MM algorithms for distance covariance based sufficient dimension reduction and sufficient variable selection

Runxiong Wu and Xin Chen

Computational Statistics & Data Analysis, 2021, vol. 155, issue C

Abstract: Sufficient dimension reduction (SDR) using distance covariance (DCOV) was recently proposed as an approach to dimension-reduction problems. Compared with other SDR methods, it is model-free without estimating link function and does not require any particular distributions on predictors. However, the DCOV-based SDR method involves optimizing a nonsmooth and nonconvex objective function over the Stiefel manifold. To tackle the numerical challenge, the original objective function is equivalently formulated into a DC (Difference of Convex functions) program and an iterative algorithm based on the majorization–minimization (MM) principle is constructed. At each step of the MM algorithm, one iteration of Riemannian Newton’s method is taken to solve the quadratic subproblem on the Stiefel manifold inexactly. In addition, the algorithm can also be readily extended to sufficient variable selection (SVS) using distance covariance. Finally, the convergence property of the proposed algorithm under some regularity conditions is established. Simulation and real data analysis show our algorithm drastically improves the computation efficiency and is robust across various settings compared with the existing method. Matlab codes implementing our methods and scripts for regenerating the numerical results are available at https://github.com/runxiong-wu/MMRN.

Keywords: Sufficient dimension reduction; Distance covariance; Variable selection; Manifold optimization; majorization–minimization; Riemannian Newton’s method (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947320301808
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:155:y:2021:i:c:s0167947320301808

DOI: 10.1016/j.csda.2020.107089

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().