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Activity Number: 471 - New Frontier in Developments of Complex-Structured High-Dimensional Data Analysis
Type: Topic Contributed
Date/Time: Wednesday, August 10, 2022 : 2:00 PM to 3:50 PM
Sponsor: International Chinese Statistical Association
Abstract #322419
Title: Subspace Estimation with Automatic Dimension and Variable Selection in Sufficient Dimension Reduction
Author(s): Jing Zeng* and Qing Mai and Xin Zhang
Companies: Florida State University and Florida State University and Florida State University
Keywords: Sufficient dimension reduction; Central subspace; Structural dimension selection; Coordinate-independent variable selection

Sufficient dimension reduction (SDR) methods target finding lower-dimensional representations of predictors to preserve all the information about the regression or classification analysis. 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. In this article, we propose a unified and flexible framework for estimating the CS in high dimensions. Our 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 dimension selection and 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.

Authors who are presenting talks have a * after their name.

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