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.