# Specifying Weight Priors in Bayesian Deep Neural Networks with Empirical Bayes

## TL;DR

This paper introduces MOPED, a method for setting informed weight priors in Bayesian deep neural networks using empirical Bayes, improving scalability and uncertainty quantification across various real-world tasks.

## Contribution

The paper proposes a two-stage hierarchical approach, MOPED, that effectively sets weight priors in Bayesian DNNs, enabling scalable variational inference.

## Key findings

- MOPED improves scalability of Bayesian DNNs.
- Provides reliable uncertainty quantification.
- Outperforms state-of-the-art Bayesian methods on multiple tasks.

## Abstract

Stochastic variational inference for Bayesian deep neural network (DNN) requires specifying priors and approximate posterior distributions over neural network weights. Specifying meaningful weight priors is a challenging problem, particularly for scaling variational inference to deeper architectures involving high dimensional weight space. We propose MOdel Priors with Empirical Bayes using DNN (MOPED) method to choose informed weight priors in Bayesian neural networks. We formulate a two-stage hierarchical modeling, first find the maximum likelihood estimates of weights with DNN, and then set the weight priors using empirical Bayes approach to infer the posterior with variational inference. We empirically evaluate the proposed approach on real-world tasks including image classification, video activity recognition and audio classification with varying complex neural network architectures. We also evaluate our proposed approach on diabetic retinopathy diagnosis task and benchmark with the state-of-the-art Bayesian deep learning techniques. We demonstrate MOPED method enables scalable variational inference and provides reliable uncertainty quantification.