Model-free conditional screening via conditional distance correlation

With the knowledge on the predetermined active predictors, we develop a feature screening procedure via the conditional distance correlation learning. The proposed procedure can significantly lower the correlation among the predictors when they are highly correlated and thus reduce the numbers of false positive and false negative. Meanwhile, when the conditional set is unable to be accessed beforehand, a data-driven method is provided to select it. We establish both the ranking consistency and the sure screening property for the new proposed procedure. To compare the performance of our method with its competitors, extensive simulations are conducted, which shows that the new procedure performs well in both the linear and nonlinear models. Finally, a real data analysis is investigated to further illustrate the effectiveness of the new method.