Direct estimation of differential networks

Abstract

It is often of interest to understand how the structure of a genetic network differs between two conditions. In this paper, each condition-specific network is modeled using the precision matrix of a multivariate normal random vector, and a method is proposed to directly estimate the difference of the precision matrices. In contrast to other approaches, such as separate or joint estimation of the individual matrices, direct estimation does not require those matrices to be sparse, and thus can allow the individual networks to contain hub nodes. Under the assumption that the true differential network is sparse, the direct estimator is shown to be consistent in support recovery and estimation. It is also shown to outperform existing methods in simulations, and its properties are illustrated on gene expression data from late-stage ovarian cancer patients.

Testing for Pathway (in)Activation by Using Gaussian Graphical Models

“…Methods that focus on identification of local differences joint precision estimation in penalized fashion can be found in Guo et al (2011), Danaher et al (2014, Zhao et al (2014), Price et al (2015), Bilgrau et al (2015) and Saegusa and Shojaie (2016). Ha et al (2015) and Xia (2017) augmented such approaches by a post hoc test procedure for differential edge identification.…”

MDiNE: A model to estimate differential co-occurrence networks in microbiome studies

“…The Joint Graphical LASSO was proposed as a solution in the case of Gaussian data (Danaher et al, 2014). Similarly, a non-parametric method for differential network estimation was proposed by Zhao et al (2014). In this algorithm, the difference in precision matrices is modeled directly, whereas the precision matrix within each group is not explicitly estimated.…”

Adding Extra Knowledge in Scalable Learning of Sparse Differential Gaussian Graphical Models

“…Here µ c , µ d ∈ R p describe the mean vectors and Σ c , Σ d ∈ R p×p represent covariance matrices. The goal of differential GGMs is to estimate the structural change ∆ defined by [27] 2 .…”

“…(3) Constrained 1 minimization based. Diff-CLIME, another regularized convex program, was proposed to directly learn structural changes ∆ without going through the learning of each individual GGMs [26]. It uses an 1 minimization formulation constrained by the covariance-precision matching, reducing the estimation problem to solving linear programs.…”