F-measure maximizing logistic regression

Logistic regression is a widely used method in several fields. When applying logistic regression to imbalanced data, wherein the majority classes dominate the minority classes, all class labels are estimated as "majority class." In this study, we use an F-measure optimization method to improve the performance of logistic regression applied to imbalanced data. Although many F-measure optimization methods adopt a ratio of the estimators to approximate the F-measure, the ratio of the estimators tends to exhibit more bias than when the ratio is directly approximated. Therefore, we employ an approximate F-measure to estimate the relative density ratio. In addition, we define and approximate a relative F-measure. We present an algorithm for a logistic regression weighted approximation relative to the F-measure. The results of an experiment using real world data demonstrate that our proposed algorithm can efficiently improve the performance of logistic regression applied to imbalanced data.