Abstract: We consider feature screening for high-dimensional response data without and with the existence of confounding factors. First, we introduce kernel covariance and kernel correlation for high-dimensional associaiton analysis, and further propose partial kernel covariance and partial kernel correlation that can handle situations with confounding factors. Then, based on the kernel correlation and partial kernel correlation, we propose two feature screening procedures. Both screening procedures possess sure screening property and ranking consistency property, and are complementary to each other by respectively dealing with situations without and with the existence of confounding factors. The proposed procedures make no assumptions on model, and are suitable for high-dimensional response variable and non-Euclidean data. Extensive simulation results and a real data analysis demonstrate the satisfying performances and advantages of the proposed procedures over existing methods.

Key words and phrases: Confounding factors, feature screening, high-dimensional response variable, kernel correlation, partial kernel correlation.