The Population Posterior and Bayesian Modeling on Streams

Many modern data analysis problems involve inferences from streaming data. However, streaming data is not easily amenable to the standard probabilistic modeling approaches, which require conditioning on finite data. We develop population variational Bayes, a new approach for using Bayesian modeling to analyze streams of data. It approximates a new type of distribution, the population posterior, which combines the notion of a population distribution of the data with Bayesian inference in a probabilistic model. We develop the population posterior for latent Dirichlet allocation and Dirichlet process mixtures. We study our method with several large-scale data sets.