Tree-based Node Aggregation in Sparse Graphical Models
This work addresses the need for more interpretable and simpler graphical models in fields like finance and biology, though it appears incremental as it builds on existing regularization techniques.
The authors tackled the problem of simplifying high-dimensional graphical models by introducing a method that aggregates nodes to produce simpler networks, resulting in a new convex regularized method called tag-lasso that estimates models that are both edge-sparse and node-aggregated, with practical advantages demonstrated in simulations and applications in finance and biology.
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.