Weighted maximum likelihood loss as a convenient shortcut to optimizing the F-measure of maximum entropy classifiers

We link the weighted maximum entropy and the optimization of the expected Fβmeasure, by viewing them in the framework of a general common multi-criteria optimization problem. As a result, each solution of the expected Fβ-measure maximization can be realized as a weighted maximum likelihood solution a well understood and behaved problem. The specific structure of maximum entropy models allows us to approximate this characterization via the much simpler class-wise weighted maximum likelihood. Our approach reveals any probabilistic learning scheme as a specific trade-off between different objectives and provides the framework to link it to the expectedFβ-measure.