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Category: stat.ML

  • Learning by Compression: Risk Estimates Attain the Law-of-Large-Numbers Rate

    Learning by Compression: Risk Estimates Attain the Law-of-Large-Numbers Rate

    [Submitted on 9 Oct 2026]

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    Abstract:Compression schemes provide a general framework for deriving data-dependent risk bounds for learning algorithms. For learning rules based on preferent compression, existing results upper-bound the risk in terms of a sample-dependent complexity $boldsymbol{k}$, defined as the cardinality of the compression augmented by the training examples on which the reconstructed hypothesis is inappropriate. These results, however, yield a margin of order $O(sqrt{ln N/N})$ above $boldsymbol{k}/N$. In this paper, we establish that the logarithmic factor is not intrinsic. We prove that, for every fixed confidence level $1-delta$, the risk is bounded with probability at least $1-delta$ by $$ frac{boldsymbol{k}}{N} + Oleft(frac{1}{sqrt{N}}right), $$ uniformly over all possible values of $boldsymbol{k}$. Thus, risk estimates for learning algorithms based on preferent compression attain the same law-of-large-numbers rate as the empirical estimate of the probability of a fixed event. We also show that the leading term $boldsymbol{k}/N$ is necessary and investigate its relation to the empirical risk. In particular, we identify regimes in which the empirical risk retains the $O(1/sqrt{N})$ convergence rate, as well as regimes in which it converges more slowly or ceases to be consistent, while the complexity-based estimator preserves the $O(1/sqrt{N})$ rate.

    Submission history

    From: Simone Garatti [view email]
    [v1] Fri, 9 Oct 2026 11:44:43 UTC (24 KB)

  • A Critical Look at Power Sampling when Test Time Sharpening LLMs

    A Critical Look at Power Sampling when Test Time Sharpening LLMs

    [Submitted on 9 Oct 2026]

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    Abstract:Reinforcement learning with verifiable rewards (RLVR) has substantially improved LLM reasoning, yet growing evidence suggests it mainly performs distribution sharpening: concentrating probability mass on reasoning paths the base model already produces. Recent work therefore seeks RLVR’s gains without needing reward signals, by sampling from the power distribution $pi_alpha propto pi_{text{base}}^alpha$ via Markov chain Monte Carlo or sequential Monte Carlo. We show that these samplers fail to converge to $pi_alpha$ under realistic compute budgets, and that their gains are largely recreated via simple Best-of-$N$ with appropriate grading . This suggests they succeed by selecting high-probability sequences, not by approximating $pi_alpha$, raising a natural question: is the power distribution itself a worthwhile target? We test this hypothesis directly by fine-tuning the base model to match $pi_alpha$, sidestepping sampler convergence issues entirely. Despite approximating the target far more faithfully than existing samplers, this strategy yields gains that are noisy and specific to certain models and sampling tasks. Together, our results suggest that the value of power sampling lies not in faithfully targeting $pi_alpha$, but in the simpler goal of extracting sequences the base model already deems likely.

    Submission history

    From: Abiel Malkani Talwar [view email]
    [v1] Fri, 9 Oct 2026 14:29:28 UTC (235 KB)

  • Equality, Equity, and Causality in Fairness Research: A Commentary on Cheng (2026)

    Equality, Equity, and Causality in Fairness Research: A Commentary on Cheng (2026)

    [Submitted on 20 Jul 2026 (v1), last revised 9 Oct 2026 (this version, v2)]

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    Abstract:This is an invited commentary on the Psychometrika focus article “Fairness Issues and Evaluation in Psychometrics and AI/ML: What Can We Learn from Each Field?” by Ying Cheng (2026, doi:https://doi.org/10.1017/psy.2026.10110). Cheng offers a systematic comparison between long-standing test fairness and modern algorithmic fairness. Her mapping of the entire testing workflow onto the AI/ML fairness paradigm, rather than only the final selection stage, is a crucial contribution to interdisciplinary fairness research. This commentary extends her discussion by examining two conceptual issues: the distinction between equality and equity, and the role of causality in fairness research. The focus article and this commentary point to directions for future fairness research across the psychometrics and AI/ML communities.

    Submission history

    From: Youmi Suk [view email]
    [v1] Mon, 20 Jul 2026 08:30:06 UTC (14 KB)
    [v2] Fri, 9 Oct 2026 12:26:26 UTC (14 KB)

  • Infinitesimal Operator World Models: Finite-Sample Guarantees for Offline Reinforcement Learning

    Infinitesimal Operator World Models: Finite-Sample Guarantees for Offline Reinforcement Learning

    [Submitted on 13 Nov 2025 (v1), last revised 9 Oct 2026 (this version, v2)]

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    Abstract:Continuous-time stochastic processes underlie many natural and engineered systems. In healthcare, autonomous driving, and industrial control, direct interaction with the environment is often unsafe or impractical, motivating offline reinforcement learning from historical data. However, there is limited statistical understanding of the approximation errors inherent in learning policies from offline datasets. We address this by linking reinforcement learning to the Hamilton-Jacobi-Bellman equation and proposing an operator-theoretic algorithm based on a simple dynamic programming recursion. Specifically, we represent our world model in terms of the infinitesimal generator of controlled diffusion processes learned in a reproducing kernel Hilbert space. By integrating statistical learning methods and operator theory, we establish global convergence of the value function under sufficiently small generator-approximation error and derive explicit finite-sample guarantees with bounds tied directly to system properties such as smoothness and stability. Our theoretical and proof-of-concept results indicate that operator-based approaches may hold promise for solving offline reinforcement learning using continuous-time optimal control.

    Submission history

    From: Nicolas Hoischen [view email]
    [v1] Thu, 13 Nov 2025 14:58:30 UTC (1,427 KB)
    [v2] Fri, 9 Oct 2026 13:08:08 UTC (2,717 KB)

  • Transformer-Based Masked Diffusion Models Provably Learn Distributions with Latent Structure

    Transformer-Based Masked Diffusion Models Provably Learn Distributions with Latent Structure

    [Submitted on 8 Oct 2026]

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    Abstract:Masked diffusion models (MDMs) generate discrete data by iteratively unmasking multiple tokens in parallel using a learned mask predictor. Their output carries two errors: parallelization error due to parallel sampling, and estimation error from the mask predictor learned with finite samples. Existing theory treats these errors separately, and the available statistical bounds typically scale with the number $V^L$ of length-$L$ sequences over a vocabulary of size $V$, suffering from the curse of dimensionality. In this work, we establish end-to-end statistical guarantees showing that transformer-based MDMs learn structured distributions with a sample complexity governed by their latent structure. Specifically, we model this structure through mixtures of hidden Markov trees, which capture latent dependencies within components and heterogeneity across components. When the data distribution is well approximated by such a mixture, a transformer-based MDM with parallel unmasking schedules achieves $varepsilon$-accurate sampling in KL divergence with $widetilde{O}(LK_{mathrm{par}}/varepsilon)$ training samples, where $K_{mathrm{par}}$ is polynomial in $L$, $V$, the number of hidden states, and the number of mixture components. The transformer network and sampling procedure require no knowledge of the tree topologies or component parameters, thereby adapting to the unknown latent structure automatically. Overall, our results provide theoretical justification for the empirical effectiveness of MDMs on real-world data.

    Submission history

    From: Jingda Wu [view email]
    [v1] Thu, 8 Oct 2026 17:54:49 UTC (90 KB)

  • Near-Minimax-Optimal Rates for Asynchronous TD Learning with Markovian Data

    Near-Minimax-Optimal Rates for Asynchronous TD Learning with Markovian Data

    [Submitted on 30 Sep 2026 (v1), last revised 9 Oct 2026 (this version, v2)]

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    Abstract:We study the last iterate of standard importance-weighted temporal-difference (TD) learning from a single trajectory of a finite Markov decision process. The trajectory follows a behavior policy $b$ with an irreducible, possibly periodic state chain; a target policy $pi$ covered by $b$ is evaluated with action importance ratios bounded by $varrho$. Write $H=(1-gamma)^{-1}$, with $mu_{min}$ the minimum stationary probability and $mathfrak h_star$ the largest expected hitting time of the reverse behavior state chain. We prove that the last iterate achieves sup-norm error at most $varepsilon$ with high probability after $widetilde O(varrho H^3/(mu_{min}varepsilon^2)+mathfrak h_star)$ transitions for $0

    Submission history

    From: Yang Peng [view email]
    [v1] Wed, 30 Sep 2026 03:31:05 UTC (44 KB)
    [v2] Fri, 9 Oct 2026 17:16:04 UTC (61 KB)

  • Probabilistic Forecasting of Electric Vehicle Charging in a Time-varying Hierarchical Infrastructure

    Probabilistic Forecasting of Electric Vehicle Charging in a Time-varying Hierarchical Infrastructure

    [Submitted on 9 Oct 2026]

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    Abstract:Uncertainty quantification for electric vehicle (EV) charging demand is essential to turn the increasing pressure of EV adoption on power systems into a source of flexibility. We study a large-scale dataset of public charging stations in Scotland, where demand exhibits a hierarchical structure, organized across multiple aggregation levels, from individual charging points to regional and national scales. The charging infrastructure is continuously evolving, with new stations deployed and existing ones occasionally removed, which calls for forecasting and uncertainty quantification methods tailored to this evolving structure. To address these challenges, we combine hierarchical forecasting with recent advances in conformal prediction with missing data. The conformal procedures considered produce valid prediction intervals at every node of the hierarchy and the algorithm CP-MNR-Nested successfully accounts for the time-varying hierarchical structure of the data.

    Submission history

    From: Guillaume Principato [view email]
    [v1] Fri, 9 Oct 2026 13:39:08 UTC (3,852 KB)

  • How Well Do Prior-Data Fitted Networks Amortize Bayesian Inference?

    How Well Do Prior-Data Fitted Networks Amortize Bayesian Inference?

    [Submitted on 9 Oct 2026]

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    Abstract:Prior-data fitted networks (PFNs) are trained to approximate the Bayesian posterior predictive distribution (PPD) of a synthetic prior, yet results about the approximation quality are surprisingly thin. Taking an empirical risk minimization perspective, we decompose the deployment error of PFNs into prior, context, and amortization error, and measure the latter against a reference PPD under a realistic prior. Results show that PFNs generally recover the targeted PPD very well. Nevertheless, we find that parts of the residual amortization error persist, especially in textit{rare} settings under the prior pretraining distribution, even when scaling the model size, which manifests in disagreement between independently pretrained PFNs and leaves uncertainty about the predictor at inference time. As a remedy, we study multiple types of Bayesian model averages and find that these can consistently reduce this uncertainty and improve predictions up to full-size TabICLv2 models.

    Submission history

    From: Manuel Hülskamp [view email]
    [v1] Fri, 9 Oct 2026 15:49:24 UTC (237 KB)

  • Bayesian dynamic scheduling of multipurpose batch processes under incomplete look-ahead information

    Bayesian dynamic scheduling of multipurpose batch processes under incomplete look-ahead information

    [Submitted on 30 Nov 2025 (v1), last revised 9 Oct 2026 (this version, v2)]

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    Abstract:Multipurpose batch processes become increasingly popular in manufacturing industries since they adapt to low-volume, high-value products and shifting demands. These processes often operate in a dynamic environment, which faces disturbances such as processing delays and demand changes. To minimise long-term cost and system nervousness (i.e., disruptive changes to schedules), schedulers must design rescheduling strategies to address such disturbances effectively. Existing methods often assume complete look-ahead information over the scheduling horizon. This assumption contrasts with realistic situations where schedulers can only access incomplete look-ahead information. Sticking with existing methods may lead to suboptimal long-term costs and high-level system nervousness. In this work we propose a Bayesian dynamic scheduling method. Our method relies on learning a Bayesian Network from the probability distribution of disturbances. Specifically, the Bayesian Network represents how likely each operation will be impacted by disturbances. During the online execution, when new disturbances become observed, this method updates the posterior distribution and therefore guides the rescheduling strategy. We compare our method with the existing periodic rescheduling strategy (which generates new schedules from scratch at fixed intervals) on four benchmark problems. Computational results show that our method achieves statistically better long-term costs and system nervousness. In the theoretical aspect, we prove that if disturbances are mutually independent, the impact-quantifying variables inherently satisfy the independence assumptions required by Bayesian Networks. As an implication, practitioners can extend the method to other scheduling problems (such as job shop scheduling and continuous processes), given that they define the problem-specific dependencies between operations.

    Submission history

    From: Taicheng Zheng [view email]
    [v1] Sun, 30 Nov 2025 21:27:52 UTC (1,350 KB)
    [v2] Fri, 9 Oct 2026 09:42:06 UTC (2,695 KB)