Operator Variational Inference

TL;DR

This paper introduces Operator Variational Inference (OPVI), a flexible framework that uses operators to design variational objectives, enabling scalable and expressive Bayesian inference beyond traditional KL-based methods.

Contribution

It reexamines variational inference through the lens of operators, proposing a general algorithm (OPVI) that accommodates diverse objectives and tradeoffs for scalable, expressive Bayesian inference.

Findings

OPVI can scale to massive data via data subsampling.

OPVI supports variational programs without requiring tractable densities.

Demonstrated benefits on mixture and image generative models.

Abstract

Variational inference is an umbrella term for algorithms which cast Bayesian inference as optimization. Classically, variational inference uses the Kullback-Leibler divergence to define the optimization. Though this divergence has been widely used, the resultant posterior approximation can suffer from undesirable statistical properties. To address this, we reexamine variational inference from its roots as an optimization problem. We use operators, or functions of functions, to design variational objectives. As one example, we design a variational objective with a Langevin-Stein operator. We develop a black box algorithm, operator variational inference (OPVI), for optimizing any operator objective. Importantly, operators enable us to make explicit the statistical and computational tradeoffs for variational inference. We can characterize different properties of variational objectives, such as objectives that admit data subsampling---allowing inference to scale to massive data---as well as objectives that admit variational programs---a rich class of posterior approximations that does not require a tractable density. We illustrate the benefits of OPVI on a mixture model and a generative model of images.