Uncertainty quantification and false selection error rate (FSR) control are crucial in many high-consequence scenarios, so we need models with good interpretability. This article introduces the optimality function for the binary classification problem in selective classification. We prove the optimality of this function in oracle situations and provide a data-driven method under the condition of exchangeability. We demonstrate it can control global FSR with the finite sample assumption and successfully extend the above situation from binary to multi-class classification. Furthermore, we demonstrate that FSR can still be controlled without exchangeability, ultimately completing the proof using the martingale method.

翻译：不确定性量化与假选择错误率（FSR）控制在高风险场景中至关重要，因此需要具备良好可解释性的模型。本文针对选择性分类中的二分类问题引入最优性函数，证明该函数在理想化场景下的最优性，并提出一种基于可交换性假设的数据驱动方法。我们证明该方法能在有限样本假设下控制全局FSR，并将上述场景从二分类成功扩展至多分类。进一步，我们论证了无需可交换性假设仍可实现FSR控制，最终通过鞅方法完成理论证明。