Factorization of probability distributions and matroid representations by partitions

The information divergence of a probability measure P from a hierarchical log-linear model is maximized over all P. A new upper bound on the maximum will be presented. For the models given by the bases of a matroid, the tightness of the bound will be analyzed and related to matroid representations by partitions. Connections to ML estimation from bad data and to secret sharing schemes will be discussed.