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Title: Sparse sufficient dimension reduction by nonconvex ADMM Authors:  Bingyuan Liu - Penn State University (United States) [presenting]
Amal Agarwal - Penn State University (United States)
Lingzhou Xue - Penn State University (United States)
Abstract: Sufficient dimension reduction (SDR) is widely used for dimension reduction and feature extraction in high-dimensional data analysis. With a better interpretability, the sparse SDR provides an appealing alternative. However, the statistical consistency and efficient estimation for sparse SDR in high dimensional setting remains an open question. We first introduce the $L_0$-constrained inverse moment method and study its asymptotic properties (including convergence rate and feature selection consistency) under the high-dimensional setting where the dimension diverges as the sample size increases. Computationally, we propose the new nonconvex alternating directional method of multipliers (ADMM) to solve the nonconvex and nonsmooth optimization in sparse SDR. We study the computational guarantees of the folded concave penalized estimation to approximate the $L_0$ penalization and show an explicit iteration complexity bound for the proposed nonconvex ADMM to reach the stationary solution. We demonstrate the numerical properties of our proposed methods in both simulation studies and a real application.