A0952
Title: Generalized iterative least squares for nonlinear sufficient dimension reduction
Authors: Chenlu Ke - Virginia Commonwealth University (United States) [presenting]
Abstract: Sufficient dimension reduction (SDR) aims to identify low-dimensional representations that fully capture the regression information. While traditional linear SDR focuses on low-dimensional linear predictors, nonlinear SDR extends this concept by using nonlinear functions of the predictors. A generalized iterative least squares approach is introduced in reproducing kernel Hilbert spaces to recover the central sigma field for nonlinear SDR. This method naturally extends ordinary least squares to a kernel-based framework and employs an iterative mechanism reminiscent of kernel principal component analysis. Distinct from existing nonlinear SDR techniques, the approach adopts a forward regression perspective and does not require the completeness of the central class. Furthermore, it is demonstrated how the proposed method facilitates stepwise feature selection under the sufficiency paradigm. The asymptotic properties of the estimator are also established, and its performance is validated through extensive numerical studies.
