Learning high-dimensional Markov forest distributions: Analysis of error rates
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Willsky-2011-Learning High.pdf
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323.6 KB
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Author(s)
Tan, Vincent Yan Fu
Anandkumar, Animashree
Willsky, Alan S.
Date Issued
May 2011
Journal
Journal of Machine Learning Research
Publisher
MIT Press
Citation
Tan, Vincent Y.F., Animashree Anandkumar and Alan S. Willsky. "Learning High-Dimensional Markov Forest Distributions: Analysis of Error Rates." Journal of Machine Learning Research, 12 (2011) 1617-1653.
Version
Final published version
Abstract
The problem of learning forest-structured discrete graphical models from i.i.d. samples is considered. An algorithm based on pruning of the Chow-Liu tree through adaptive thresholding is proposed. It is shown that this algorithm is both structurally consistent and risk consistent and the error probability of structure learning decays faster than any polynomial in the number of samples under fixed model size. For the high-dimensional scenario where the size of the model d and the number of edges k scale with the number of samples n, sufficient conditions on (n,d,k) are given for the algorithm to satisfy structural and risk consistencies. In addition, the extremal structures for learning are identified; we prove that the independent (resp., tree) model is the hardest (resp., easiest) to learn using the proposed algorithm in terms of error rates for structure learning.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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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.
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DOI of Published Version
http://jmlr.csail.mit.edu/papers/volume12/tan11a/tan11a.pdf
