This paper proposes a calibrated concave convex procedure (calibrated CCCP) for high-dimensional graphical model selection. The calibrated CCCP approach for the smoothly clipped absolute deviation (SCAD) penalty is known to be path-consistent with probability converging to one in linear regression models. We implement the calibrated CCCP method with the SCAD penalty for the graphical model selection. We use a quadratic objective function for undirected Gaussian graphical models and adopt the SCAD penalty for sparse estimation. For the tuning procedure, we propose to use columnwise tuning on the quadratic objective function adjusted for test data. In a simulation study, we compare the performance of the proposed method with two existing graphical model estimators for high-dimensional data in terms of matrix error norms and support recovery rate. We also compare the bias and the variance of the estimated matrices. Then, we apply the method to functional magnetic resonance imaging (fMRI) data of an attention deficit hyperactivity disorders (ADHD) patient.
Bibliographical noteFunding Information:
Cheolwoo Park's work was supported in part by National Science Foundation (NSF IIS-1607919) and Yongho Jeon's work by Basic Science Research Program of the National Research Foundation of Korea (NRF-2019R1A2C1005979) funded by the Korean government. We would like to thank the referees for their invaluable comments, which contributed to substantial improvement of the quality of the contents in this paper. We would also like to thank the editor for the kind instructions on the resubmission process and the encouraging comments.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty