B1224
Title: Subspace estimation with automatic dimension and variable selection in sufficient dimension reduction
Authors: Jing Zeng - University of Science and Technology of China (China) [presenting]
Qing Mai - Florida State University (United States)
Xin Zhang - Florida State University (United States)
Abstract: Sufficient dimension reduction (SDR) methods target finding lower-dimensional representations of a multivariate predictor to preserve all the information about the conditional distribution of the response given the predictor. The reduction is commonly achieved by projecting the predictor onto a low-dimensional subspace. The smallest such subspace is known as the Central Subspace (CS) and is the key parameter of interest for most SDR methods. We propose a unified and flexible framework for estimating the CS in high dimensions. The approach generalizes a wide range of model-based and model-free SDR methods to high-dimensional settings, where the CS is assumed to involve only a subset of the predictors. We formulate the problem as a quadratic convex optimization so that the global solution is feasible. The proposed estimation procedure simultaneously achieves the structural dimension selection and coordinate-independent variable selection of the CS. Theoretically, our method achieves dimension selection, variable selection, and subspace estimation consistency at a high convergence rate under mild conditions. We demonstrate the effectiveness and efficiency of our method with extensive simulation studies and real data examples.
