Classification with Abstention Under Class-Conditional Error Constraints
Abstract
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.
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BibTeX
@misc{kalan2026classification,
title = {{Classification with Abstention Under Class-Conditional Error Constraints}},
author = {Mohammadreza M. Kalan and Yuyang Deng and Sanaz Hamidi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22632},
eprint = {2609.22632},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22632},
}
RIS
TY - UNPB
TI - Classification with Abstention Under Class-Conditional Error Constraints
AU - Mohammadreza M. Kalan
AU - Yuyang Deng
AU - Sanaz Hamidi
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.22632
UR - https://arxiv.org/abs/2609.22632
AB - 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.
ER -