# Classification with Rejection Based on Cost-sensitive Classification

arXiv: https://arxiv.org/abs/2010.11748 · HTML: https://mlsanity.com/paper/2010.11748/

## Key facts

- Cited by 55 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2020.

## Built on by (most cited first, 30 of 55)

- [Machine Learning with a Reject Option: A survey](https://mlsanity.com/paper/2107.11277/) (2021)
- [Is Out-of-Distribution Detection Learnable?](https://mlsanity.com/paper/2210.14707/) (2022)
- [Who Should Predict? Exact Algorithms For Learning to Defer to Humans](https://mlsanity.com/paper/2301.06197/) (2023)
- [Calibrated Learning to Defer with One-vs-All Classifiers](https://mlsanity.com/paper/2202.03673/) (2022)
- [Learning Noise Transition Matrix from Only Noisy Labels via Total Variation Regularization](https://mlsanity.com/paper/2102.02414/) (2021)
- [Learning to Defer to Multiple Experts: Consistent Surrogate Losses, Confidence Calibration, and Conformal Ensembles](https://mlsanity.com/paper/2210.16955/) (2022)
- [When Does Confidence-Based Cascade Deferral Suffice?](https://mlsanity.com/paper/2307.02764/) (2023)
- [Sample Efficient Learning of Predictors that Complement Humans](https://mlsanity.com/paper/2207.09584/) (2022)
- [Predictor-Rejector Multi-Class Abstention: Theoretical Analysis and Algorithms](https://mlsanity.com/paper/2310.14772/) (2023)
- [Calibrated Selective Classification](https://mlsanity.com/paper/2208.12084/) (2022)
- [Learning to Reject with a Fixed Predictor: Application to Decontextualization](https://mlsanity.com/paper/2301.09044/) (2023)
- [Learning to Defer to a Population: A Meta-Learning Approach](https://mlsanity.com/paper/2403.02683/) (2024)
- [In Defense of Softmax Parametrization for Calibrated and Consistent Learning to Defer](https://mlsanity.com/paper/2311.01106/) (2023)
- [Realizable H-Consistent and Bayes-Consistent Loss Functions for Learning to Defer](https://mlsanity.com/paper/2407.13732/) (2024)
- [Towards Better Selective Classification](https://mlsanity.com/paper/2206.09034/) (2022)
- [A Universal Growth Rate for Learning with Smooth Surrogate Losses](https://mlsanity.com/paper/2405.05968/) (2024)
- [Mastering Multiple-Expert Routing: Realizable H-Consistency and Strong Guarantees for Learning to Defer](https://mlsanity.com/paper/2506.20650/) (2025)
- [Surrogate Regret Bounds for Polyhedral Losses](https://mlsanity.com/paper/2110.14031/) (2021)
- [Plugin estimators for selective classification with out-of-distribution detection](https://mlsanity.com/paper/2301.12386/) (2023)
- [Budgeted Multiple-Expert Deferral](https://mlsanity.com/paper/2510.26706/) (2025)
- [Regression with Cost-based Rejection](https://mlsanity.com/paper/2311.04550/) (2023)
- [Unsupervised Anomaly Detection with Rejection](https://mlsanity.com/paper/2305.13189/) (2023)
- [Online Algorithms for Hierarchical Inference in Deep Learning applications at the Edge](https://mlsanity.com/paper/2304.00891/) (2023)
- [Unified Risk Analysis for Weakly Supervised Learning](https://mlsanity.com/paper/2309.08216/) (2023)
- [Learning to Complement with Multiple Humans](https://mlsanity.com/paper/2311.13172/) (2023)
- [A Unifying Post-Processing Framework for Multi-Objective Learn-to-Defer Problems](https://mlsanity.com/paper/2407.12710/) (2024)
- [Learning Conservative Neural Control Barrier Functions from Offline Data](https://mlsanity.com/paper/2505.00908/) (2025)
- [Stratified Adversarial Robustness with Rejection](https://mlsanity.com/paper/2305.01139/) (2023)
- [Online Decision Mediation](https://mlsanity.com/paper/2310.18601/) (2023)
- [Classification with Conceptual Safeguards](https://mlsanity.com/paper/2411.04342/) (2024)

## Abstract (arXiv)

The goal of classification with rejection is to avoid risky misclassification in error-critical applications such as medical diagnosis and product inspection. In this paper, based on the relationship between classification with rejection and cost-sensitive classification, we propose a novel method of classification with rejection by learning an ensemble of cost-sensitive classifiers, which satisfies all the following properties: (i) it can avoid estimating class-posterior probabilities, resulting in improved classification accuracy, (ii) it allows a flexible choice of losses including non-convex ones, (iii) it does not require complicated modifications when using different losses, (iv) it is applicable to both binary and multiclass cases, and (v) it is theoretically justifiable for any classification-calibrated loss. Experimental results demonstrate the usefulness of our proposed approach in clean-labeled, noisy-labeled, and positive-unlabeled classification.