Feature Screening for Ultrahigh Dimensional Mixed Data via Wasserstein Distance

Abstract

This article develops a novel feature screening procedure for ultrahigh dimensional mixed data based on Wasserstein distance, termed as Wasserstein-SIS. To handle the mixture of continuous and discrete data, we use Wasserstein distance as a new marginal utility to measure the difference between the joint distribution and the product of marginal distributions. In theory, we establish the sure screening property under less restrictive assumptions on data types. The proposed procedure does not require model specification, gives a more effective geometric measure to compare the discrepancy between distributions and avoids introducing biases caused by the choice of slicing rules for continuous data. Numerical comparison indicates that the proposed Wasserstein-SIS method performs better than existing methods in various models. A real data application also validates the better practicability of Wasserstein-SIS.