Divergence from factorizable distributions and matroid representations by partitions

Authors:
František Matúš
Affiliations:
Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Prague, Czech Republic
Venue:
IEEE Transactions on Information Theory
Year:
2009

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Abstract

Maximization of the information divergence from any hierarchical log-linear model is studied. A new upper bound on the maximum is presented and its tightness analyzed. For the models given by the bases of a matroid, the latter is related to matroid representations by partitions or, equivalently, to ideal secret-sharing schemes. A new link between the divergence maximization, the maximum-likelihood principle, and secret sharing is established.