Random Coordinate Underdamped Langevin Monte Carlo

The Underdamped Langevin Monte Carlo (ULMC) is a popular Markov chain Monte Carlo sampling method. It requires the computation of the full gradient of the log-density at each iteration, an expensive operation if the dimension of the problem is high. We propose a sampling method called Random Coordin...

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Bibliographic Details
Main Authors Ding, Zhiyan, Li, Qin, Lu, Jianfeng, Wright, Stephen J
Format Journal Article
LanguageEnglish
Published 21.10.2020
Subjects
Computer Science - Learning
Statistics - Machine Learning
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Summary:The Underdamped Langevin Monte Carlo (ULMC) is a popular Markov chain Monte Carlo sampling method. It requires the computation of the full gradient of the log-density at each iteration, an expensive operation if the dimension of the problem is high. We propose a sampling method called Random Coordinate ULMC (RC-ULMC), which selects a single coordinate at each iteration to be updated and leaves the other coordinates untouched. We investigate the computational complexity of RC-ULMC and compare it with the classical ULMC for strongly log-concave probability distributions. We show that RC-ULMC is always cheaper than the classical ULMC, with a significant cost reduction when the problem is highly skewed and high dimensional. Our complexity bound for RC-ULMC is also tight in terms of dimension dependence.
DOI:10.48550/arxiv.2010.11366