Functional inequalities for perturbed measures with applications to log-concave measures and to some Bayesian problems

2021/01/27 by Patrick Cattiaux, Arnaud Guillin, Cattiaux, Patrick +1 · 1 voice · 3 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Methods and Inference #Statistics Theory (math.ST) #math.PR #math.ST

paper · pdf · doi:10.48550/arxiv.2101.11257

openalex publication_date 2021/01/27 · arxiv published 2021/01/27 · arxiv updated 2021/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study functional inequalities (Poincaré, Cheeger, log-Sobolev) for probability measures obtained as perturbations. Several explicit results for general measures as well as log-concave distributions are given.The initial goal of this work was to obtain explicit bounds on the constants in view of statistical applications for instance. These results are then applied to the Langevin Monte-Carlo method used in statistics in order to compute Bayesian estimators.

Cited by

• Continuous Semi-Implicit Models
• Improved generalization bounds for binary linear classification via isoperimetry
• Entropic continuity bounds for conditional covariances with applications to Schr" odinger and Sinkhorn bridges

Discussions

• This work - arxiv.org/abs/2101.11257 - is rather theoretical and technical, but does hit on some of the directions which I'd like to see developed further, i.e. establishing that the posterior is "coa [bsky, 2 points, 1 comments]

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