Transformation Models for Flexible Posteriors in Variational Bayes

TL;DR

This paper introduces transformation model-based variational inference (TM-VI), a flexible approach to approximate complex posteriors in Bayesian models, including neural networks, overcoming the limitations of traditional Gaussian variational methods.

Contribution

The paper proposes TM-VI, a novel variational inference method using transformation models to better approximate complex posteriors in Bayesian models.

Findings

TM-VI accurately approximates complex posteriors in single-parameter models.

TM-VI is effective in mean-field settings for multi-parameter models like neural networks.

Transformation models provide greater flexibility than Gaussian variational distributions.

Abstract

The main challenge in Bayesian models is to determine the posterior for the model parameters. Already, in models with only one or few parameters, the analytical posterior can only be determined in special settings. In Bayesian neural networks, variational inference is widely used to approximate difficult-to-compute posteriors by variational distributions. Usually, Gaussians are used as variational distributions (Gaussian-VI) which limits the quality of the approximation due to their limited flexibility. Transformation models on the other hand are flexible enough to fit any distribution. Here we present transformation model-based variational inference (TM-VI) and demonstrate that it allows to accurately approximate complex posteriors in models with one parameter and also works in a mean-field fashion for multi-parameter models like neural networks.