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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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    1. Tan, Kean Ming & Witten, Daniela & Shojaie, Ali, 2015. "The cluster graphical lasso for improved estimation of Gaussian graphical models," Computational Statistics & Data Analysis, Elsevier, vol. 85(C), pages 23-36.
    2. Peng, Jie & Wang, Pei & Zhou, Nengfeng & Zhu, Ji, 2009. "Partial Correlation Estimation by Joint Sparse Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 735-746.
    3. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    4. Yuanpei Cao & Wei Lin & Hongzhe Li, 2019. "Large Covariance Estimation for Compositional Data Via Composition-Adjusted Thresholding," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 759-772, April.
    5. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    6. Zachary D Kurtz & Christian L Müller & Emily R Miraldi & Dan R Littman & Martin J Blaser & Richard A Bonneau, 2015. "Sparse and Compositionally Robust Inference of Microbial Ecological Networks," PLOS Computational Biology, Public Library of Science, vol. 11(5), pages 1-25, May.
    7. Cai, Tony & Liu, Weidong & Luo, Xi, 2011. "A Constrained â„“1 Minimization Approach to Sparse Precision Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 594-607.
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