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Activity Number: 308 - Highlights in Bayesian Analysis: Innovations in Bayesian Learning
Type: Invited
Date/Time: Tuesday, August 9, 2022 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #320434
Title: Informative Bayesian Neural Network Priors for Weak Signals
Author(s): Tianyu Cui* and Aki Havulinna and Pekka Marttinen and Samuel Kaski
Companies: Aalto University and Finnish Institute for Health and Welfare (THL) and Aalto University and Aalto University and University of Manchester
Keywords: Informative prior; Neural network; Proportion of variance explained; Sparsity

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 publicly available datasets and in a genetics application where signals are weak and sparse, often outperforming even computationally intensive cross-validation for hyperparameter tuning.

Authors who are presenting talks have a * after their name.

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