🤖 AI Summary
本文针对模型信息不足时的可靠性集合估计问题，提出一种结合校准过程和自适应设计的统一框架，以降低决策风险并控制误包含风险。
📝 Abstract
Reliability set estimation identifies input regions where a response probability exceeds a target level, bridging estimation and safety-critical decisions. Practitioners typically start with a working model, an imperfect approximation of the true response surface. Relying on this imperfect model may incur decision risk, potentially certifying unsafe regions as safe. We develop a unified framework that turns such a working model into a trustworthy decision rule. First, a modeling-then-calibration procedure decouples estimation from decision. Since the true set is unobservable, we introduce an asymmetric, observable surrogate loss and use a separate calibration set to select a bias-correcting threshold, reducing decision risk and achieving $O_P(1/n)$ volume convergence. Second, we leverage conformal risk control with the surrogate loss to control false inclusion risk, which is the most safety-critical error, at a pre-specified level regardless of working model quality. Together, these calibration procedures show that a separate calibration set is necessary for risk control. Third, an adaptive design concentrates observations on the reliability set and its boundary, improving model quality where errors most affect decisions while controlling budget elsewhere. Numerical studies show not only more accurate set estimates but also calibrated finite-sample risk control that classical plug-in methods lack.