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Tree-based Node Aggregation in Sparse Graphical Models

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  • Ines Wilms
  • Jacob Bien

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.

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  • Ines Wilms & Jacob Bien, 2021. "Tree-based Node Aggregation in Sparse Graphical Models," Papers 2101.12503, arXiv.org.
    • Handle: RePEc:arx:papers:2101.12503
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    References listed on IDEAS

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