Feature screening for multiple responses

Feature screening has been widely investigated in many literatures and quite a few procedures have been proposed. However, most of the existing methods are developed based on regularization strategy and model assumptions such as linear model and Gaussian distribution, which limit their application range. And also, they were mainly designed to deal with univariate response and cannot handle multiple responses situations. To tackle these issues, we introduce a new association measure for multiple responses and univariate predictor, called multiple explained variability (MEV), and further propose a feature screening procedure, named MEV-SIS, based on MEV. MEV-SIS removes the commonly used model assumptions and can conduct feature screening for multiple responses simultaneously. The asymptotic properties of MEV are deduced, and the sure screening property and ranking consistency property of MEV-SIS are obtained. Extensive simulation studies and real data application demonstrate the advantage of MEV-SIS over the existing screening procedures in sufficiency and robustness.