Posterior Regularized Bayesian Neural Network Incorporating Soft and Hard Knowledge Constraints
This work addresses the need for better uncertainty quantification and domain knowledge integration in Bayesian neural networks, particularly for applications like aviation and solar energy, though it appears incremental as it builds on existing BNN methods.
The authors tackled the problem of Bayesian neural networks lacking uncertainty quantification and domain knowledge integration by proposing a Posterior-Regularized Bayesian Neural Network (PR-BNN) that incorporates soft and hard knowledge constraints as a posterior regularization term, resulting in performance improvements over traditional BNNs in simulation and case studies on aviation landing and solar energy prediction.
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.