Sparse graphical models via calibrated concave convex procedure with application to fMRI data

Abstract

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.

Keywords: CCCP; Inverse covariance matrix; SCAD; fMRI data; partial correlation.