Inference of Multiscale Gaussian Graphical Model

TL;DR

This paper introduces Multiscale Graphical Lasso (MGLasso), a novel method that simultaneously infers sparse Gaussian graphical models and clustering structures at multiple scales to enhance interpretability in high-dimensional data analysis.

Contribution

The paper proposes MGLasso, a new convex framework combining multiscale clustering with graphical model inference, extending sparse group fused lasso to undirected graphs.

Findings

MGLasso outperforms existing methods on synthetic data.

Effective in real-world microbiome and methylation datasets.

Provides interpretable multiscale network structures.

Abstract

Gaussian Graphical Models (GGMs) are widely used in high-dimensional data analysis to synthesize the interaction between variables. In many applications, such as genomics or image analysis, graphical models rely on sparsity and clustering to reduce dimensionality and improve performances. This paper explores a slightly different paradigm where clustering is not knowledge-driven but performed simultaneously with the graph inference task. We introduce a novel Multiscale Graphical Lasso (MGLasso) to improve networks interpretability by proposing graphs at different granularity levels. The method estimates clusters through a convex clustering approach - a relaxation of k-means, and hierarchical clustering. The conditional independence graph is simultaneously inferred through a neighborhood selection scheme for undirected graphical models. MGLasso extends and generalizes the sparse group fused lasso problem to undirected graphical models. We use continuation with Nesterov smoothing in a shrinkage-thresholding algorithm (CONESTA) to propose a regularization path of solutions along the group fused Lasso penalty, while the Lasso penalty is kept constant. Extensive experiments on synthetic data compare the performances of our model to state-of-the-art clustering methods and network inference models. Applications to gut microbiome data and poplar's methylation mixed with transcriptomic data are presented.