# Calibrated Surrogate Maximization of Linear-fractional Utility in Binary Classification

arXiv: https://arxiv.org/abs/1905.12511 · HTML: https://mlsanity.com/paper/1905.12511/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2019.

## Built on by (most cited first, 10 of 10)

- [Implicit Rate-Constrained Optimization of Non-decomposable Objectives](https://mlsanity.com/paper/2107.10960/) (2021)
- [RankSEG: A Consistent Ranking-based Framework for Segmentation](https://mlsanity.com/paper/2206.13086/) (2022)
- [Principled Algorithms for Optimizing Generalized Metrics in Binary Classification](https://mlsanity.com/paper/2512.23133/) (2025)
- [Multiclass Learning from Noisy Labels for Non-decomposable Performance Measures](https://mlsanity.com/paper/2402.01055/) (2024)
- [Enriching Disentanglement: From Logical Definitions to Quantitative Metrics](https://mlsanity.com/paper/2305.11512/) (2023)
- [Noisy Image Segmentation With Soft-Dice](https://mlsanity.com/paper/2304.00801/) (2023)
- [Aligning Multiclass Neural Network Classifier Criterion with Task Performance Metrics](https://mlsanity.com/paper/2405.20954/) (2024)
- [Principled Algorithms for Optimizing Generalized Metrics in Multi-Label Learning](https://mlsanity.com/paper/2605.28767/) (2026)
- [Weighted Score-Oriented Losses for Temporally Localized Event Prediction](https://mlsanity.com/paper/2606.23145/) (2026)
- [Exponential Convex Calibration Dimension for the Multi-Label Jaccard Measure](https://mlsanity.com/paper/2608.13549/) (2026)

## Abstract (arXiv)

Complex classification performance metrics such as the Fβ-measure and Jaccard index are often used, in order to handle class-imbalanced cases such as information retrieval and image segmentation. These performance metrics are not decomposable, that is, they cannot be expressed in a per-example manner, which hinders a straightforward application of M-estimation widely used in supervised learning. In this paper, we consider linear-fractional metrics, which are a family of classification performance metrics that encompasses many standard ones such as the Fβ-measure and Jaccard index, and propose methods to directly maximize performances under those metrics. A clue to tackle their direct optimization is a calibrated surrogate utility, which is a tractable lower bound of the true utility function representing a given metric. We characterize sufficient conditions which make the surrogate maximization coincide with the maximization of the true utility. Simulation results on benchmark datasets validate the effectiveness of our calibrated surrogate maximization especially if the sample sizes are extremely small.