A large-deviation analysis for the maximum likelihood learning of tree structures
Author(s)Tong, Lang; Tan, Vincent Yan Fu; Anandkumar, Animashree; Willsky, Alan S.
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The problem of maximum-likelihood learning of the structure of an unknown discrete distribution from samples is considered when the distribution is Markov on a tree. Large-deviation analysis of the error in estimation of the set of edges of the tree is performed. Necessary and sufficient conditions are provided to ensure that this error probability decays exponentially. These conditions are based on the mutual information between each pair of variables being distinct from that of other pairs. The rate of error decay, or error exponent, is derived using the large-deviation principle. The error exponent is approximated using Euclidean information theory and is given by a ratio, to be interpreted as the signal-to-noise ratio (SNR) for learning. Numerical experiments show the SNR approximation is accurate.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Stochastic Systems Group
IEEE International Symposium on Information Theory, 2009. ISIT 2009.
Tan, V.Y.F. et al. “A large-deviation analysis for the maximum likelihood learning of tree structures.” Information Theory, 2009. ISIT 2009. IEEE International Symposium on. 2009. 1140-1144. Web.
Final published version
INSPEC Accession Number: 10842161
Error exponents, Euclidean Information Theory, Large-deviations, Tree structure learning