指出训练条件共形预测不适用于安全认证，传统置信区间更可靠
On Training-Conditional Conformal Prediction and Binomial Proportion Confidence Intervals
- 用训练条件共形预测做安全认证时无法保证有效性
- 共形预测在伯努利期望估计中会失效，导致误判风险
- 适合关注控制系统的统计安全验证的读者参考
基于N次独立试验估计伯努利随机变量期望是经典统计问题，通常采用二项比例置信区间（BPCI）。在控制系统领域，许多关键任务——如动态系统统计安全性的验证——可建模为BPCI问题。共形预测（CP）是一种无需分布假设的不确定性量化技术，近年来被广泛应用于各类控制系统问题，尤其用于处理学习动力学或控制器中的不确定性。近期有研究提出使用训练条件共形预测（training-conditional CP）解决安全认证问题。本文指出，在此场景下使用训练条件共形预测无法提供有效的安全保证。我们证明了共形预测不适用于BPCI问题，并主张传统BPCI方法更适合用于统计安全认证。
原文摘要 · Abstract (English)
Estimating the expectation of a Bernoulli random variable based on N independent trials is a classical problem in statistics, typically addressed using Binomial Proportion Confidence Intervals (BPCI). In the control systems community, many critical tasks-such as certifying the statistical safety of dynamical systems-can be formulated as BPCI problems. Conformal Prediction (CP), a distribution-free technique for uncertainty quantification, has gained significant attention in recent years and has been applied to various control systems problems, particularly to address uncertainties in learned dynamics or controllers. A variant known as training-conditional CP was recently employed to tackle the problem of safety certification. In this note, we highlight that the use of training-conditional CP in this context does not provide valid safety guarantees. We demonstrate why CP is unsuitable for BPCI problems and argue that traditional BPCI methods are better suited for statistical safety certification.
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