2024/12/24 by El Mahdi Khribch, Pierre Alquier, Khribch, El Mahdi +1 · 2 voices · 2 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #Statistical Methods and Inference #cs.LG #math.ST #stat.ML
paper · pdf · doi:10.48550/arxiv.2412.18539
openalex publication_date 2024/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recent advances in statistical learning theory have revealed profound connections between mutual information (MI) bounds, PAC-Bayesian theory, and Bayesian nonparametrics. This work introduces a novel mutual information bound for statistical models. The derived bound has wide-ranging applications in statistical inference. It yields improved contraction rates for fractional posteriors in Bayesian nonparametrics. It can also be used to study a wide range of estimation methods, such as variational inference or Maximum Likelihood Estimation (MLE). By bridging these diverse areas, this work advances our understanding of the fundamental limits of statistical inference and the role of information in learning from data. We hope that these results will not only clarify connections between statistical inference and information theory but also help to develop a new toolbox to study a wide range of estimators.