Conformal methods provide prediction sets for outcomes with confidence guarantees. We study their use in a selective inference setting, where inference is performed only when the prediction set is informative. The analyst may consider as informative, for example, cases with prediction sets that are sufficiently small, exclude null values, or satisfy other appropriate monotone constraints. Because inference is typically restricted to informative cases in practical applications, accounting for the resulting selection bias is crucial to maintaining false coverage rate (FCR) control. A general framework for constructing such informative conformal prediction sets while controlling the FCR on the selected sample was suggested in Gazin et al. (2025). In this work we focus on oracle-guided procedures. We derive the optimal decision policy under a suitable power objective in the oracle setting where the probability of belonging to each prediction set can be computed. In practice, of course, only estimated probabilities are available. We therefore introduce a calibration procedure that adjusts the oracle policy to maintain finite sample FCR control. We show that this approach can achieve substantially higher power than available alternatives. We demonstrate the effectiveness of our new methods for classification outcomes on both real and simulated data.

翻译：摘要：共形方法为具有置信保证的结果提供预测集。本文研究其在选择性推断场景中的应用，即仅当预测集具有信息量时执行推断。分析者可将以下情形定义为信息量：预测集足够小、排除零值或满足其他适当的单调约束。由于实际应用中推断通常局限于信息量情形，因此考虑由此产生的选择偏差对于维持错误覆盖率（FCR）控制至关重要。Gazin等（2025）提出了在选定样本上构建此类信息量共形预测集并同时控制FCR的通用框架。本文聚焦于基于最优准则的流程。在可获得每个预测集归属概率的理论最优设定下，我们推导了基于适当统计功效目标的决策策略。当然在实际中仅能获得估计概率，因此我们引入校准程序，调整理论最优策略以维持有限样本的FCR控制。研究表明，该方法相比现有替代方案可实现显著更高的统计功效。我们通过真实与模拟数据验证了新方法在分类结果上的有效性。