C-ISTA: Iterative Shrinkage-Thresholding Algorithm for Sparse Covariance Matrix Estimation

Wenfu Xia, Ziping Zhao, Ying Sun

Abstract: Covariance matrix estimation is a fundamental task in many fields related to data analysis. As the dimension of the covariance matrix becomes large, it is desirable to obtain a sparse estimator and an efficient algorithm to compute it. In this paper, we consider the covariance matrix estimation problem by minimizing a Gaussian negative log-likelihood loss function with an ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> penalty, which is a constrained non-convex optimization problem. We propose to solve the covariance estimator via a simple iterative shrinkage-thresholding algorithm (C-ISTA) with provable convergence. Numerical simulations with comparison to the benchmark methods demonstrate the computational efficiency and good estimation performance of C-ISTA.