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.
Acknowledgements
We would like to thank Prof. Zaiwen Wen for the discussions on sparse inverse covariance estimation. We also thank Prof. Weidong Liu for discussing the detail of the numerical experiment, and thank Dr Jingwei Liang for helpful discussions. The authors are grateful to editor and anonymous referees for their detailed and valuable comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the authors.