论文标题
后正规化贝叶斯神经网络，结合了软知识约束
Posterior Regularized Bayesian Neural Network Incorporating Soft and Hard Knowledge Constraints
论文作者
论文摘要
神经网络（NNS）由于能够建模复杂的非线性模式（通常以高维数据（例如图像和文本）的形式显示），因此已被广泛用于监督学习}。但是，传统的NN通常缺乏不确定性量化的能力。贝叶斯NNS（BNN）可以通过考虑NN模型参数的分布来帮助测量不确定性。此外，通常可以使用域知识，如果可以适当地纳入BNN的性能。在这项工作中，我们提出了一种新型的后验调查贝叶斯神经网络（PR-BNN）模型，通过将不同类型的知识约束（例如软性和硬约束）作为后正则化项来提出。此外，我们建议将增强的拉格朗日方法和现有的BNN求解器结合起来，以有效地推断。关于航空着陆预测和太阳能输出预测的仿真和两个案例研究的实验表明，知识的限制和绩效改善了所提出的模型，而不是传统的BNN，而没有约束。
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.
