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.
Runjing Liu is supported by the National Science Foundation graduate research fellowship program. Ryan Giordano and Tamara Broderick were supported in part by an NSF CAREER Award and an ONR Early Career Grant.
We are indebted to helpful discussions with Nelle Varoquaux, Matthew Stephens, Michael C. Hughes, Eric Sudderth, and Jake Soloff, and to useful suggestions from anonymous reviewers.
Ryan Giordano. Runjing Liu. Michael I. Jordan. Tamara Broderick. "Evaluating Sensitivity to the Stick-Breaking Prior in Bayesian Nonparametrics (with Discussion)." Bayesian Anal. 18 (1) 287 - 366, March 2023. https://doi.org/10.1214/22-BA1309