Convergence of Statistical Estimators via Mutual Information Bounds

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Dades bibliogràfiques
Publicat a:	arXiv.org (Dec 24, 2024), p. n/a
Autor principal:	El Mahdi Khribch
Altres autors:	Alquier, Pierre
Publicat:	Cornell University Library, arXiv.org
Matèries:	Statistical methods Learning theory Maximum likelihood estimation Estimators Bayesian analysis Information theory Statistical models Statistical inference
Accés en línia:	Citation/Abstract Full text outside of ProQuest
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Descripció
Resum:	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.
ISSN:	2331-8422
Font:	Engineering Database