Markov Chain Importance Sampling - a highly efficient estimator for MCMC
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- 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.
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| Author: | Ilja Klebanov, Ingmar Schuster |
|---|---|
| Document Type: | Article |
| Parent Title (English): | Journal of Computational and Graphical Statistics |
| Year of first publication: | 2020 |
| DOI: | https://doi.org/10.1080/10618600.2020.1826953 |
