Dealing with label switching in mixture models
Dealing with label switching in mixture models
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DOI：
10.1111/1467-9868.00265
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发表时间：
2000-01-01
影响因子：
5.8
通讯作者：
Stephens, M
中科院分区：
文献类型：
--
作者：
Stephens, M
在有限混合模型的贝叶斯分析中，参数估计和聚类有时不如预期的那么简单。特别是，通过后验均值估计参数，并通过边缘分布总结联合后验分布的常见做法往往会导致无意义的答案。这是由于所谓的“标签切换”问题，这是由模型参数的可能性的对称性引起的。对这个问题的一个常见的反应是通过使用人工可识别性约束来去除对称性。我们证明，这在一般情况下无法解决这个问题，我们描述了另一类方法，重新标记算法，这是由于试图尽量减少后验预期损失下的一类损失函数。我们详细描述了一个特别简单和一般的重新标记算法，并说明其成功地处理标签切换问题的两个例子。
In a Bayesian analysis of finite mixture models, parameter estimation and clustering are sometimes less straightforward than might be expected. In particular, the common practice of estimating parameters by their posterior mean, and summarizing joint posterior distributions by marginal distributions, often leads to nonsensical answers. This is due to the so-called 'label switching' problem, which is caused by symmetry in the likelihood of the model parameters. A frequent response to this problem is to remove the symmetry by using artificial identifiability constraints. We demonstrate that this fails in general to solve the problem, and we describe an alternative class of approaches, relabelling algorithms, which arise from attempting to minimize the posterior expected loss under a class of loss functions. We describe in detail one particularly simple and general relabelling algorithm and illustrate its success in dealing with the label switching problem on two examples.