We develop a fast distribution-free conformal prediction algorithm for obtaining multiple coverage of interchangeable data in a batch setting. Multiple scope guarantees are stronger than limit scope guarantees in two ways: (1) they conditionally preserve group membership; Group into a finite collection $\mathcal{G}$ of regions in the feature space. (2) They hold conditioned on the threshold values used to generate the predictions set in a particular example. In fact, the multi-scope guarantee holds even when group membership and thresholds are conditioned at the same time.
It offers two algorithms. Both take as input any collection of groups $\mathcal{G}$ that may intersect with any lack-of-fit score, and can equip any black-box predictor with a set of predictions. The first algorithm (BatchGCP) is a direct extension of quantile regression, needing to solve only a single convex minimization problem, and has group conditional guarantees for each group of $\mathcal{G}$. produces an estimator with The second algorithm (BatchMVP) is iterative and fully guarantees multiple valid conformal predictions (a set of predictions that are conditionally valid on both group membership and lack-of-fit threshold). We evaluate the performance of both algorithms in an extensive series of experiments. Code to replicate all experiments can be found at https://github.com/ProgBelarus/BatchMultivalidConformal.
