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The classification models obtained via maximum likelihood-based training do not necessarily reach the optimal $$F_\\beta $$ F β -measure for some user's choice of $$\\beta $$ β that is achievable with the chosen parametrization. In this work we link the weighted maximum entropy and the optimization of the expected $$F_\\beta $$ F β -measure, by viewing them in the framework of a general common multi-criteria optimization problem. As a result, each solution of the expected $$F_\\beta $$ F β -measure maximization can be realized as a weighted maximum likelihood solution within the maximum entropy model - a well understood and behaved problem for which standard (off the shelf) gradient methods can be used. Based on this insight, we present an efficient algorithm for optimization of the expected $$F_\\beta $$ F β using weighted maximum likelihood with dynamically adaptive weights.

Efficient $$F$$ F measure maximization via weighted maximum likelihood