# Inference of Multiscale Gaussian Graphical Model

arXiv: https://arxiv.org/abs/2202.05775 · HTML: https://mlsanity.com/paper/2202.05775/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 71 references that are in the map.
- First posted on arXiv 11 Feb 2022.

## Builds on (most cited first, 11 of 11)

- [Network Lasso: Clustering and Optimization in Large Graphs](https://mlsanity.com/paper/1507.00280/) (2015)
- [Splitting Methods for Convex Clustering](https://mlsanity.com/paper/1304.0499/) (2013)
- [An Overview on the Estimation of Large Covariance and Precision Matrices](https://mlsanity.com/paper/1504.02995/) (2015)
- [The huge Package for High-dimensional Undirected Graph Estimation in R](https://mlsanity.com/paper/2006.14781/) (2020)
- [Block-diagonal covariance selection for high-dimensional Gaussian graphical models](https://mlsanity.com/paper/1511.04033/) (2015)
- [The Cluster Graphical Lasso for improved estimation of Gaussian graphical models](https://mlsanity.com/paper/1307.5339/) (2013)
- [Continuation of Nesterov's Smoothing for Regression with Structured Sparsity in High-Dimensional Neuroimaging](https://mlsanity.com/paper/1605.09658/) (2016)
- [Clustered Gaussian Graphical Model via Symmetric Convex Clustering](https://mlsanity.com/paper/1905.13251/) (2019)
- [Estimation of sparse Gaussian graphical models with hidden clustering structure](https://mlsanity.com/paper/2004.08115/) (2020)
- [Local Neighborhood Fusion in Locally Constant Gaussian Graphical Models](https://mlsanity.com/paper/1410.8766/) (2014)
- [Sparse Group Fused Lasso for Model Segmentation](https://mlsanity.com/paper/1912.07761/) (2019)

## Abstract (arXiv)

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.