Divergence From Factorizable Distributions and Matroid Representations by Partitions

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.