Work

Convergence in total variation for the kinetic Langevin algorithm

Year: 2025

Type: article

Abstract: We prove non-asymptotic total variation estimates for the kinetic Langevin algorithm in high dimension when the target measure satisfies a Poincaré inequality and has gradient Lipschitz potential. The main point is that the estimate improves significantly upon the corresponding bound for the non-kinetic version of the algorithm, due to Dalalyan. In particular, the dimension dependence drops from O(n) to O(\sqrt{n}) .

Source: Mathematical Statistics and Learning

DOI: 10.4171/msl/49

Author: Joseph Lehec

Institutions: Centre National de la Recherche Scientifique, Université de Poitiers, Laboratoire de Mathématiques et Applications

Language: English

Topic: Markov Chains and Monte Carlo Methods

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Agence Nationale de la Recherche

Award: Convergence and Interactions via Analysis and Probability