Wavelet Feature Screening

An initial screening of which covariates are relevant is a common practice in high-dimensional regression models. The classic feature screening selects only a subset of covariates correlated with the response variable. However, many important features might have a relevant albeit highly nonlinear relation with the response. One screening approach that handles nonlinearity is to compute the correlation between the response and nonparametric functions of each covariate. Wavelets are powerful tools for nonparametric and functional data analysis but are still seldom used in the feature screening literature. We propose a wavelet feature screening method that can be easily implemented, and we prove that, under suitable conditions, it captures the true covariates with high probability. Simulation results also show that our approach outperforms other screening methods in highly nonlinear models. We apply feature screening to two datasets about ozone concentration and epilepsy. In both applications, the proposed method selects features that match findings in the literature of their respective research fields, illustrating the applicability of feature screening. Supplementary material for this article is available online.