Markov Chain Importance Sampling -- a highly efficient estimator for MCMC

2018/05/18 by Ingmar Schuster, Schuster, Ingmar, Ilja Klebanov +1
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Markov Chains and Monte Carlo Methods #Statistical Methods and Bayesian Inference

paper · pdf · doi:10.48550/arxiv.1805.07179

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.

Related

• Importance is Important: Generalized Markov Chain Importance Sampling Methods
• Markov Interacting Importance Samplers
• Estimating standard errors for importance sampling estimators with multiple Markov chains
• MCMC Importance Sampling via Moreau-Yosida Envelopes
• Markov chain Monte Carlo importance samplers for Bayesian models with intractable likelihoods