By integrating domain knowledge with labeled samples, informed machine learning has been emerging to improve the learning performance for a wide range of applications. Nonetheless, rigorous understanding of the role of injected domain knowledge has been under-explored. In this paper, we consider an informed deep neural network (DNN) with over-parameterization and domain knowledge integrated into its training objective function, and study how and why domain knowledge benefits the performance. Concretely, we quantitatively demonstrate the two benefits of domain knowledge in informed learning - regularizing the label-based supervision and supplementing the labeled samples - and reveal the trade-off between label and knowledge imperfectness in the bound of the population risk. Based on the theoretical analysis, we propose a generalized informed training objective to better exploit the benefits of knowledge and balance the label and knowledge imperfectness, which is validated by the population risk bound. Our analysis on sampling complexity sheds lights on how to choose the hyper-parameters for informed learning, and further justifies the advantages of knowledge informed learning.

通过将领域知识与标记样本相结合，本文提出了一种基于深度神经网络的知情学习模型，研究并量化了领域知识对模型性能的正则化和样本补充的两个优势，提出了一种通用的知情培训目标来更好地利用知识，平衡标签和知识不完美，并平衡了总体风险的上限。

宽神经网络的知情学习：收敛性、泛化性和采样复杂性