The Joint Graphical Lasso for Inverse Covariance Estimation Across Multiple Classes

Abstract

Summary We consider the problem of estimating multiple related Gaussian graphical models from a high-dimensional data set with observations belonging to distinct classes. We propose the joint graphical lasso, which borrows strength across the classes in order to estimate multiple graphical models that share certain characteristics, such as the locations or weights of nonzero edges. Our approach is based upon maximizing a penalized log likelihood. We employ generalized fused lasso or group lasso penalties, and implement a fast ADMM algorithm to solve the corresponding convex optimization problems. The performance of the proposed method is illustrated through simulated and real data examples.

Pediatric obesity is associated with an altered gut microbiota and discordant shifts in Firmicutes populations

“…Indicator species analysis was performed using the indicspecies package (De Caceres et al ., 2009). Network analysis was performed for all OTUs present in at least 30% of samples as recommended in (Berry and Widder, 2014) using graphical lasso technique cclasso to mitigate biases associated with compositional data (Danaher et al ., 2014). Network topological and node‐level properties were determined using the igraph package (Csardi, 2015) and networks were visualized using Cytoscape (Shannon et al ., 2003).…”

Joint sparse canonical correlation analysis for detecting differential imaging genetics modules

“…Our main results in this paper presented an extension of sparse CCA to discover differential association modules from different disease statuses. Inspired by the idea of a joint sparse model (Baron et al, 2005) and fused graphical lasso (Danaher et al, 2014;Yang et al, 2015), we proposed an JSCCA method and verified its performance in a schizophrenia dataset. The dataset consists of fMRI data and SNP data with 116 healthy controls and 92 schizophrenia patients.…”

“…A very efficient algorithm for the solution is available (Danaher et al, 2014;Hocking et al, 2011). Specifically, (4) can be solved in successively three steps: a fusion step, a sparsification step and a normalization step.…”

“…; v K are the canonical vectors of X k and Y k respectively, jjVjj 2 F ¼ P k jjv k jj 2 2 ; k w ; k v ; s are regularization parameters. In (3), we apply the general fused lasso penalty (Danaher et al, 2014;Hoefling, 2010) on V. The L 1 -penalty on each v k , controlled by k v , encourages the sparsity over each individual canonical vector. The L 1 -penalty on the differences between every two canonical vectors from different classes encourages them to share a similar structure.…”

“…We also apply a fused lasso penalty on the K canonical vectors for genetic data to encourage them to share a similar (but not the same) structure. The fused lasso penalty is chosen because it has been successfully applied to jointly estimate multiple graphical models to find differential dependency networks (Danaher et al, 2014;Tian et al, 2014;Yang et al, 2015). Inspired by the optimization framework for penalized CCA in , we design an efficient algorithm based on block coordinate descent for solving JSCCA.…”