Collapsed finite mixture models for simultaneous model selection and clustering.

Arthur White (Trinity College Dublin)

Friday 27th January, 2017 15:00-16:00 Maths 203


I will discuss two related methods to perform Bayesian model-based clustering (MBC), whereby the data are assumed to be generated by a finite mixture of probability distributions. Suitably chosen prior functions allow several parameters to be integrated from the model, leading to a collapsed inference method. This approach facilitates the clustering of the data while simultaneously performing model selection as a search over a large discrete space, and leads to substantially improved computational performance. Firstly, we consider an MCMC approach for selecting the number of clusters and the best clustering variables to perform latent class analysis, an MBC method for multivariate categorical responses. Secondly, we consider a greedy search algorithm to optimally cluster Poisson mixture models, based on the exact integrated complete likelihood (ICL), a popular clustering criterion. We compare the performance of this approach to standard clustering methods based on an EM algorithm and an approximation to the ICL. The approaches are demonstrated on simulated and real data.

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