Tractable Approximate Gaussian Inference for Bayesian Neural Networks

TL;DR

This paper introduces TAGI, an analytical method for efficient Gaussian inference in Bayesian neural networks that matches existing methods' performance with lower computational complexity.

Contribution

It presents a novel analytical approach for approximate Gaussian inference in Bayesian neural networks with linear complexity in parameters.

Findings

Matches performance of gradient-based methods on benchmarks

Computational complexity is linear in number of parameters

Enables analytical inference of posterior distributions

Abstract

In this paper, we propose an analytical method for performing tractable approximate Gaussian inference (TAGI) in Bayesian neural networks. The method enables the analytical Gaussian inference of the posterior mean vector and diagonal covariance matrix for weights and biases. The method proposed has a computational complexity of $\mathcal{O}(n)$ with respect to the number of parameters $n$, and the tests performed on regression and classification benchmarks confirm that, for a same network architecture, it matches the performance of existing methods relying on gradient backpropagation.