A0367
Title: Clustering consistency with Dirichlet process mixtures
Authors: Filippo Ascolani - Bocconi University (Italy)
Antonio Lijoi - Bocconi University (Italy)
Giovanni Rebaudo - University of Turin and Collegio Carlo Alberto (Italy) [presenting]
Giacomo Zanella - Bocconi University (Italy)
Abstract: Dirichlet process mixtures are flexible nonparametric models particularly suited to density estimation and probabilistic clustering. The posterior distribution induced is studied by Dirichlet process mixtures as the sample size increases and, more specifically, focuses on consistency for the unknown number of clusters when the observed data are generated from a finite mixture. Crucially, the situation is considered where a prior is placed on the concentration parameter of the underlying Dirichlet process. Previous findings in the literature suggest that Dirichlet process mixtures are typically inconsistent for the number of clusters if the concentration parameter is fixed and data come from a finite mixture. It is shown that consistency for the number of clusters can be achieved if the concentration parameter is adapted in a fully Bayesian way, as commonly done in practice. The results are derived for data from a class of finite mixtures, with mild assumptions on the prior for the concentration parameter and for various choices of likelihood kernels for the mixture.
