Fast algorithms for sparse inverse covariance estimation

Abstract

Sparse precision matrix (i.e. inverse covariance matrix in statistic term) estimation is an important problem in many applications of multivariate analysis. The problem becomes very challenging when the dimension of data is much larger than the number of samples. In this paper, we propose a convex relaxation model for the sparse covariance selection problem, which is solved by the well-known alternating direction method of multipliers (ADMM). Furthermore, a new model with positive semi-definite constraint is proposed. Numerical results show that the ADMM-based methods perform favourably compared with the column-wise manner on both synthetic and real data.