Generalized Variational Inference in Function Spaces: Gaussian Measures meet Bayesian Deep Learning

TL;DR

This paper introduces Gaussian Wasserstein inference, a novel variational method in function spaces that combines neural networks with Gaussian process-like uncertainty quantification, achieving state-of-the-art results.

Contribution

It develops a generalized variational inference framework in infinite-dimensional spaces using Wasserstein distance, enabling neural network-based Bayesian inference with principled uncertainty.

Findings

Achieves state-of-the-art performance on benchmark datasets.

Effectively combines neural networks with Gaussian process uncertainty quantification.

Avoids pathologies of standard variational inference in function spaces.

Abstract

We develop a framework for generalized variational inference in infinite-dimensional function spaces and use it to construct a method termed Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance between Gaussian measures on the Hilbert space of square-integrable functions in order to determine a variational posterior using a tractable optimisation criterion and avoids pathologies arising in standard variational function space inference. An exciting application of GWI is the ability to use deep neural networks in the variational parametrisation of GWI, combining their superior predictive performance with the principled uncertainty quantification analogous to that of Gaussian processes. The proposed method obtains state-of-the-art performance on several benchmark datasets.