High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion
Author(s)
Willsky, Alan S.; Tan, Vincent Yan Fu; Anandkumar, Animashree
DownloadAnandkumar-2012-High-Dimensional Gaussian Graphical Model Selection.pdf (467.5Kb)
PUBLISHER_POLICY
Publisher Policy
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Terms of use
Metadata
Show full item recordAbstract
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=omega(J_{min}^{-2} log p), where p is the number of variables and J_{min} 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.
Date issued
2012-01Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems; Massachusetts Institute of Technology. Stochastic Systems GroupJournal
Journal of Machine Learning Research
Publisher
Association for Computing Machinery (ACM)
Citation
Anandkumar, Animashree, Vincent Y. F. Tan, and Alan. S. Willsky. "High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion." Journal of Machine Learning Research 13.1 (2012): 2293-2337.
Version: Final published version
ISSN
1532-4435
1533-7928