasoning is most effective with sufficiently rich pretraining and in-context information, whereas limited pretraining or context makes longer reasoning prone to error amplification or saturation. We also validate these predictions through experiments on fully learned linear attention and softmax attention models. Our results provide a unified theoretical account of how test-time CoT depth affects generalization.

stat.ML · cs.LG

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.36657

PDE-Based Bounds on Optimal Exponents in Active Simple Hypothesis Testing

Sushant Vijayan, Himadri Mandal

原文摘要

We present general upper and lower bounds on the optimal error exponent for the Active Simple Hypothesis Testing (ASHT) problem. ASHT has been extensively studied across diverse fields including Information Theory, Bandits, and Operations Research, a precise characterization of this optimal exponent has remained elusive. This work combines a recent Partial Differential Equation (PDE) characterization of the optimal exponent by Vijayan (2025) with the comparison principle of viscosity solutions of Hamilton-Jacobi PDEs. This leads to bounds that are parametrized by convex functions, sets and lower Hamiltonian relaxations, a flexibility that generalizes many known results in the literature.

cs.IT · cs.GT · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.36581

Wasserstein approximation of measures via orthogonal frames: statistical and computational complexities

Mateo Díaz, Nicolás García Trillos, Daniel López-Castaño, Congwei Yang

原文摘要

Dimension-reduction methods such as PCA identify a subspace capturing most of the variation in the data, but not a distinguished basis within it. Selecting a basis in which the samples are sparsely represented is a recurring task in unsupervised learning, addressed by methods in factor analysis, dictionary learning, and subspace clustering. We pose this task as Wasserstein approximation of the data distribution by measures supported on the axes of an orthogonal frame, which, in turn, reduces to a nonsmooth optimization problem over the orthogonal group $\mathrm{O}(d)$. We show that, under mild assumptions, both empirical risk minimizers and a locally initialized stochastic gradient method recover the population-optimal frame at the near-parametric rate $\widetilde{O}_d(n^{-1/2})$, where $n$ is the sample size. The main difficulty is that, although the population objective is smooth, the empirical objective is not-this mismatch precludes standard covering arguments. We overcome this issue by replacing Lipschitz continuity of the empirical gradient with a coarsely Lipschitz bound, a tool that may be of independent interest. Numerical experiments support our theoretical findings.

math.ST · math.OC · stat.ML

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2609.30078

Nuclear Norm-Regularized Bayesian Matrix Completion

Calvin Tolbert

原文摘要

Nuclear-norm-regularized least squares is a standard approach to matrix completion, but it yields only a point estimate. Its Bayesian counterpart, a prior combining the nuclear norm with a Frobenius-norm term, gives a strongly log-concave though nonsmooth posterior when the noise precision is known. In practice the precision is unknown, and placing a truncated Jeffreys prior on it makes the joint posterior neither log-concave nor smooth. To our knowledge, we give the first sampler for this model with an explicit non-asymptotic guarantee: its output is within a prescribed total-variation or Wasserstein distance of the posterior on the matrix after a number of steps polynomial in the matrix dimensions and the reciprocal of the target accuracy. The sampler never targets a continuous distribution that is not strongly log-concave. It discretizes the precision onto a grid, estimates its posterior by thermodynamic integration along the tilted conditional posteriors of the matrix, and bounds the error this propagates to the posterior on the matrix. The approach applies whenever non-log-concavity is confined to a bounded scalar hyperparameter and the conditional distributions are strongly log-concave with smooth-plus-Lipschitz potentials. Our result establishes feasibility; the polynomial complexity is not intended as a practical algorithm at current problem scales.

stat.ML · cs.LG

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.29515

BRIDGE: An Acceptance Gate to Block False Improvements in Model Updates, with a Retrospective Clinical Evaluation

Dwi Sunaryono

原文摘要

Models are updated repeatedly, and an update that looks better on validation data but not on new data is a false improvement that can misguide clinical decisions. The naive rule accepts every positive validation gain and is optimistic when the same data choose and judge the update. BRIDGE is a model-agnostic acceptance gate that decides each update from predictions and the available labels, with fixed settings. Each fold of the data judges the update chosen on the other folds (cross-fitting) to reduce selection bias; acceptance requires the gain's lower bootstrap bound to exceed a margin. The four settings are (A) 11 new datasets, (B) synthetic tasks, (C) 12 retrospective clinical tasks, and (D) 39 supporting datasets. The false-improvement rate falls from 19.1% (naive) to 1.1% (BRIDGE) in (A), 20.7% to 1.7% (B), 20.0% to 0% (C), and 12.5% to 0.5% (D); every 95% confidence interval of the reduction over datasets or tasks excludes zero (not over the clinical sources). An equal-size random draw from the naive acceptances contains more false improvements in (A)-(E) (post hoc, p<0.001). On the OpenML collection (E) of 14 new datasets, the false-improvement rate falls from 25.6% to 1.0%. BRIDGE removes 97% to 100% of the false improvements that the naive rule accepts, and its mean gain per deployed update is 1.8 to 3.1 times the naive rule's. The 95% upper bound on the false-improvement rate is below 5.5%: formal in (B) for independent tasks (3.56%), and conditional on the real data tested (0.33% to 5.40%).

cs.LG · stat.ML

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2602.01825

Learning Sequential Decisions from Multiple Sources via Group-Robust Markov Decision Processes

Mingyuan Xu, Zongqi Xia, Tianxi Cai, Doudou Zhou, Nian Si

原文摘要

Learning a common policy from multiple source environments requires accounting for cross-source heterogeneity, and the offline setting introduces an additional challenge of limited data coverage. We formulate this problem as a distributionally robust Markov decision process under a shared linear MDP representation with source-specific transition and reward components. The uncertainty set is constructed through feature-wise mixtures of these components, yielding a $d$-rectangular structure that captures cross-source heterogeneity and admits a robust Bellman recursion. Building on this formulation, we develop Group-Robust Pessimistic Value Iteration (GR-PEVI), an offline policy-learning algorithm that combines feature-wise worst-case aggregation with a data-dependent pessimism penalty. Under a robust partial coverage condition, we establish finite-sample suboptimality guarantees for GR-PEVI and extend the analysis to clustered sources, characterizing the trade-off between the statistical gain from pooling similar sources and the approximation error induced by within-cluster heterogeneity. Simulation studies demonstrate the effectiveness of GR-PEVI, with empirical behavior consistent with the theoretical analysis. We apply GR-PEVI to a multi-source electronic health record study of multiple sclerosis treatment decisions to illustrate its use in a clinical setting.

stat.ME · cs.LG · math.OC · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.36502

Algorithmics for Graphical Separation Criteria

Moisés Chavira-Flores, Sebastian Weichwald, Leonard Henckel

原文摘要

Statistical graphical models are representations of the dependences between the components of a random vector. They encode these dependences via graphical separation criteria. We consider the algorithmic problem of checking separation statements for the various graph classes and separation criteria that have been developed by the community. We establish that all criteria we study can be checked by modular variations of reachability. For all separation criteria but $σ$-separation, this yields a linear-time algorithm. This is effectively the optimal attainable time since loading the graph itself is linear-time in the number of edges in the graph. Using the CIfly framework for deploying modular variations of reachability, we also provide R and Python code implementing our algorithms. We evaluate empirical runtime and scaling behavior in a simulation study.

stat.ML · cs.LG

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.36488

Second-order Sinkhorn Geometry and $\sqrt{n}$-Inference

Tristan Luca Saidi, Florian Gunsilius, Gonzalo Mena

原文摘要

The Sinkhorn divergence, a debiased form of entropic optimal transport, has been widely used in various scientific disciplines due to its computational and statistical tractability. Unlike the Wasserstein distance, however, the Sinkhorn divergence is not a metric and it does not naturally admit a formal Riemannian structure. These properties are central to many applications of optimal transport methods that utilize interpolation, barycentric averaging, parallel transport or other geometric operations. Recent work addresses these shortcomings by constructing a formal Riemannian tangent space and a metric tensor on the space of probability measures that quadratically approximates the Sinkhorn divergence. In this work, we extend this framework with two major threads of contributions. For a suitable class of finite-smoothness cost functions, we prove Hadamard differentiability of the Sinkhorn metric tensor and we derive the Levi-Civita covariant derivative in this geometry; we then use the covariant derivative to obtain the geodesic and parallel transport equations, each of which amount to an ODE on a fixed Reproducing Kernel Hilbert Space (RKHS) with smooth coefficients. Our second contribution is to linearize the solutions to the geodesic and parallel transport equations using standard tools from Banach space ODE theory. We show that under standard regularity conditions these linearizations imply $\sqrt{n}$-limiting Gaussian processes centered at population values for the plugin estimators of the exponential map, the logarithmic map, parallel transport and the induced Sinkhorn distance. Moreover, we show that the nonparametric bootstrap is consistent for all objects mentioned. To the best of our knowledge, these are the first $\sqrt{n}$--limit theorems and bootstrap consistency results for canonical geometric operations in a transport-based geometry on the space of probability measures.

stat.ML · cs.LG · math.ST

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arXiv ↗PDF ↗