Distance-Based Probability Distributions on Set Partitions for Bayesian Nonparametric Models

• Activity Number: 597
• Type: Invited
• Date/Time: Thursday, August 5, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): David Dahl*+ and Ryan Day and Jerry Tsai
• Companies: Texas A&M University and University of the Pacific and University of the Pacific
• Keywords: Bayesian nonparametrics ; clustering methods ; Dirichlet process mixture model ; non-exchangeable priors ; partition models ; protein structure prediction

Abstract

Clustering methods are either model-based or distance-based, but we propose a framework that is both. The Dirichlet process induces a partition distribution in which the probability an item is clustered with another is uniform across all items. We propose two distributions for partitions which are indexed by pairwise distances among the items being clustered. The first is defined algorithmically by a Markov chain. The second explicitly specifies a probability mass function incorporating pairwise distances. Both have the Dirichlet process-induced clustering distribution as a special case. A new class of Bayesian nonparametric models that utilizes these distance-based probability distributions is defined. Applying these methods to a model for protein structure prediction, we find that the methods incorporating distance information substantially improve predictive accuracy.