A Greedy Algorithm for Sparse Precision Matrix Approximation

Abstract

Precision matrix estimation is an important problem in statistical data analysis. This paper proposes a sparse precision matrix estimation approach, based on CLIME estimator and an efficient algorithm GISS$^{{\rho}}$ that was originally proposed for $l_1$ sparse signal recovery in compressed sensing. The asymptotic convergence rate for sparse precision matrix estimation is analyzed with respect to the new stopping criteria of the proposed GISS$^{{\rho}}$ algorithm. Finally, numerical comparison of GISS$^{\rho}$ with other sparse recovery algorithms, such as ADMM and HTP in three settings of precision matrix estimation is provided and the numerical results show the advantages of the proposed algorithm.