An exploration of testing genetic associations using goodness-of-fit statistics based on deep ReLU neural networks

As a driving force of the fourth industrial revolution, deep neural networks are now widely used in various areas of science and technology. Despite the success of deep neural networks in making accurate predictions, their interpretability remains a mystery to researchers. From a statistical point of view, how to conduct statistical inference (e.g., hypothesis testing) based on deep neural networks is still unknown. In this paper, goodness-of-fit statistics are proposed based on commonly used ReLU neural networks, and their potential to test significant input features is explored. A simulation study demonstrates that the proposed test statistic has higher power compared to the commonly used t-test in linear regression when the underlying signal is nonlinear, while controlling the type I error at the desired level. The testing procedure is also applied to gene expression data from the Alzheimer's Disease Neuroimaging Initiative (ADNI).