Tree-based Node Aggregation in Sparse Graphical Models

Ines Wilms, Jacob Bien

Research output: Working paper / PreprintWorking paper

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.
Original languageEnglish
PublisherCornell University - arXiv
Number of pages41
Publication statusPublished - 2021

Publication series

SeriesarXiv.org
NumberarXiv:2101.12503

Keywords

  • aggregation
  • graphic model
  • high-dimensionality
  • regularization
  • sparsity

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