Automatic Variational Inference in Stan

TL;DR

This paper introduces ADVI, an automatic variational inference method implemented in Stan, enabling scalable Bayesian inference without model-specific derivations or conjugacy assumptions.

Contribution

It presents a fully automated variational inference algorithm that works broadly across models, removing the need for tedious manual derivations.

Findings

ADVI performs comparably to MCMC in various models.

ADVI scales to large datasets, such as a quarter million images.

The method is easy to use within the Stan framework.

Abstract

Variational inference is a scalable technique for approximate Bayesian inference. Deriving variational inference algorithms requires tedious model-specific calculations; this makes it difficult to automate. We propose an automatic variational inference algorithm, automatic differentiation variational inference (ADVI). The user only provides a Bayesian model and a dataset; nothing else. We make no conjugacy assumptions and support a broad class of models. The algorithm automatically determines an appropriate variational family and optimizes the variational objective. We implement ADVI in Stan (code available now), a probabilistic programming framework. We compare ADVI to MCMC sampling across hierarchical generalized linear models, nonconjugate matrix factorization, and a mixture model. We train the mixture model on a quarter million images. With ADVI we can use variational inference on any model we write in Stan.