Joint Learning of Multiple Differential Networks with Latent Variables

Le Ou-Yang, Xiao Fei Zhang, Xing Ming Zhao, Debby D. Wang, Fu Lee Wang, Baiying Lei, Hong Yan

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

Graphical models have been widely used to learn the conditional dependence structures among random variables. In many controlled experiments, such as the studies of disease or drug effectiveness, learning the structural changes of graphical models under two different conditions is of great importance. However, most existing graphical models are developed for estimating a single graph and based on a tacit assumption that there is no missing relevant variables, which wastes the common information provided by multiple heterogeneous data sets and underestimates the influence of latent/unobserved relevant variables. In this paper, we propose a joint differential network analysis (JDNA) model to jointly estimate multiple differential networks with latent variables from multiple data sets. The JDNA model is built on a penalized D-trace loss function, with group lasso or generalized fused lasso penalties. We implement a proximal gradient-based alternating direction method of multipliers to tackle the corresponding convex optimization problems. Extensive simulation experiments demonstrate that JDNA model outperforms state-of-the-art methods in estimating the structural changes of graphical models. Moreover, a series of experiments on several real-world data sets have been performed and experiment results consistently show that our proposed JDNA model is effective in identifying differential networks under different conditions.

Original languageEnglish
Article number8405747
Pages (from-to)3494-3506
Number of pages13
JournalIEEE Transactions on Cybernetics
Volume49
Issue number9
DOIs
Publication statusPublished - Sept 2019

Keywords

  • Differential network analysis
  • fused lasso
  • graphical model
  • group lasso
  • latent variable

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