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Probabilistic relabelling strategies for the label switching problem in Bayesian mixture models

机译：贝叶斯混合模型中标签切换问题的概率重标记策略

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摘要

The label switching problem is caused by the likelihood of a Bayesian mixture model being invariant to permutations of the labels. The permutation can change multiple times between Markov Chain Monte Carlo (MCMC) iterations making it difficult to infer component-specific parameters of the model. Various so-called 'relabelling' strategies exist with the goal to 'undo' the label switches that have occurred to enable estimation of functions that depend on component-specific parameters. Existing deterministic relabelling algorithms rely upon specifying a loss function, and relabelling by minimising its posterior expected loss. In this paper we develop probabilistic approaches to relabelling that allow for estimation and incorporation of the uncertainty in the relabelling process. Variants of the probabilistic relabelling algorithm are introduced and compared to existing deterministic relabelling algorithms. We demonstrate that the idea of probabilistic relabelling can be expressed in a rigorous framework based on the EM algorithm.
机译：标签切换问题是由贝叶斯混合模型不变于标签排列的可能性引起的。该排列可以在Markov Chain Monte Carlo（MCMC）迭代之间多次更改，从而难以推断模型的特定于组件的参数。存在各种所谓的“重新标记”策略，其目的是“撤消”已发生的标记开关，以使得能够估计依赖于组件特定参数的功能。现有的确定性重新标记算法依赖于指定损失函数，并通过最小化其预期后损失来重新标记。在本文中，我们开发了重新标记的概率方法，该方法允许估计和合并重新标记过程中的不确定性。介绍了概率重标记算法的变体，并将其与现有的确定性重标记算法进行了比较。我们证明概率重新标记的想法可以在基于EM算法的严格框架中表达。

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  • 来源
    《Statistics and computing》 |2010年第3期|P.357-366|共10页
  • 作者

    M. Sperrin; T. Jaki; E. Wit;

  • 作者单位

    Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK;

    rnDepartment of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK;

    rnInstitute of Mathematics and Computing Science, University of Groningen, Nijenborgh 9, 9747 AG Groningen, The Netherlands;

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  • 原文格式 PDF
  • 正文语种 eng
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  • 关键词

    bayesian; identifiability; label switching; MCMC; mixture model;

    机译：贝叶斯可识别性;标签切换;MCMC;混合模型;

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