High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion
Name
Anandkumar-2012-High-Dimensional Gaussian Graphical Model Selection.pdf
Size
467.58 KB
Format
Adobe PDF
Checksum (MD5)
bd132d4402c0107f3c9e0ed456a2f5bc
Author(s)
Willsky, Alan S.
Tan, Vincent Yan Fu
Anandkumar, Animashree
Date Issued
January 2012
Journal
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
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=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.
MIT Department
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 Group
Terms of Use
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.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.48550/arXiv.1107.1270
