Error-controlled feature selection for ultrahigh-dimensional and highly correlated feature space using deep learning

Deep learning has been at the center of analytics in recent years due to its impressive empirical success in analyzing complex data objects. Despite this success, most existing tools behave like black-box machines, thus the increasing interest in interpretable, reliable, and robust deep learning models applicable to a broad class of applications. Feature-selected deep learning has emerged as a promising tool in this realm. However, the recent developments do not accommodate ultrahigh-dimensional and highly correlated features or high noise levels. In this article, we propose a novel screening and cleaning method with the aid of deep learning for a data-adaptive multi-resolutional discovery of highly correlated predictors with a controlled error rate. Extensive empirical evaluations over a wide range of simulated scenarios and several real datasets demonstrate the effectiveness of the proposed method in achieving high power while keeping the false discovery rate at a minimum.