# Classification with Abstention Under Class-Conditional Error Constraints

arXiv: https://arxiv.org/abs/2609.22632 · HTML: https://mlsanity.com/paper/2609.22632/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 43 references that are in the map.
- First posted on arXiv 18 Sep 2026.

## Builds on (most cited first, 19 of 19)

- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [Consistent Estimators for Learning to Defer to an Expert](https://mlsanity.com/paper/2006.01862/) (2020)
- [A vector-contraction inequality for Rademacher complexities](https://mlsanity.com/paper/1605.00251/) (2016)
- [Optimal strategies for reject option classifiers](https://mlsanity.com/paper/2101.12523/) (2021)
- [Selective Classification via One-Sided Prediction](https://mlsanity.com/paper/2010.07853/) (2020)
- [Neyman-Pearson (NP) classification algorithms and NP receiver operating characteristics (NP-ROC)](https://mlsanity.com/paper/1608.03109/) (2016)
- [Neyman-Pearson classification: parametrics and sample size requirement](https://mlsanity.com/paper/1802.02557/) (2018)
- [Consistent Algorithms for Multiclass Classification with a Reject Option](https://mlsanity.com/paper/1505.04137/) (2015)
- [Uncertainty-aware abstention in medical diagnosis based on medical texts](https://mlsanity.com/paper/2502.18050/) (2025)
- [Neyman-Pearson Classification under High-Dimensional Settings](https://mlsanity.com/paper/1508.03106/) (2015)
- [Machine Learning with Abstention for Automated Liver Disease Diagnosis](https://mlsanity.com/paper/1811.04463/) (2018)
- [Transfer Neyman-Pearson Algorithm for Outlier Detection](https://mlsanity.com/paper/2501.01525/) (2025)
- [Binary Classification with Bounded Abstention Rate](https://mlsanity.com/paper/1905.09561/) (2019)
- [Tight Rates in Supervised Outlier Transfer Learning](https://mlsanity.com/paper/2310.04686/) (2023)
- [FiFAR: A Fraud Detection Dataset for Learning to Defer](https://mlsanity.com/paper/2312.13218/) (2023)
- [Distribution-Free Rates in Neyman-Pearson Classification](https://mlsanity.com/paper/2402.09560/) (2024)
- [Neyman-Pearson Classification under Both Null and Alternative Distributions Shift](https://mlsanity.com/paper/2511.06641/) (2025)
- [Cost-Sensitive Conformal Prediction and Human-in-the-Loop Abstention for Imbalanced High-Stakes Decision Support: A Multi-Domain Benchmark](https://mlsanity.com/paper/2607.27143/) (2026)

## Abstract (arXiv)

We study binary classification with abstention under separate class-conditional error constraints, with the objective of minimizing abstention while keeping both errors below prescribed thresholds. We characterize the distribution-free minimax rate of excess abstention risk, up to logarithmic factors, in terms of the complexity of the hypothesis class and the sample size. To make the framework amenable to computation with models such as neural networks, we introduce surrogate-loss formulations and derive finite-sample guarantees for excess surrogate ambiguity risk. We formulate the resulting learning task as a constrained optimization problem and characterize its computational complexity in the convex setting. Finally, we evaluate our approach on various datasets and compare its performance with a competing method for this problem.