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Front. Genet. | doi: 10.3389/fgene.2019.00623

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

 Nuosi Wu1,  Jiang Huang2, Xiao-Fei Zhang3,  Le Ou-Yang4, 5*,  Shan He6,  Zexuan Zhu2* and Weixin Xie1
  • 1College of Information Engineering, Shenzhen University, China
  • 2College of Computer Science and Software Engineering, Shenzhen University, China
  • 3School of Mathematics and Statistics, Central China Normal University, China
  • 4Shenzhen University, China
  • 5Shenzhen Key Laboratory of Media Security, College of Information Engineering, Shenzhen University, China
  • 6School of Computer Science, College of Engineering and Physical Sciences, University of Birmingham, United Kingdom

Gene regulatory networks (GRNs) are often inferred based on Gaussian graphical models which 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 data sets. Hub genes in our identified stated-specific networks show some shared and specific patterns, which indicates the efficiency of our model in revealing the underlying mechanisms of complex diseases.

Keywords: Gaussian graphical model, Precision matrix, Pathway graphical lasso, Fused lasso penalty, Gene network analysis

Received: 01 Mar 2019; Accepted: 13 Jun 2019.

Edited by:

Alfredo Pulvirenti, University of Catania, Italy

Reviewed by:

Hongwu Ma, Tianjin Institute of Industrial Biotechnology (CAS), China
Anand Anbarasu, VIT University, India  

Copyright: © 2019 Wu, Huang, Zhang, Ou-Yang, He, Zhu and Xie. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence:
Dr. Le Ou-Yang, Shenzhen University, Shenzhen, China, leouyang@szu.edu.cn
Prof. Zexuan Zhu, College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China, zhuzx@szu.edu.cn