Informative Bayesian Neural Network Priors for Weak Signals

TL;DR

This paper introduces a novel Bayesian prior for neural networks that encodes domain knowledge about feature sparsity and signal-to-noise ratio, improving prediction accuracy especially in weak signal scenarios.

Contribution

It proposes a joint prior over local scale parameters and a Stein gradient method for hyperparameter tuning, enhancing neural network performance with limited data.

Findings

Improved prediction accuracy over existing priors.

Effective in weak and sparse signal settings.

Outperforms cross-validation in hyperparameter tuning.

Abstract

Encoding domain knowledge into the prior over the high-dimensional weight space of a neural network is challenging but essential in applications with limited data and weak signals. Two types of domain knowledge are commonly available in scientific applications: 1. feature sparsity (fraction of features deemed relevant); 2. signal-to-noise ratio, quantified, for instance, as the proportion of variance explained (PVE). We show how to encode both types of domain knowledge into the widely used Gaussian scale mixture priors with Automatic Relevance Determination. Specifically, we propose a new joint prior over the local (i.e., feature-specific) scale parameters that encodes knowledge about feature sparsity, and a Stein gradient optimization to tune the hyperparameters in such a way that the distribution induced on the model's PVE matches the prior distribution. We show empirically that the new prior improves prediction accuracy, compared to existing neural network priors, on several publicly available datasets and in a genetics application where signals are weak and sparse, often outperforming even computationally intensive cross-validation for hyperparameter tuning.