  In recent years, deep learning has been at the center of analytics due to its
impressive empirical success in analyzing complex data objects. Despite this
success, most of the 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 ultra-high dimensional and highly correlated features, in
addition to the high noise level. 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.
