Optimal friction matrix for underdamped Langevin sampling

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2023-10-18 DOI:10.1051/m2an/2023083

Martin Chak, Nikolas Kantas, Tony Lelièvre, Grigorios Pavliotis

引用次数: 5

Abstract

We propose a procedure for optimising the friction matrix of underdamped Langevin dynamics when used for continuous time Markov Chain Monte Carlo. Starting from a central limit theorem for the ergodic average, we present a new expression of the gradient of the asymptotic variance with respect to friction matrix. In addition, we present an approximation method that uses simulations of the associated first variation/tangent process. Our algorithm is applied to a variety of numerical examples such as toy problems with tractable asymptotic variance, diffusion bridge sampling and Bayesian inference problem for high dimensional logistic regression.

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欠阻尼朗格万采样的最优摩擦矩阵

提出了一种用于连续时间马尔可夫链蒙特卡罗的欠阻尼朗格万动力学摩擦矩阵的优化方法。从遍历平均的中心极限定理出发，给出了关于摩擦矩阵的渐近方差梯度的新表达式。此外，我们提出了一种近似方法，该方法使用了相关的第一次变化/切线过程的模拟。该算法应用于具有可处理渐近方差的玩具问题、扩散桥抽样和高维逻辑回归的贝叶斯推理问题等多种数值实例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Esaim-Probability and Statistics STATISTICS & PROBABILITY-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.