Random Coordinate Underdamped Langevin Monte Carlo
Abstract
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.
Cite
@article{arxiv.2010.11366,
title = {Random Coordinate Underdamped Langevin Monte Carlo},
author = {Zhiyan Ding and Qin Li and Jianfeng Lu and Stephen J. Wright},
journal= {arXiv preprint arXiv:2010.11366},
year = {2020}
}