A Greedy Algorithm for Sparse Precision Matrix Approximation (Journal of Computational Mathematics, 2021)
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$^{ρ}$ 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$^{ρ}$ algorithm. Finally, numerical comparison of GISS$^{ρ}$ 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.
Keywords: Precision matrix estimation; CLIME estimator; Sparse recovery; Inverse scale space method; Greedy methods.