A0851
Title: Learning the number of clusters: Conjugate prior for the Dirichlet process precision parameter
Authors: Tommaso Rigon - University of Milano-Bicocca (Italy) [presenting]
Alessandro Zito - Duke University (United States)
David Dunson - Duke University (United States)
Abstract: A new and flexible prior distribution for the precision parameter of a Dirichlet process is introduced. We show how this prior is conjugate to the distribution of the number of distinct values arising from the process, thus admitting a posterior within that same family. Moments, properties and hyperparameters interpretation of the distribution are extensively studied, as well as its relationship with the class of exponential families. Interestingly, certain choices for the hyperparameters allow computing the normalizing constant explicitly. We show how this allows drawing a parallel with common Bayesian nonparametric models within the class of Gibbs-type processes. We illustrate the computational and practical advantages of using this prior over common alternatives proposed in the literature when adopting a Dirichlet process-based clustering algorithm.
