Hilbert Space Embedding for Dirichlet Process Mixtures

TL;DR

This paper introduces a Hilbert space embedding for Dirichlet Process mixture models to enable efficient inference, combining Bayesian nonparametric flexibility with the computational advantages of kernel methods.

Contribution

It presents a novel Hilbert space embedding for Dirichlet Process mixtures, facilitating more tractable inference and bridging Bayesian and frequentist approaches.

Findings

Provides a new embedding technique for Dirichlet Process mixtures

Enables more efficient inference in Bayesian nonparametrics

Bridges the gap between Bayesian and frequentist methods

Abstract

This paper proposes a Hilbert space embedding for Dirichlet Process mixture models via a stick-breaking construction of Sethuraman. Although Bayesian nonparametrics offers a powerful approach to construct a prior that avoids the need to specify the model size/complexity explicitly, an exact inference is often intractable. On the other hand, frequentist approaches such as kernel machines, which suffer from the model selection/comparison problems, often benefit from efficient learning algorithms. This paper discusses the possibility to combine the best of both worlds by using the Dirichlet Process mixture model as a case study.