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Latent variable models have become a key tool for the modern statistician, letting us express complex assumptions about the hidden structures that underlie our data. Latent variable models have been successfully applied in numerous fields.

The central computational problem in latent variable modeling is posterior inference, the problem of approximating the conditional distribution of the latent variables given the observations. Posterior inference is central to both exploratory tasks and predictive tasks. Approximate posterior inference algorithms have revolutionized Bayesian statistics, revealing its potential as a usable and general-purpose language for data analysis.

Bayesian statistics, however, has not yet reached this potential. First, statisticians and scientists regularly encounter massive data sets, but existing approximate inference algorithms do not scale well. Second, most approximate inference algorithms are not generic; each must be adapted to the specific model at hand.