Skip to main content
eScholarship
Open Access Publications from the University of California

UC Irvine

UC Irvine Previously Published Works bannerUC Irvine

High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion

  • Author(s): Anandkumar, Animashree;
  • Tan, Vincent Y.F.;
  • Huang, Furong;
  • Willsky, Alan S.
  • et al.
Abstract

We consider the problem of high-dimensional Gaussian graphical model selection.  We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional covariances. Under a set of transparent conditions, we establish structural consistency (or sparsistency) for the proposed algorithm, when the number of samples n = Ω(J−2 log p), where p is the number of variables and Jmin is the minimum (absolute) edge potential of the graphical model. The sufficient conditions for sparsistency are based on the notion of walk-summability of the model and the presence of sparse local vertex separators in the  underlying graph.  We also derive novel non-asymptotic necessary conditions on the number of samples required for sparsistency.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View