Classification with Abstention Under Class-Conditional Error Constraints

2026-09-18

AI Summary

研究了在类条件错误约束下通过最小化弃权同时控制两类错误的方法，提出代理损失公式并转化为优化问题求解。

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.

Problem

• binary classification
• abstention
• class-conditional error constraints

Innovation

• abstention
• class-conditional error constraints
• surrogate-loss formulations
• constrained optimization