Variational Inference in Nonconjugate Models

TL;DR

This paper introduces two generic variational inference methods, Laplace and delta method variational inference, enabling efficient approximate posterior inference in a broad class of nonconjugate models.

Contribution

The paper develops two universal variational inference techniques for nonconjugate models, simplifying derivations and extending applicability beyond model-specific algorithms.

Findings

Methods perform well on real-world datasets

Unified framework extends existing algorithms

Effective in models like Bayesian logistic regression

Abstract

Mean-field variational methods are widely used for approximate posterior inference in many probabilistic models. In a typical application, mean-field methods approximately compute the posterior with a coordinate-ascent optimization algorithm. When the model is conditionally conjugate, the coordinate updates are easily derived and in closed form. However, many models of interest---like the correlated topic model and Bayesian logistic regression---are nonconjuate. In these models, mean-field methods cannot be directly applied and practitioners have had to develop variational algorithms on a case-by-case basis. In this paper, we develop two generic methods for nonconjugate models, Laplace variational inference and delta method variational inference. Our methods have several advantages: they allow for easily derived variational algorithms with a wide class of nonconjugate models; they extend and unify some of the existing algorithms that have been derived for specific models; and they work well on real-world datasets. We studied our methods on the correlated topic model, Bayesian logistic regression, and hierarchical Bayesian logistic regression.