Population Empirical Bayes

Abstract

Bayesian predictive inference employs a model to analyze a dataset and make predictions about new observations. When a model does not match the data, predictive accuracy suffers. We develop population empirical Bayes, a hierarchical framework that explicitly models the empirical population distribution as part of Bayesian analysis. We introduce a latent dataset as a hierarchical variable and set the empirical population as its prior. This leads to a new predictive density that mitigates model mismatch. We efficiently apply this method to complex models by proposing a stochastic variational inference algorithm, called bumping variational inference. We demonstrate improved predictive accuracy over classical Bayesian inference in three models: a linear regression model of health data, a Bayesian mixture model of natural images, and a latent Dirichlet allocation topic model of a text corpus.