Robust sparse Gaussian graphical modeling

Kei Hirose, Hironori Fujisawa, Jun Sese

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Gaussian graphical modeling is popular as a means of exploring network structures, such as gene regulatory networks and social networks. An L1 penalized maximum likelihood approach is often used to learn high-dimensional graphical models. However, the penalized maximum likelihood procedure is sensitive to outliers. To overcome this problem, we introduce a robust estimation procedure based on the γ-divergence. The proposed method has a redescending property, which is a desirable feature in robust statistics. The parameter estimation procedure is constructed using the Majorize-Minimization algorithm, which guarantees that the objective function monotonically decreases at each iteration. Extensive simulation studies show that our procedure performs much better than the existing methods, in particular, when the contamination ratio is large. Two real data analyses are used for illustration purposes.

Original languageEnglish
Pages (from-to)172-190
Number of pages19
JournalJournal of Multivariate Analysis
Volume161
DOIs
Publication statusPublished - Sep 1 2017

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Graphical Modeling
Maximum likelihood
Penalized Maximum Likelihood
Parameter estimation
Contamination
Genes
Statistics
Robust Statistics
Gene Regulatory Network
Robust Estimation
Graphical Models
Network Structure
Social Networks
Outlier
Parameter Estimation
Divergence
High-dimensional
Objective function
Simulation Study
Iteration

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

Cite this

Robust sparse Gaussian graphical modeling. / Hirose, Kei; Fujisawa, Hironori; Sese, Jun.

In: Journal of Multivariate Analysis, Vol. 161, 01.09.2017, p. 172-190.

Research output: Contribution to journalArticle

Hirose, Kei ; Fujisawa, Hironori ; Sese, Jun. / Robust sparse Gaussian graphical modeling. In: Journal of Multivariate Analysis. 2017 ; Vol. 161. pp. 172-190.
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