Model based labeling for mixture models |
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Authors: | Weixin Yao |
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Institution: | (1) Department of Statistics, University of Glasgow, Glasgow, G12 8QW, U.K |
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Abstract: | Label switching is one of the fundamental problems for Bayesian mixture model analysis. Due to the permutation invariance
of the mixture posterior, we can consider that the posterior of a m-component mixture model is a mixture distribution with m! symmetric components and therefore the object of labeling is to recover one of the components. In order to do labeling,
we propose to first fit a symmetric m!-component mixture model to the Markov chain Monte Carlo (MCMC) samples and then choose the label for each sample by maximizing
the corresponding classification probabilities, which are the probabilities of all possible labels for each sample. Both parametric
and semi-parametric ways are proposed to fit the symmetric mixture model for the posterior. Compared to the existing labeling
methods, our proposed method aims to approximate the posterior directly and provides the labeling probabilities for all possible
labels and thus has a model explanation and theoretical support. In addition, we introduce a situation in which the “ideally”
labeled samples are available and thus can be used to compare different labeling methods. We demonstrate the success of our
new method in dealing with the label switching problem using two examples. |
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Keywords: | |
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