Tree-based Node Aggregation in Sparse Graphical Models
Abstract
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.
Cite
@article{arxiv.2101.12503,
title = {Tree-based Node Aggregation in Sparse Graphical Models},
author = {Ines Wilms and Jacob Bien},
journal= {arXiv preprint arXiv:2101.12503},
year = {2021}
}