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Analysis of the maximal posterior partition in the Dirichlet Process Gaussian Mixture Model. (arXiv:1606.03275v2 [math.ST] UPDATED)

来源于:arXiv
Mixture models are a natural choice in many applications, but it can be difficult to place an apriori upper bound on the number of components. To circumvent this, investigators are turning increasingly to Dirichlet process mixture models (DPMMs) and, more generally, Pitman-Yor mixtures. These models are well suited to Bayesian density estimation. An interesting question is whether they can be turned to the problem of {\em classification} or {\em clustering}, which involves allocating observations to clusters. This is becoming increasingly widely used among investigators. This article considers the MAP (maximal posterior partition) clustering for the Gauss-Gauss DPM (where the cluster means have Gaussian distribution and, for each cluster, the observations within the cluster have Gaussian distribution; the number and sizes of the clusters generated according to a Chinese Restaurant Process). It is proved that the convex hulls of the clusters created by the MAP are pairwise `almost disjo 查看全文>>