# Tree-based Node Aggregation in Sparse Graphical Models

arXiv: https://arxiv.org/abs/2101.12503 · HTML: https://mlsanity.com/paper/2101.12503/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 39 references that are in the map.
- First posted on arXiv 29 Jan 2021.

## Builds on (most cited first, 6 of 6)

- [Trend Filtering on Graphs](https://mlsanity.com/paper/1410.7690/) (2014)
- [High-Dimensional Inference for Cluster-Based Graphical Models](https://mlsanity.com/paper/1806.05139/) (2018)
- [The Cluster Graphical Lasso for improved estimation of Gaussian graphical models](https://mlsanity.com/paper/1307.5339/) (2013)
- [Rare Feature Selection in High Dimensions](https://mlsanity.com/paper/1803.06675/) (2018)
- [Large Covariance Estimation for Compositional Data via Composition-Adjusted Thresholding](https://mlsanity.com/paper/1601.04397/) (2016)
- [The Simulator: An Engine to Streamline Simulations](https://mlsanity.com/paper/1607.00021/) (2016)

## Built on by (most cited first, 3 of 3)

- [Controlling the False Split Rate in Tree-Based Aggregation](https://mlsanity.com/paper/2108.05350/) (2021)
- [Sparse outlier-robust PCA for multi-source data](https://mlsanity.com/paper/2407.16299/) (2024)
- [Clusterpath Gaussian Graphical Modeling](https://mlsanity.com/paper/2407.00644/) (2024)

## Abstract (arXiv)

High-dimensional graphical models are often estimated using regularization that is aimed at reducing the number of edges in a network. In this work, we show how even simpler networks can be produced by aggregating the nodes of the graphical model. We develop a new convex regularized method, called the tree-aggregated graphical lasso or tag-lasso, that estimates graphical models that are both edge-sparse and node-aggregated. The aggregation is performed in a data-driven fashion by leveraging side information in the form of a tree that encodes node similarity and facilitates the interpretation of the resulting aggregated nodes. We provide an efficient implementation of the tag-lasso by using the locally adaptive alternating direction method of multipliers and illustrate our proposal's practical advantages in simulation and in applications in finance and biology.