# Learning by Minimizing the Sum of Ranked Range

arXiv: https://arxiv.org/abs/2010.01741 · HTML: https://mlsanity.com/paper/2010.01741/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2020.

## Built on by (most cited first, 27 of 27)

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- [TkML-AP: Adversarial Attacks to Top-k Multi-Label Learning](https://mlsanity.com/paper/2108.00146/) (2021)
- [Rank-based Decomposable Losses in Machine Learning: A Survey](https://mlsanity.com/paper/2207.08768/) (2022)
- [Sum of Ranked Range Loss for Supervised Learning](https://mlsanity.com/paper/2106.03300/) (2021)
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- [Distributionally Robust Survival Analysis: A Novel Fairness Loss Without Demographics](https://mlsanity.com/paper/2211.10508/) (2022)
- [UU-Mamba: Uncertainty-aware U-Mamba for Cardiac Image Segmentation](https://mlsanity.com/paper/2405.17496/) (2024)
- [Fairness in Survival Analysis with Distributionally Robust Optimization](https://mlsanity.com/paper/2409.10538/) (2024)
- [Robust COVID-19 Detection in CT Images with CLIP](https://mlsanity.com/paper/2403.08947/) (2024)
- [Open-Eye: An Open Platform to Study Human Performance on Identifying AI-Synthesized Faces](https://mlsanity.com/paper/2205.06680/) (2022)
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- [Robust AI-Generated Face Detection with Imbalanced Data](https://mlsanity.com/paper/2505.02182/) (2025)
- [Robust Fairness Vision-Language Learning for Medical Image Analysis](https://mlsanity.com/paper/2505.03153/) (2025)
- [An Uncertainty-Aware Generalization Framework for Cardiovascular Image Segmentation](https://mlsanity.com/paper/2409.14305/) (2024)
- [Meta-Learning with Heterogeneous Tasks](https://mlsanity.com/paper/2410.18894/) (2024)
- [GBM-based Bregman Proximal Algorithms for Constrained Learning](https://mlsanity.com/paper/2308.10767/) (2023)
- [Synergistic Network Learning and Label Correction for Noise-robust Image Classification](https://mlsanity.com/paper/2202.13472/) (2022)
- [When Measures are Unreliable: Imperceptible Adversarial Perturbations toward Top-k Multi-Label Learning](https://mlsanity.com/paper/2309.00007/) (2023)
- [Statistical Robustness of Interval CVaR Based Regression Models under Perturbation and Contamination](https://mlsanity.com/paper/2601.11420/) (2026)

## Abstract (arXiv)

In forming learning objectives, one oftentimes needs to aggregate a set of individual values to a single output. Such cases occur in the aggregate loss, which combines individual losses of a learning model over each training sample, and in the individual loss for multi-label learning, which combines prediction scores over all class labels. In this work, we introduce the sum of ranked range (SoRR) as a general approach to form learning objectives. A ranked range is a consecutive sequence of sorted values of a set of real numbers. The minimization of SoRR is solved with the difference of convex algorithm (DCA). We explore two applications in machine learning of the minimization of the SoRR framework, namely the AoRR aggregate loss for binary classification and the TKML individual loss for multi-label/multi-class classification. Our empirical results highlight the effectiveness of the proposed optimization framework and demonstrate the applicability of proposed losses using synthetic and real datasets.