Interaction screening in high-dimensional multi-response regression via projected distance correlation

Interaction screening for high-dimensional data is a challenging issue, especially for the strongly correlated predictors. A new two-stage interaction screening procedure based on the projected distance correlation is proposed when the predictors are highly correlated. To remove the confounding effect from the target variable that is induced by its correlated variables, we project the predictors and responses onto a conditional set. Our method can successfully identify important variables when the variables are highly correlated, and it can also identify variables that make a contribution to the response conditionally but not marginally. Moreover, our method is computationally efficient and simple, generally applicable without the requirement of the heredity assumption. Theoretical results show that the proposed method can yield the sure screening property. Simulation studies and real data analysis demonstrate the utility and validity of our method.