Canonical kernel dimension reduction

A new kernel dimension reduction (KDR) method based on the gradient space of canonical functions is proposed for sufficient dimension reduction (SDR). Similar to existing KDR methods, this new method achieves SDR for arbitrary distributions, but with more flexibility and improved computational efficiency. The choice of loss function in cross-validation is discussed, and a two-stage screening procedure is proposed. Empirical evidence shows that the new method yields favorable performance, both in terms of accuracy and scalability, especially for large and more challenging datasets compared with other distribution-free SDR methods.