Deep neural network-based feature selection with local false discovery rate estimation

Feature selection, aiming at identifying the most significant subset of features from the original data, plays a prominent role in high-dimensional data processing. To a certain extent, feature selection can mitigate the issue of poor interpretability of deep neural networks (DNNs). Despite recent advancements in DNN-based feature selection, most methods overlook the error control of selected features and lack reproducibility. In this paper, we propose a new method called DeepTD to perform error-controlled feature selection for DNNs, in which artificial decoy features are constructed and subjected to competition with the original features according to the feature importance scores computed from the trained network, enabling p-value-free local false discovery rate (FDR) estimation of selected features. The merits of DeepTD include: a new DNN-derived measure of feature importance combining the weights and gradients of the network; the first algorithm that estimates the local FDR based on DNN-derived scores; confidence assessment of individual selected features; better robustness to small numbers of important features and low FDR thresholds than competition-based FDR control methods, e.g., the knockoff filter. On multiple synthetic datasets, DeepTD accurately estimated the local FDR and empirically controlled the FDR with 10%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document} higher power on average than knockoff filter. At lower FDR thresholds, the power of our method has even reached two to three times that of other state-of-the-art methods. DeepTD was also applied to real datasets and selected 31%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}-49%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document} more features than alternatives, demonstrating its validity and utility.