  Deep neural networks (DNN) have been used successfully in many scientific
problems for their high prediction accuracy, but their application to genetic
studies remains challenging due to their poor interpretability. In this paper,
we consider the problem of scalable, robust variable selection in DNN for the
identification of putative causal genetic variants in genome sequencing
studies. We identified a pronounced randomness in feature selection in DNN due
to its stochastic nature, which may hinder interpretability and give rise to
misleading results. We propose an interpretable neural network model,
stabilized using ensembling, with controlled variable selection for genetic
studies. The merit of the proposed method includes: (1) flexible modelling of
the non-linear effect of genetic variants to improve statistical power; (2)
multiple knockoffs in the input layer to rigorously control false discovery
rate; (3) hierarchical layers to substantially reduce the number of weight
parameters and activations to improve computational efficiency; (4)
de-randomized feature selection to stabilize identified signals. We evaluated
the proposed method in extensive simulation studies and applied it to the
analysis of Alzheimer disease genetics. We showed that the proposed method,
when compared to conventional linear and nonlinear methods, can lead to
substantially more discoveries.
