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Markov Chain Importance Sampling – a highly efficient estimator for MCMC
Journal of Computational and Graphical Statistics ( IF 2.4 ) Pub Date : 2021-01-01 , DOI: 10.1080/10618600.2020.1826953
Ingmar Schuster 1 , Ilja Klebanov 2
Affiliation  

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.

中文翻译:

马尔可夫链重要性采样——一个高效的 MCMC 估计器

马尔可夫链 (MC) 算法在机器学习和统计学以及许多其他学科中无处不在。通常,这些算法可以表述为接受拒绝方法。在这项工作中,我们提出了一种适用于这些方法的新颖估计器,称为马尔可夫链重要性采样(MCIS),它有效地利用了被拒绝的提议。对于未经调整的朗之万算法,它提供了一种修正离散化误差的新方法。我们的估计器满足中心极限定理,并且通常在很大程度上改进了每个 CPU 周期的错误。作为副产品,它可以估计归一化常数,这是贝叶斯机器学习和统计中的一个重要数量。
更新日期:2021-01-01
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