Exact Hybrid Covariance Thresholding for Joint Graphical Lasso

Abstract

This paper studies precision matrix estimation for multiple related Gaussian graphical models from a dataset consisting of different classes, based upon the formulation of this problem as group graphical lasso. In particular, this paper proposes a novel hybrid covariance thresholding algorithm that can effectively identify zero entries in the precision matrices and split a large joint graphical lasso problem into many small subproblems. Our hybrid covariance thresholding method is superior to existing uniform thresholding methods in that our method can split the precision matrix of each individual class using different partition schemes and thus, split group graphical lasso into much smaller subproblems, each of which can be solved very fast. This paper also establishes necessary and sufficient conditions for our hybrid covariance thresholding algorithm. Experimental results on both synthetic and real data validate the superior performance of our thresholding method over the others.