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This paper considers the problem of estimating multiple related Gaussiangraphical models from a $p$-dimensional dataset consisting of differentclasses. Our work is based upon the formulation of this problem as groupgraphical lasso. This paper proposes a novel hybrid covariance thresholdingalgorithm that can effectively identify zero entries in the precision matricesand split a large joint graphical lasso problem into small subproblems. Ourhybrid covariance thresholding method is superior to existing uniformthresholding methods in that our method can split the precision matrix of eachindividual class using different partition schemes and thus split groupgraphical lasso into much smaller subproblems, each of which can be solved veryfast. In addition, this paper establishes necessary and sufficient conditionsfor our hybrid covariance thresholding algorithm. The superior performance ofour thresholding method is thoroughly analyzed and illustrated by a fewexperiments on simulated data and real gene expression data.

Exact Hybrid Covariance Thresholding for Joint Graphical Lasso