[综述] Probabilistic Inference Using Markov Chain Monte Carlo Methods Inference, Monte, Chain, Using, Carlo

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Probabilistic inference is an attractive approach to uncertain reasoning and empirical learning in articial intelligence. Computational diculties arise, however, because probabilistic models with the necessary realism and exibility lead to complex distributions over high-dimensional spaces.

Related problems in other elds have been tackled using Monte Carlo methods based on sampling using Markov chains, providing a rich array of techniques that can be applied to problems in articial intelligence. The "Metropolis algorithm" has been used to solve dicult problems in statistical physics for over forty years, and, in the last few years, the related method of \Gibbs sampling" has been applied to problems of statistical inference. Concurrently, an alternative method for solving problems in statistical physics by means of dynamical simulation has been developed as well, and has recently been unied with the Metropolis algorithm to produce the \hybrid
Monte Carlo" method. In computer science, Markov chain sampling is the basis of the heuristic optimization technique of \simulated annealing", and has recently been used in randomized algorithms for approximate counting of large sets.

In this review, I outline the role of probabilistic inference in articial intelligence, present the theory of Markov chains, and describe various Markov chain Monte Carlo algorithms, along with a number of supporting techniques. I try to present a comprehensive picture of the range of methods that have been developed, including
techniques from the varied literature that have not yet seen wide application in articial intelligence, but which appear relevant. As illustrative examples, I use the problems of probabilistic inference in expert systems, discovery of latent classes from data, and Bayesian learning for neural networks.