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Bayesian models based on the Dirichlet process and other stick-breakingpriors have been proposed as core ingredients for clustering, topic modeling,and other unsupervised learning tasks. However, due to the flexibility of thesemodels, the consequences of prior choices can be opaque. And so priorspecification can be relatively difficult. At the same time, prior choice canhave a substantial effect on posterior inferences. Thus, considerations ofrobustness need to go hand in hand with nonparametric modeling. In the currentpaper, we tackle this challenge by exploiting the fact that variationalBayesian methods, in addition to having computational advantages in fittingcomplex nonparametric models, also yield sensitivities with respect toparametric and nonparametric aspects of Bayesian models. In particular, wedemonstrate how to assess the sensitivity of conclusions to the choice ofconcentration parameter and stick-breaking distribution for inferences underDirichlet process mixtures and related mixture models. We provide boththeoretical and empirical support for our variational approach to Bayesiansensitivity analysis.

Evaluating Sensitivity to the Stick-Breaking Prior in Bayesian Nonparametrics