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.
Highlights
Most biological processes within cells involve multiple genes (Schlitt and Brazma, 2007; Zhang et al, 2014)
In Gaussian graphical model (GGM), each node of the graph represents a random variable from a random vector subjected to multivariate normal distribution, and there is an edge between two nodes if the corresponding two random variables are conditionally dependent, which means the corresponding element of the precision matrix is non-zero (Dempster, 1972; Uhler, 2017)
To address the above problems, in this paper, we proposed a novel weighted fused pathway graphical lasso (WFPGL) to jointly estimate multiple gene networks as well as their difference by incorporating prior knowledge derived from known pathways and gene interactions
Summary
Most biological processes within cells involve multiple genes (Schlitt and Brazma, 2007; Zhang et al, 2014). We compare the performance of WFPGL with that of five stateof-the-art graphical models: 1) graphical lasso (GL) (Meinshausen and Bühlmann, 2006), which is a classical algorithm for precision matrix estimation; 2) pathway graphical lasso (PGL) (Grechkin et al, 2015), which is a framework that uses pathway knowledge to estimate single Gaussian graphical model; 3) fused graphical lasso (FGL) (Danaher et al, 2014), which is a method for joint estimation of multiple precision matrices across multiple states; 4) differential network estimation via D-trace loss (Dtrace) (Yuan et al, 2017), which is a method for direct estimation of a differential network between two states; and 5) weighted D-trace loss (WDtrace) (Xu et al, 2018), which is an algorithm proposed for inferring differential network rewiring by integrating static gene regulatory network information. Θ (k′) ij According to the above definitions, TPR and FPR measure the accuracy of network estimation, whereas TPDR and FPDR measure the accuracy of differential network estimation
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