Deterministic Variational Inference for Robust Bayesian Neural Networks

TL;DR

This paper introduces a deterministic variational inference method for Bayesian neural networks that enhances robustness and efficiency by eliminating gradient variance and automatically tuning prior variances.

Contribution

It proposes a novel deterministic approximation for moments in neural networks and a hierarchical prior with Empirical Bayes for automatic prior variance selection.

Findings

Achieves good predictive performance in heteroscedastic regression

Demonstrates robustness and efficiency over existing methods

Reduces the need for careful initialization and tuning

Abstract

Bayesian neural networks (BNNs) hold great promise as a flexible and principled solution to deal with uncertainty when learning from finite data. Among approaches to realize probabilistic inference in deep neural networks, variational Bayes (VB) is theoretically grounded, generally applicable, and computationally efficient. With wide recognition of potential advantages, why is it that variational Bayes has seen very limited practical use for BNNs in real applications? We argue that variational inference in neural networks is fragile: successful implementations require careful initialization and tuning of prior variances, as well as controlling the variance of Monte Carlo gradient estimates. We provide two innovations that aim to turn VB into a robust inference tool for Bayesian neural networks: first, we introduce a novel deterministic method to approximate moments in neural networks, eliminating gradient variance; second, we introduce a hierarchical prior for parameters and a novel Empirical Bayes procedure for automatically selecting prior variances. Combining these two innovations, the resulting method is highly efficient and robust. On the application of heteroscedastic regression we demonstrate good predictive performance over alternative approaches.