Combining Model and Parameter Uncertainty in Bayesian Neural Networks

Abstract

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using Bayesian approach: Parameter and prediction uncertainty become easily available, facilitating rigid statistical analysis. Furthermore, prior knowledge can be incorporated. However so far there have been no scalable techniques capable of combining both model (structural) and parameter uncertainty. In this paper we introduce the concept of model uncertainty in BNNs and hence make inference in the joint space of models and parameters. Moreover, we suggest an adaptation of a scalable variational inference approach with reparametrization of marginal inclusion probabilities to incorporate the model space constraints. Finally, we show that incorporating model uncertainty via Bayesian model averaging and Bayesian model selection allows to drastically sparsify the structure of BNNs.

16 pages, 8 Figures, 2 Tables

References in corpus (6)

• Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms
• Weight Uncertainty in Neural Networks
• Markov Chain Monte Carlo and Variational Inference: Bridging the Gap
• The Optimal Reward Baseline for Gradient-Based Reinforcement Learning
• Model Selection in Bayesian Neural Networks via Horseshoe Priors
• Variational Inference to Measure Model Uncertainty in Deep Neural Networks