High-Dimensional Graphical Model Selection: Tractable Graph Families and Necessary Conditions
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AnandkumarTanWillskyNIPS11.pdf
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Author(s)
Anandkumar, Animashree
Tan, Vincent Y. F.
Willsky, Alan S.
Date Issued
December 2011
Journal
Advances in Neural Information Processing Systems 24
Publisher
Neural Information Processing Systems Foundation
Citation
Anandkumar, Animashree, Vincent Tan, and Alan S. Willsky. “High-Dimensional Graphical Model Selection: Tractable Graph Families and Necessary Conditions.” Advances in Neural Information Processing Systems 24. Ed. J. Shawe-Taylor et al. 2011. 1863–1871. Print.
Version
Author's final manuscript
Abstract
We consider the problem of Ising and Gaussian graphical model selection given n i.i.d. samples from the model. We propose an efficient threshold-based algorithm for structure estimation based known as conditional mutual information test. This simple local algorithm requires only low-order statistics of the data and decides whether two nodes are neighbors in the unknown graph. Under some transparent assumptions, we establish that the proposed algorithm is structurally consistent (or sparsistent) when the number of samples scales as n= Omega(J_{min}^{-4} log p), where p is the number of nodes and J_{min} is the minimum edge potential. We also prove novel non-asymptotic necessary conditions for graphical model selection.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
http://books.nips.cc/papers/files/nips24/NIPS2011_1050.pdf
