# Informative Bayesian Neural Network Priors for Weak Signals

arXiv: https://arxiv.org/abs/2002.10243 · HTML: https://mlsanity.com/paper/2002.10243/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2020.

## Built on by (most cited first, 5 of 5)

- [A Primer on Bayesian Neural Networks: Review and Debates](https://mlsanity.com/paper/2309.16314/) (2023)
- [BioBO: Biology-informed Bayesian Optimization for Perturbation Design](https://mlsanity.com/paper/2509.19988/) (2025)
- [Incorporating functional summary information in Bayesian neural networks using a Dirichlet process likelihood approach](https://mlsanity.com/paper/2207.01234/) (2022)
- [Incorporating priors in learning: a random matrix study under a teacher-student framework](https://mlsanity.com/paper/2509.22124/) (2025)
- [A Bayesian Semiparametric Method For Estimating Causal Quantile Effects](https://mlsanity.com/paper/2211.01591/) (2022)

## Abstract (arXiv)

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.