# Clusterpath Gaussian Graphical Modeling

arXiv: https://arxiv.org/abs/2407.00644 · HTML: https://mlsanity.com/paper/2407.00644/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 80 references that are in the map.
- First posted on arXiv 30 Jun 2024.

## Builds on (most cited first, 21 of 21)

- [A Unified Framework for Structured Graph Learning via Spectral Constraints](https://mlsanity.com/paper/1904.09792/) (2019)
- [Splitting Methods for Convex Clustering](https://mlsanity.com/paper/1304.0499/) (2013)
- [Node-Based Learning of Multiple Gaussian Graphical Models](https://mlsanity.com/paper/1303.5145/) (2013)
- [Convex Clustering: Model, Theoretical Guarantee and Efficient Algorithm](https://mlsanity.com/paper/1810.02677/) (2018)
- [Algorithms for Learning Graphs in Financial Markets](https://mlsanity.com/paper/2012.15410/) (2020)
- [Convex Biclustering](https://mlsanity.com/paper/1408.0856/) (2014)
- [Estimation of Graphical Models through Structured Norm Minimization](https://mlsanity.com/paper/1609.09010/) (2016)
- [Simultaneous Clustering and Estimation of Heterogeneous Graphical Models](https://mlsanity.com/paper/1611.09391/) (2016)
- [Dynamic Visualization and Fast Computation for Convex Clustering via Algorithmic Regularization](https://mlsanity.com/paper/1901.01477/) (2019)
- [High-Dimensional Inference for Cluster-Based Graphical Models](https://mlsanity.com/paper/1806.05139/) (2018)
- [Biconvex Clustering](https://mlsanity.com/paper/2008.01760/) (2020)
- [The Cluster Graphical Lasso for improved estimation of Gaussian graphical models](https://mlsanity.com/paper/1307.5339/) (2013)
- [Multilayer Clustered Graph Learning](https://mlsanity.com/paper/2010.15456/) (2020)
- [On the inconsistency of ℓ1-penalised sparse precision matrix estimation](https://mlsanity.com/paper/1603.02532/) (2016)
- [Partial Correlation Graphical LASSO](https://mlsanity.com/paper/2104.10099/) (2021)
- [Convex Clustering through MM: An Efficient Algorithm to Perform Hierarchical Clustering](https://mlsanity.com/paper/2211.01877/) (2022)
- [Tree-based Node Aggregation in Sparse Graphical Models](https://mlsanity.com/paper/2101.12503/) (2021)
- [Clustered Gaussian Graphical Model via Symmetric Convex Clustering](https://mlsanity.com/paper/1905.13251/) (2019)
- [A Canonical Representation of Block Matrices with Applications to Covariance and Correlation Matrices](https://mlsanity.com/paper/2012.02698/) (2020)
- [Learning block structured graphs in Gaussian graphical models](https://mlsanity.com/paper/2206.14274/) (2022)
- [Simultaneous Identification of Sparse Structures and Communities in Heterogeneous Graphical Models](https://mlsanity.com/paper/2405.09841/) (2024)

## Abstract (arXiv)

Graphical models serve as effective tools for visualizing conditional dependencies between variables. However, as the number of variables grows, interpretation becomes increasingly difficult, and estimation uncertainty increases due to the large number of parameters relative to the number of observations. To address these challenges, we introduce the Clusterpath estimator of the Gaussian Graphical Model (CGGM) that encourages variable clustering in the graphical model in a data-driven way. Through the use of an aggregation penalty, we group variables together, which in turn results in a block-structured precision matrix whose block structure remains preserved in the covariance matrix. The CGGM estimator is formulated as the solution to a convex optimization problem, making it easy to incorporate other popular penalization schemes which we illustrate through the combination of an aggregation and sparsity penalty. We present a computationally efficient implementation of the CGGM estimator by using a cyclic block coordinate descent algorithm. In simulations, we show that CGGM not only matches, but oftentimes outperforms other state-of-the-art methods for variable clustering in graphical models. We also demonstrate CGGM's practical advantages and versatility on a diverse collection of empirical applications.