Probabilistic Inference Using Markov Chain Monte Carlo Methods
Probabilistic Inference Using Markov Chain Monte Carlo Methods
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发表时间：
2011
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通讯作者：
Radford M. Neal
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作者：
Radford M. Neal
概率推理是人工智能中不确定推理和经验学习的一种有吸引力的方法。然而，由于具有必要的真实性和灵活性的概率模型会导致高维空间上的复杂分布，因此出现了计算困难。其他领域的相关问题已经使用基于马尔可夫链采样的蒙特卡罗方法得到解决，提供了丰富的可应用于人工智能问题的技术。四十多年来，“Metropolis 算法”一直被用来解决统计物理学中的难题，而在最近几年，“吉布斯采样”的相关方法已被应用于统计推断问题。与此同时，还开发了一种通过动力学模拟来解决统计物理问题的替代方法，并且最近与 Metropolis 算法相结合，产生了“混合蒙特卡罗”方法。在计算机科学中，马尔可夫链采样是“模拟退火”启发式优化技术的基础，最近已用于随机算法中对大集合进行近似计数。在这篇综述中，我概述了概率推理在人工智能中的作用，介绍了马尔可夫链理论，并描述了各种马尔可夫链蒙特卡罗算法以及许多支持技术。我试图全面介绍已开发的一系列方法，包括来自各种文献的技术，这些技术尚未在人工智能中得到广泛应用，但似乎是相关的。作为说明性示例，我使用专家系统中的概率推理、从数据中发现潜在类别以及神经网络的贝叶斯学习等问题。
Probabilistic inference is an attractive approach to uncertain reasoning and empirical learning in artificial intelligence. Computational difficulties arise, however, because probabilistic models with the necessary realism and flexibility lead to complex distributions over high-dimensional spaces. Related problems in other fields 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 artificial intelligence. The “Metropolis algorithm” has been used to solve difficult 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 unified 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 artificial 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 artificial 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.