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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.
摘要：
本文提出了一种用于高维图形模型选择的校准凹凸程序（校准CCCP）。已知用于平滑限幅绝对偏差（SCAD）惩罚的校准CCCP方法与线性回归模型中收敛到一个的概率是路径一致的。我们使用SCAD惩罚来实现校准的CCCP方法，以进行图形模型选择。我们对无向高斯图形模型使用二次目标函数，并采用SCAD惩罚进行稀疏估计。对于调谐程序，我们建议对针对测试数据进行调整的二次目标函数使用逐列调整。在模拟研究中,我们将所提出的方法与两种现有的图形模型估计器在矩阵误差范数和支持恢复率方面的性能进行了比较。我们还比较了估计矩阵的偏差和方差。然后，我们将该方法应用于注意缺陷多动障碍（ADHD）患者的功能磁共振成像（fMRI）数据。
