A0704
Title: Forward sufficient dimension reduction for multiclass classification
Authors: Jongkyoung Kang - Kangwon National University (Korea, South) [presenting]
Abstract: Since its introduction in sliced inverse regression, inverse regression methods have played a central role in sufficient dimension reduction (SDR). While forward approaches like the weighted outer product of gradients (wOPG) estimator have shown strong performance in binary classification by avoiding restrictive modeling assumptions, their extension to multiclass settings remains underexplored. A unified forward SDR framework is proposed for multiclass classification that generalizes wOPG via two complementary strategies: a one-vs-rest decomposition and a simultaneous central subspace estimation. First, it is established that the gradients of multiclass large-margin classifiers retain Fisher consistency for SDR, extending the theoretical guarantees of binary wOPG to multiclass problems. For one vs rest, K-independent binary sub-problems are solved, each estimating class-specific gradient outer products against pooled remaining classes. Simultaneous estimation directly optimizes a multinomial likelihood under a low-rank central subspace to capture shared discriminative structures across classes. Both strategies exhaustively recover the central subspace without relying on linearity or constant variance assumptions, addressing the inherent limitations of inverse methods in fragmented multiclass settings. The consistency of the proposed methods is also established, and their promising finite-sample performance is demonstrated through both simulated and real data examples.
