  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.
