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Title: A weighted learning approach for sufficient dimension reduction in binary classification Authors:  Seung Jun Shin - Korea University (Korea, South) [presenting]
Abstract: Since the proposal of the sliced inverse regression (SIR), inverse-regression methods have been widely used for sufficient dimension reduction (SDR). In binary classification, the inverse-regression methods including SIR often suffer from the lack of resolution of the binary response. We propose a weighted large-margin classifiers to recover the central subspace. Toward this, we establish that the gradient vector of the weighted large-margin classifier is unbiased for SDR if the corresponding weighted loss function is Fisher consistent. This enables us to propose what we call weighted outer-product of gradients (wOPG) method for SDR in binary classification. The proposed wOPG method can recover the central subspace exhaustively without linearity condition or constant variance condition and shows promising performance for both simulated and real data examples.