Population Empirical Bayes

Alp Kucukelbir; David M. Blei

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arXiv · 1411.0292

Population Empirical Bayes

Alp Kucukelbir·David M. Blei

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Abstract

Bayesian predictive inference analyzes a dataset to make predictions about new observations. When a model does not match the data, predictive accuracy suffers. We develop population empirical Bayes (POP-EB), a hierarchical framework that explicitly models the empirical population distribution as part of Bayesian analysis. We introduce a new concept, the 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 (BUMP-VI). 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 scientific documents.

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BibTeX RIS

Alp Kucukelbir, David M. Blei. 2015-06-08. Population Empirical Bayes. https://arxiv.org/abs/1411.0292

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