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A framework of regularized low-rank matrix models for regression and classification.

Authors :
Huang, Hsin-Hsiung
Yu, Feng
Fan, Xing
Zhang, Teng
Source :
Statistics & Computing; Feb2024, Vol. 34 Issue 1, p1-19, 19p
Publication Year :
2024

Abstract

While matrix-covariate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional matrix-valued covariates. To address these issues, this paper proposes a framework of matrix-covariate regression models based on a low-rank constraint and an additional regularization term for structured signals, with considerations of models of both continuous and binary responses. We propose an efficient Riemannian-steepest-descent algorithm for regression coefficient estimation. We prove that the consistency of the proposed estimator is in the order of O (r (q + m) + p / n) , where r is the rank, p × m is the dimension of the coefficient matrix and p is the dimension of the coefficient vector. When the rank r is small, this rate improves over O (q m + p / n) , the consistency of the existing work (Li et al. in Electron J Stat 15:1909-1950, 2021) that does not apply a rank constraint. In addition, we prove that all accumulation points of the iterates have similar estimation errors asymptotically and substantially attaining the minimax rate. We validate the proposed method through a simulated dataset on two-dimensional shape images and two real datasets of brain signals and microscopic leucorrhea images. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
09603174
Volume :
34
Issue :
1
Database :
Complementary Index
Journal :
Statistics & Computing
Publication Type :
Academic Journal
Accession number :
173302503
Full Text :
https://doi.org/10.1007/s11222-023-10318-z