Uncertainty Quantification and Statistical Inference for Biologically Informed Neural Networks

In precision medicine, deep learning models play an important role in identifying relevant biomarkers and making predictions for the early diagnosis and prognosis of diseases. While successful in developing accurate prediction models for prognosis and diagnosis, the ‘black box’ nature of deep learning poses significant challenges, which makes it difficult to have a meaningful biological interpretation. Recently, several biologically informed neural networks (BINNs), such as the Visible Neural Network and P-NET, have been proposed to incorporate biological knowledge for improved interpretation. These models assess node importance using quantitative measures such as SHAP and DeepLIFT. However, these approaches have limitations because they typically provide a single estimate of node importance without any information on the uncertainty of these estimates. This study aims to assess uncertainty of node importance through a novel statistical framework. Bootstrapping is used to calculate confidence interval of node importance. Our findings validate that the proposed statistical framework quantifies the uncertainty of nodes in BINNs. By providing robust confidence intervals of pathways and genes, this framework enhances the interpretability and reliability of BINNs.