Exact Hybrid Covariance Thresholding for Joint Graphical Lasso

TL;DR

This paper introduces a hybrid covariance thresholding algorithm for joint graphical lasso that efficiently identifies zero entries in precision matrices, enabling faster estimation of multiple related Gaussian graphical models.

Contribution

A novel hybrid covariance thresholding method that outperforms existing uniform methods by allowing different partition schemes for each class, reducing computational complexity.

Findings

The hybrid method effectively splits large problems into smaller, manageable subproblems.

The method demonstrates superior performance on simulated and real gene expression data.

Necessary and sufficient conditions for the thresholding algorithm are established.

Abstract

This paper considers the problem of estimating multiple related Gaussian graphical models from a $p$-dimensional dataset consisting of different classes. Our work is based upon the formulation of this problem as group graphical lasso. 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 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. In addition, this paper establishes necessary and sufficient conditions for our hybrid covariance thresholding algorithm. The superior performance of our thresholding method is thoroughly analyzed and illustrated by a few experiments on simulated data and real gene expression data.