Publication record · 18.cifr/2003.andrieu.mcmc-ml

An Introduction to MCMC for Machine Learning

v1.0.0

Christophe Andrieu (University of Cambridge), Nando de Freitas (University of British Columbia), Arnaud Doucet (University of Cambridge), Michael I. Jordan (UC Berkeley)

RAI18.cifr/2003.andrieu.mcmc-ml

Machine Learning· 2003· doi:10.1023/A:1020281327116

This purpose of this introductory paper is threefold. First, it introduces the Monte Carlo method with emphasis on probabilistic machine learning. Second, it reviews the most common MCMC methods: the Metropolis-Hastings algorithm, Gibbs sampling and the Hybrid Monte Carlo algorithm. Third, it presents the fundamentals of particle filters. Throughout, the methodology is illustrated with relevant machine learning examples.

MCMCBayesian inferenceMetropolis-HastingsGibbs samplingHybrid Monte Carlomachine learning

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Bayesian inference over high-dimensional posteriors is analytically intractable for most realistic ML models. ML researchers lacked a unified reference connecting MCMC theory to concrete tasks like mixture models and neural networks. This paper provides accessible entry point with worked examples.

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This tutorial paper provides a unified, accessible treatment of MCMC methods specifically oriented toward ML applications, connecting Metropolis-Hastings, Gibbs sampling, and Hybrid Monte Carlo to concrete ML inference problems. It bridges statistical physics origins with probabilistic ML and introduces particle filtering in the same framework.

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