A proximal point dual newton algorithm for solving group graphical lasso problems

YANGJING ZHANG, NING ZHANG, DEFENG SUN, KIM CHUAN TOH

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

Undirected graphical models have been especially popular for learning the conditional independence structure among a large number of variables where the observations are drawn independently and identically from the same distribution. However, many modern statistical problems would involve categorical data or time-varying data, which might follow different but related underlying distributions. In order to learn a collection of related graphical models simultaneously, various joint graphical models inducing sparsity in graphs and similarity across graphs have been proposed. In this paper, we aim to propose an implementable proximal point dual Newton algorithm (PPDNA) for solving the group graphical Lasso model, which encourages a shared pattern of sparsity across graphs. Though the group graphical Lasso regularizer is nonpolyhedral, the asymptotic superlinear convergence of our proposed method PPDNA can be obtained by leveraging on the local Lipschitz continuity of the Karush-Kuhn-Tucker solution mapping associated with the group graphical Lasso model. A variety of numerical experiments on real data sets illustrates that the PPDNA for solving the group graphical Lasso model can be highly efficient and robust.

Original languageEnglish
Pages (from-to)2197-2220
Number of pages24
JournalSIAM Journal on Optimization
Volume30
Issue number3
DOIs
Publication statusE-pub ahead of print - 12 Aug 2020

Keywords

  • Group graphical Lasso
  • Lipschitz continuity
  • Proximal point algorithm
  • Semismooth Newton method

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science

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