JRmGRN: joint reconstruction of multiple gene regulatory networks with common hub genes using data from multiple tissues or conditions

Abstract

Supplementary data are available at Bioinformatics online.

Extended Graphical Lasso for Multiple Interaction Networks for High Dimensional Omics Data

“…In this situation, we need to explore some theoretical properties of the problem that can be used to provide guidance on our search of tuning parameters. This approach follows Deng et al [15] and we provide the following theorems that extend their theoretical results to our present case with class-specific hubs.…”

“…Using the theorem, one can inspect the empirical covariance matrices in order to determine whether the solution to the EDOHA optimization problem is block diagonal after some permutation of the features. Previous studies [14, 15] use uniform thresholding to decompose the precision matrices of different classes in exactly the same way. Non-uniform thresholding generates a non-uniform feasible partition by thresholding the K empirical covariance matrices separately.…”

“…In addition, a few hub nodes are expected to have a large number of interactions with many other nodes, some of which are common among all classes and others are specific to different classes. Unlike JRmGRN [15], our method aims to investigate these class-specific hub nodes explicitly. The precision matrix Θ (k) is decomposed into two January 22, 2021 3/17 parts: the elementary symmetric network for the kth class Z (k) , mainly containing the non-hub node correlation information, and the network for hub nodes V (k) for the kth class, including common and class-specific ones, where V (k) is a matrix with entirely zero or almost completely nonzero columns.…”

“…Here ρ is a positive parameter for the scaled Lagrangian form. We set ρ = 2.5 as is used in Deng et al [15].…”

“…The joint graphical lasso (JGL) [14] is proposed to estimate multiple models simultaneously, which ignores the scale-free network and is unable to detect hubs explicitly. In the model of JRmGRN [15], it identifies common hub elements across multiple classes by jointly using distinct datasets. In many situations, hub nodes that are specific to an individual network also exist.…”