Estimating high dimensional faithful Gaussian Graphical Models by low-order conditioning

  • Authors:

  • Dhafer Malouche;Sylvie Sevestre-Ghalila

  • Affiliations:

  • LEGI-EPT-ESSAI, Tunisia, El Charguia;University El Manar, Tunisia, and University Ren Descarte, Paris, France

  • Venue:
  • AIA '08 Proceedings of the 26th IASTED International Conference on Artificial Intelligence and Applications
  • Year:
  • 2008

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Abstract

The aim of this paper is to devise a new PC-algorithm (partial correlation), uPC-algorithm, for estimating a high dimensional undirected graph associated to a faithful Gaussian Graphical Model. First, we define the separability order of a graph as the maximum cardinality among all its minimal separators. We construct a sequence of graphs by increasing the number of the conditioning variables. We prove that these graphs are nested and at a limited stage, equal to the separability order, this sequence is constant and equal to the true graph. Thus, the uPC-algorithm devised in this paper, is a step-down procedure based on a recursive estimation of these nested graphs. We show on simulated data its accuracy and consistency and we compare it with the 0--1 covariance graph estimation recently proposed by [11].