Nonparametric variational inference

TL;DR

This paper introduces a nonparametric variational inference method using kernel density estimation, enabling flexible approximation of complex posteriors with multiple modes, applicable to various graphical models.

Contribution

The authors propose a novel nonparametric variational approach that optimizes kernel locations and bandwidths as variational parameters, overcoming conjugacy limitations of traditional methods.

Findings

Achieves predictive performance comparable or superior to existing methods.

Effectively captures multiple modes in posterior distributions.

Eases application to complex graphical models.

Abstract

Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of variational approximations inspired by nonparametric kernel density estimation. The locations of these kernels and their bandwidth are treated as variational parameters and optimized to improve an approximate lower bound on the marginal likelihood of the data. Using multiple kernels allows the approximation to capture multiple modes of the posterior, unlike most other variational approximations. We demonstrate the efficacy of the nonparametric approximation with a hierarchical logistic regression model and a nonlinear matrix factorization model. We obtain predictive performance as good as or better than more specialized variational methods and sample-based approximations. The method is easy to apply to more general graphical models for which standard variational methods are difficult to derive.