Efficient \(F\) measure maximization via weighted maximum likelihood

摘要

The classification models obtained via maximum likelihood-based training do not necessarily reach the optimal \(F_\beta \)-measure for some user’s choice of \(\beta \) that is achievable with the chosen parametrization. In this work we link the weighted maximum entropy and the optimization of the expected \(F_\beta \)-measure, by viewing them in the framework of a general common multi-criteria optimization problem. As a result, each solution of the expected \(F_\beta \)-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 \(F_\beta \) using weighted maximum likelihood with dynamically adaptive weights.