A Monte Carlo Metropolis-Hastings Algorithm for Sampling from Distributions with Intractable Normalizing Constants
A Monte Carlo Metropolis-Hastings Algorithm for Sampling from Distributions with Intractable Normalizing Constants
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DOI：
10.1162/neco_a_00466
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发表时间：
2013-08-01
影响因子：
2.9
通讯作者：
Jin, Ick-Hoon
中科院分区：
文献类型：
--
作者：
Liang, Faming;Jin, Ick-Hoon
用难以处理的归一化常数从分布进行模拟一直是机器学习中的一个长期问题。在这封信中，我们提出了一种新的算法--蒙特卡洛Metropolis-Hastings(MCMH)算法来解决这个问题。MCMH算法是Metropolis-Hastings算法的蒙特卡罗版本。它在模拟中用蒙特卡罗估计代替未知的归一化常数比，同时仍然收敛到期望的目标分布，如信中所示，在温和的条件下。用空间自回归模型和指数随机图模型对MCMH算法进行了说明。与其他辅助变量马尔可夫链蒙特卡罗(MCMC)算法(如Moller和Exchange算法)不同，MCMH算法避免了对完美抽样的要求，因此可以应用于许多无法获得完美抽样或非常昂贵的统计模型。MCMH算法还可以应用于随机效应模型的贝叶斯推断和涉及从具有难以处理的积分的分布进行模拟的丢失数据问题。
Simulating from distributions with intractable normalizing constants has been a long-standing problem in machine learning. In this letter, we propose a new algorithm, the Monte Carlo Metropolis-Hastings (MCMH) algorithm, for tackling this problem. The MCMH algorithm is a Monte Carlo version of the Metropolis-Hastings algorithm. It replaces the unknown normalizing constant ratio by a Monte Carlo estimate in simulations, while still converges, as shown in the letter, to the desired target distribution under mild conditions. The MCMH algorithm is illustrated with spatial autologistic models and exponential random graph models. Unlike other auxiliary variable Markov chain Monte Carlo (MCMC) algorithms, such as the Moller and exchange algorithms, the MCMH algorithm avoids the requirement for perfect sampling, and thus can be applied to many statistical models for which perfect sampling is not available or very expensive. The MCMH algorithm can also be applied to Bayesian inference for random effect models and missing data problems that involve simulations from a distribution with intractable integrals.