  The applications of traditional statistical feature selection methods to
high-dimension, low sample-size data often struggle and encounter challenging
problems, such as overfitting, curse of dimensionality, computational
infeasibility, and strong model assumption. In this paper, we propose a novel
two-step nonparametric approach called Deep Feature Screening (DeepFS) that can
overcome these problems and identify significant features with high precision
for ultra high-dimensional, low-sample-size data. This approach first extracts
a low-dimensional representation of input data and then applies feature
screening based on multivariate rank distance correlation recently developed by
Deb and Sen (2021). This approach combines the strengths of both deep neural
networks and feature screening, and thereby has the following appealing
features in addition to its ability of handling ultra high-dimensional data
with small number of samples: (1) it is model free and distribution free; (2)
it can be used for both supervised and unsupervised feature selection; and (3)
it is capable of recovering the original input data. The superiority of DeepFS
is demonstrated via extensive simulation studies and real data analyses.
