Evaluating Sensitivity to the Stick-Breaking Prior in Bayesian Nonparametrics

TL;DR

This paper investigates how the choice of stick-breaking priors affects Bayesian nonparametric models, using variational methods to assess sensitivity and improve robustness in clustering and topic modeling tasks.

Contribution

It introduces a variational approach to evaluate the sensitivity of Bayesian nonparametric models to prior choices, enhancing understanding of robustness and prior influence.

Findings

Variational methods effectively assess prior sensitivity.

Prior choices significantly impact posterior inferences.

The approach provides both theoretical and empirical validation.

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. However, due to the flexibility of these models, the consequences of prior choices can be opaque. And so prior specification can be relatively difficult. At the same time, prior choice 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.