优化的确定性等价风险控制预测集
Optimized Certainty Equivalent Risk-Controlling Prediction Sets
AI总结：
本文提出OCE-RCPS框架，通过上置信界提供高概率保证，有效控制风险度量如CVaR和熵风险，在图像分割任务中表现出更高的可靠性。
摘要：
在医疗图像分割等安全关键应用中，预测系统必须提供超越传统预期损失控制的可靠性保证。虽然风险控制预测集（RCPS）提供了对预期风险的概率保证，但它们未能捕捉到尾部行为和最坏情况，这些在高风险环境中至关重要。本文介绍了一种新的优化确定性等价RCPS（OCE-RCPS）框架，该框架为通用优化确定性等价（OCE）风险度量提供了高概率保证，包括条件价值-at-风险（CVaR）和熵风险。OCE-RCPS利用上置信界来识别满足用户指定风险容忍水平的预测集参数，并具有可证明的可靠性。我们建立了理论保证，证明OCE-RCPS满足损失函数（如误覆盖率和假阴性率）所需的概率约束。在图像分割实验中，OCE-RCPS在各种风险度量和可靠性配置下始终达到目标满足率，而OCE-CRC未能提供概率保证。
英文摘要：
In safety-critical applications such as medical image segmentation, prediction systems must provide reliability guarantees that extend beyond conventional expected loss control. While risk-controlling prediction sets (RCPS) offer probabilistic guarantees on the expected risk, they fail to capture tail behavior and worst-case scenarios that are crucial in high-stakes settings. This paper introduces optimized certainty equivalent RCPS (OCE-RCPS), a novel framework that provides high-probability guarantees on general optimized certainty equivalent (OCE) risk measures, including conditional value-at-risk (CVaR) and entropic risk. OCE-RCPS leverages upper confidence bounds to identify prediction set parameters that satisfy user-specified risk tolerance levels with provable reliability. We establish theoretical guarantees showing that OCE-RCPS satisfies the desired probabilistic constraint for loss functions such as miscoverage and false negative rate. Experiments on image segmentation demonstrate that OCE-RCPS consistently meets target satisfaction rates across various risk measures and reliability configurations, while OCE-CRC fails to provide probabilistic guarantees.
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