Posterior Regularized Bayesian Neural Network Incorporating Soft and Hard Knowledge Constraints

TL;DR

This paper introduces a novel Posterior Regularized Bayesian Neural Network that incorporates soft and hard domain knowledge constraints to improve uncertainty quantification and predictive performance.

Contribution

It proposes a new PR-BNN model with a combined inference method, integrating knowledge constraints as posterior regularization, and demonstrates its effectiveness through simulations and case studies.

Findings

Knowledge constraints improve BNN performance

The proposed method enhances uncertainty quantification

Case studies show better prediction accuracy

Abstract

Neural Networks (NNs) have been widely {used in supervised learning} due to their ability to model complex nonlinear patterns, often presented in high-dimensional data such as images and text. However, traditional NNs often lack the ability for uncertainty quantification. Bayesian NNs (BNNS) could help measure the uncertainty by considering the distributions of the NN model parameters. Besides, domain knowledge is commonly available and could improve the performance of BNNs if it can be appropriately incorporated. In this work, we propose a novel Posterior-Regularized Bayesian Neural Network (PR-BNN) model by incorporating different types of knowledge constraints, such as the soft and hard constraints, as a posterior regularization term. Furthermore, we propose to combine the augmented Lagrangian method and the existing BNN solvers for efficient inference. The experiments in simulation and two case studies about aviation landing prediction and solar energy output prediction have shown the knowledge constraints and the performance improvement of the proposed model over traditional BNNs without the constraints.