Evaluating Sensitivity to the Stick-Breaking Prior in Bayesian Nonparametrics

TL;DR

This paper investigates how the choice of priors in Bayesian nonparametric models, especially stick-breaking priors, affects inferences, using variational methods to assess sensitivity to prior parameters.

Contribution

It introduces a variational Bayesian sensitivity analysis framework for evaluating the impact of prior choices in Dirichlet process models.

Findings

Variational methods effectively quantify prior sensitivity.

Sensitivity analysis reveals significant effects of prior parameters.

The approach is supported by theoretical and empirical evidence.

Abstract

Bayesian models based on the Dirichlet process and other stick-breaking priors have been proposed as core ingredients for clustering, topic modeling, and other unsupervised learning tasks. Prior specification is, however, relatively difficult for such models, given that their flexibility implies that the consequences of prior choices are often relatively opaque. Moreover, these choices can have a substantial effect on posterior inferences. Thus, considerations of robustness need to go hand in hand with nonparametric modeling. In the current paper, we tackle this challenge by exploiting the fact that variational Bayesian methods, in addition to having computational advantages in fitting complex nonparametric models, also yield sensitivities with respect to parametric and nonparametric aspects of Bayesian models. In particular, we demonstrate how to assess the sensitivity of conclusions to the choice of concentration parameter and stick-breaking distribution for inferences under Dirichlet process mixtures and related mixture models. We provide both theoretical and empirical support for our variational approach to Bayesian sensitivity analysis.