CAP: A General Algorithm for Online Selective Conformal Prediction with FCR Control

Understand

We study the problem of post-selection predictive inference in an online fashion.

• To avoid devoting resources to unimportant units, a preliminary selection of the current individual before reporting its prediction interval is common and meaningful in online predictive tasks.
• Since the online selection causes a temporal multiplicity in the selected prediction intervals, it is important to control the real-time false coverage-statement rate (FCR) which measures the overall miscoverage level.
• We develop a general framework named CAP (Calibration after Adaptive Pick) that performs an adaptive pick rule on historical data to construct a calibration set if the current individual is selected and then outputs a conformal prediction interval for the unobserved label.