Mathematics

CLC number: O212

ADMM Algorithmic Regularization Paths for Sparse and Large Scale Positive-Definite Covariance Matrix Estimation

¹ School of Computer and Software Engineering, Anhui Institute of Information Technology, Wuhu 241002, Anhui, China
² School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
³ School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, Anhui, China

Received: 4 November 2021

Abstract

Estimating sparse positive-definite covariance matrices in high dimensions has received extensive attention in the past two decades. However, many existing algorithms are proposed for a single regularization parameter and little attention has been paid to estimating the covariance matrices over the full range of regularization parameters. In this paper we suggest to compute the regularization paths of estimating the positive-definite covariance matrices through a one-step approximation of the warm-starting Alternating Direction Method of Multipliers (ADMM) algorithm, which quickly outlines a sequence of sparse solutions at a fine resolution. We demonstrate the effectiveness and computational savings of our proposed algorithm through elaborative analysis of simulated examples.