Markov Chain Importance Sampling -- a highly efficient estimator for MCMC
Machine Learning
2020-08-07 v4 Machine Learning
Abstract
Markov chain (MC) algorithms are ubiquitous in machine learning and statistics and many other disciplines. Typically, these algorithms can be formulated as acceptance rejection methods. In this work we present a novel estimator applicable to these methods, dubbed Markov chain importance sampling (MCIS), which efficiently makes use of rejected proposals. For the unadjusted Langevin algorithm, it provides a novel way of correcting the discretization error. Our estimator satisfies a central limit theorem and improves on error per CPU cycle, often to a large extent. As a by-product it enables estimating the normalizing constant, an important quantity in Bayesian machine learning and statistics.
Cite
@article{arxiv.1805.07179,
title = {Markov Chain Importance Sampling -- a highly efficient estimator for MCMC},
author = {Ingmar Schuster and Ilja Klebanov},
journal= {arXiv preprint arXiv:1805.07179},
year = {2020}
}