Tree-based Node Aggregation in Sparse Graphical Models

High-dimensional graphical models are often estimated using regularization.

The literature primarily relies on edge sparsity as a simplifying assumption. In this work, we combine this edge dimension reduction through sparsity with node dimension reduction through aggregation. In particular, we seek to merge nodes so as to obtain more parsimonious graphical models that provide a simpler description of the dependence structure than would otherwise be possible. We develop a convex regularizer, called the tree-aggregated graphical lasso or tag-lasso, to perform this node aggregation in sparse graphical models. 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 illustrate our proposal's practical advantages in simulations and applications.