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In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…

Computation · Statistics 2025-04-14 Subhayan De , Reza Farzad , Patrick T. Brewick , Erik A. Johnson , Steven F. Wojtkiewicz

A fundamental question in the theory of reinforcement learning is: suppose the optimal $Q$-function lies in the linear span of a given $d$ dimensional feature mapping, is sample-efficient reinforcement learning (RL) possible? The recent and…

Machine Learning · Computer Science 2021-10-22 Yuanhao Wang , Ruosong Wang , Sham M. Kakade

We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…

Methodology · Statistics 2014-02-05 Adel Javanmard , Andrea Montanari

Linear models with a growing number of parameters have been widely used in modern statistics. One important problem about this kind of model is the variable selection issue. Bayesian approaches, which provide a stochastic search of…

Statistics Theory · Mathematics 2012-02-03 Zuofeng Shang , Murray K. Clayton

Embedding-based representations in Euclidean space $\mathbb{R}^d$ are a cornerstone of modern machine learning, where a major goal is to use the \emph{smallest dimension} that faithfully captures data relations. In this work, we prove sharp…

Data Structures and Algorithms · Computer Science 2026-05-06 Dionysis Arvanitakis , Vaggos Chatziafratis , Yiyuan Luo

In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…

Computation · Statistics 2022-06-08 Max Ehre , Rafael Flock , Martin Fußeder , Iason Papaioannou , Daniel Straub

We study generalized Bayesian inference under misspecification, i.e. when the model is 'wrong but useful'. Generalized Bayes equips the likelihood with a learning rate $\eta$. We show that for generalized linear models (GLMs),…

Statistics Theory · Mathematics 2021-06-01 Rianne de Heide , Alisa Kirichenko , Nishant Mehta , Peter Grünwald

Standard evaluations of Bayesian deep learning methods assume that metric estimates are reliable, but we show this assumption fails under data scarcity. Method rankings are not only unreliable at small $n$, but also dataset-dependent in…

Machine Learning · Computer Science 2026-04-28 Qishi Zhan , Minxuan Hu , Guansu Wang , Jiaxin Liu , Liang He

We empirically show that Bayesian inference can be inconsistent under misspecification in simple linear regression problems, both in a model averaging/selection and in a Bayesian ridge regression setting. We use the standard linear model,…

Statistics Theory · Mathematics 2018-10-30 Peter Grünwald , Thijs van Ommen

In-context learning (ICL) has emerged as a particularly remarkable characteristic of Large Language Models (LLM): given a pretrained LLM and an observed dataset, LLMs can make predictions for new data points from the same distribution…

Machine Learning · Statistics 2024-06-04 Fabian Falck , Ziyu Wang , Chris Holmes

In-context learning (ICL) has transformed the use of large language models (LLMs) for NLP tasks, enabling few-shot learning by conditioning on labeled examples without finetuning. Despite its effectiveness, ICL is prone to errors,…

Computation and Language · Computer Science 2025-03-21 Mario Sanz-Guerrero , Katharina von der Wense

High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods…

Statistics Theory · Mathematics 2018-08-21 Chao Gao , Aad W. van der Vaart , Harrison H. Zhou

This paper develops a finite-sample statistical theory for in-context learning (ICL), analyzed within a meta-learning framework that accommodates mixtures of diverse task types. We introduce a principled risk decomposition that separates…

Machine Learning · Statistics 2025-12-09 Tomoya Wakayama , Taiji Suzuki

Model selection and order selection problems frequently arise in statistical practice. A popular approach to addressing these problems in the frequentist setting involves information criteria based on penalised maxima of log-likelihoods for…

Statistics Theory · Mathematics 2025-10-29 Hien Duy Nguyen , Mayetri Gupta , Jacob Westerhout , TrungTin Nguyen

Large language models often produce confident but incorrect outputs, creating a critical need for reliable uncertainty quantification with formal abstention guarantees. We introduce information-lift certificates that compare model…

Machine Learning · Computer Science 2025-11-20 Sanjeda Akter , Ibne Farabi Shihab , Anuj Sharma

In this paper we analyze a budgeted learning setting, in which the learner can only choose and observe a small subset of the attributes of each training example. We develop efficient algorithms for ridge and lasso linear regression, which…

Machine Learning · Computer Science 2014-10-24 Doron Kukliansky , Ohad Shamir

We consider Bayesian multiple statistical classification problem in the case where the unknown source distributions are estimated from the labeled training sequences, then the estimates are used as nominal distributions in a robust…

Information Theory · Computer Science 2021-10-11 Hüseyin Afşer

Reinforcement Learning (RL) enhances LLM reasoning, yet a paradox emerges as models scale: strong base models saturate standard benchmarks (e.g., MATH), yielding correct but homogeneous solutions. In such environments, the lack of failure…

Machine Learning · Computer Science 2026-04-21 Zhenwen Liang , Yujun Zhou , Sidi Lu , Xiangliang Zhang , Haitao Mi , Dong Yu

Bayesian neural networks often approximate the weight-posterior with a Gaussian distribution. However, practical posteriors are often, even locally, highly non-Gaussian, and empirical performance deteriorates. We propose a simple parametric…

Machine Learning · Statistics 2023-06-13 Federico Bergamin , Pablo Moreno-Muñoz , Søren Hauberg , Georgios Arvanitidis

Data duplication during pretraining can degrade generalization and lead to memorization, motivating aggressive deduplication pipelines. However, at web scale, it is unclear what constitutes a ``duplicate'': beyond surface-form matches,…

Machine Learning · Computer Science 2026-03-10 Joshua Kazdan , Noam Levi , Rylan Schaeffer , Jessica Chudnovsky , Abhay Puri , Bo He , Mehmet Donmez , Sanmi Koyejo , David Donoho