Weighted Fused Pathway Graphical Lasso for Joint Estimation of Multiple Gene Networks

Abstract

Gene regulatory networks (GRNs) are often inferred based on Gaussian graphical models that could identify the conditional dependence among genes by estimating the corresponding precision matrix. Classical Gaussian graphical models are usually designed for single network estimation and ignore existing knowledge such as pathway information. Therefore, they can neither make use of the common information shared by multiple networks, nor can they utilize useful prior information to guide the estimation. In this paper, we propose a new weighted fused pathway graphical lasso (WFPGL) to jointly estimate multiple networks by incorporating prior knowledge derived from known pathways and gene interactions. Based on the assumption that two genes are less likely to be connected if they do not participate together in any pathways, a pathway-based constraint is considered in our model. Moreover, we introduce a weighted fused lasso penalty in our model to take into account prior gene interaction data and common information shared by multiple networks. Our model is optimized based on the alternating direction method of multipliers (ADMM). Experiments on synthetic data demonstrate that our method outperforms other five state-of-the-art graphical models. We then apply our model to two real datasets. Hub genes in our identified state-specific networks show some shared and specific patterns, which indicates the efficiency of our model in revealing the underlying mechanisms of complex diseases.

Estimation of Gene Regulatory Networks from Cancer Transcriptomics Data

“…The GGM has also been modified to integrate biological knowledge. In the modified version of the GGM, lasso is frequently used for the estimation of partial correlations between genes [87][88][89][90]. Most of these methods, including weighted graphical lasso [87], information-incorporated GGM, prior lasso [88], graphical adaptive lasso [89], and fused pathway graphical lasso [90], use a weight matrix that assigns weights to the links between the genes based on prior biological information.…”

“…In the modified version of the GGM, lasso is frequently used for the estimation of partial correlations between genes [87][88][89][90]. Most of these methods, including weighted graphical lasso [87], information-incorporated GGM, prior lasso [88], graphical adaptive lasso [89], and fused pathway graphical lasso [90], use a weight matrix that assigns weights to the links between the genes based on prior biological information. These methods have been validated for gene expression data of liver, lung, ovarian, and breast cancers and were found to perform better than the benchmark methods.…”

Joint Gene Network Construction by Single-Cell RNA Sequencing Data

“…However, its performance may be improved by utilizing the network similarity across the related conditions. As such, joint graphical modeling is preferred (Danaher et al, 2014;Oates et al, 2014;Chun et al, 2015;Yang et al, 2015;Haslbeck and Waldorp, 2015;Cai et al, 2016;Qiu et al, 2016;Hallac et al, 2017;Huang et al, 2017;Lyu et al, 2018;Zhu and Koyejo, 2018;Lee et al, 2018;Geng et al, 2019;Jia and Liang, 2019;Zhang et al, 2019;Wu et al, 2019Wu et al, , 2020.…”

Inferring Differential Networks by Integrating Gene Expression Data With Additional Knowledge

“…As the changes of regulatory relationships between two different states is more likely to occur between genes that are known to have regulatory interactions, considering prior gene regulatory interactions may help to improve the accuracy of differential network estimation. Moreover, researchers have found that genes within same pathways usually interact with each other to carry out their biological functions, and genes belong to different pathways seldom interact with each other ( Wu et al, 2019 ). Thus, taking into account pathway information may also facilitate the inference of differential networks.…”