# F-measure Maximizing Logistic Regression

## TL;DR

This paper introduces a novel F-measure optimization method for logistic regression to enhance classification performance on imbalanced datasets, addressing bias issues in previous ratio-based approaches.

## Contribution

It proposes an approximate F-measure approach using relative density ratios and develops an algorithm for weighted logistic regression tailored for imbalanced data.

## Key findings

- Improved F-measure performance on real-world imbalanced datasets
- Efficient algorithm for logistic regression with relative F-measure optimization
- Demonstrated superiority over traditional methods in experimental results

## Abstract

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.