Dirichlet processes: interpretations, inference and extensions

par/by Aaron Courville
Département d'Informatique et de Recherche Opérationnelle
Université de Montréal

Dirichlet processes (DP) and its extensions have been at the center of much recent work in machine learning and statistics. As a distribution over measures, the DP permits one to define a conjugate prior over a mixture model with a countably infinite number of components. Advances in approximate inference methods for Dirichlet process-based models has significantly increased their potential for practical application.

In this talk, I will review some of the theoretical and practical aspects of Dirichlet processes and their use as a prior over the parameters in Bayesian hierarchical models. The goal will be to provide a tutorial-style treatment of the Dirichlet process and its numerous interpretations. I will describe how one can perform approximate inference in the DP framework via Gibbs sampling. I will also provide a brief overview of some of the many emergent extensions of the Dirichlet process.