A0541
Title: A forward approach for sufficient dimension reduction in binary classification
Authors: Jongkyeong Kang - Korea University (Korea, South)
Seung Jun Shin - Korea University (Korea, South) [presenting]
Abstract: Since the seminal sliced inverse regression (SIR) proposed, the inverse-type methods have been canonical in sufficient dimension reduction (SDR). However, they often suffer in binary classification since the binary response yields two slices at most. We develop a forward approach for SDR in binary classification based on weighted large-margin classifiers. We first show that the gradient of a large-margin classifier is unbiased for SDR as long as the corresponding loss function is Fisher consistent. This leads us to propose what we call the weighted outer-product of gradients (wOPG) method. The WOPG can recover the central subspace exhaustively without linearity or constant variance conditions routinely required for the inverse-type methods. We study the asymptotic behavior of the proposed estimator and demonstrate its promising finite-sample performance for both simulated and real data examples.
