F-measure Maximizing Logistic Regression

Logistic regression is a widely used method in several fields. When applying logistic regression to imbalanced data, for which majority classes dominate over minority classes, all class labels are estimated as `majority class.' In this article, we use an F-measure optimization method to improve the performance of logistic regression applied to imbalanced data. While many F-measure optimization methods adopt a ratio of the estimators to approximate the F-measure, the ratio of the estimators tends to have more bias than when the ratio is directly approximated. Therefore, we employ an approximate F-measure for estimating the relative density ratio. In addition, we define a relative F-measure and approximate the relative F-measure. We show an algorithm for a logistic regression weighted approximated relative to the F-measure. The experimental results using real world data demonstrated that our proposed method is an efficient algorithm to improve the performance of logistic regression applied to imbalanced data.