A1532
Title: Sufficient dimension reduction via explained kernel embedding variation
Authors: Chenlu Ke - Virginia Commonwealth University (United States) [presenting]
Abstract: A new framework for sufficient dimension reduction based on explained kernel embedding variation is proposed. The main idea is to view dimension reduction through a model-free ANOVA decomposition in reproducing kernel Hilbert spaces and to estimate low-dimensional linear combinations of predictors that maximize kernel regression sum of squares. This formulation unifies several sufficient dimension reduction targets: with characteristic kernels it targets the central subspace, while with linear kernels it reduces to central mean subspace estimation. On the computational side, a sequential procedure that builds an ordered set of directions is combined with a joint refinement step over the Grassmann manifold. A validation-based backward test is also used to determine the structural dimension. The framework is further extended to right-censored outcomes and an IPCW version of kernel regression sum of squares for estimating sufficient reductions for the event time is developed. Numerical studies show that the proposed method can recover the relevant dimension and directions in both fully observed and censored settings.
