Importance is Important: Generalized Markov Chain Importance Sampling Methods
Computation
2024-10-03 v2 Methodology
Machine Learning
Abstract
We show that for any multiple-try Metropolis algorithm, one can always accept the proposal and evaluate the importance weight that is needed to correct for the bias without extra computational cost. This results in a general, convenient, and rejection-free Markov chain Monte Carlo (MCMC) sampling scheme. By further leveraging the importance sampling perspective on Metropolis--Hastings algorithms, we propose an alternative MCMC sampler on discrete spaces that is also outside the Metropolis--Hastings framework, along with a general theory on its complexity. Numerical examples suggest that the proposed algorithms are consistently more efficient than the original Metropolis--Hastings versions.
Cite
@article{arxiv.2304.06251,
title = {Importance is Important: Generalized Markov Chain Importance Sampling Methods},
author = {Guanxun Li and Aaron Smith and Quan Zhou},
journal= {arXiv preprint arXiv:2304.06251},
year = {2024}
}