Title: Trading Coverage for Precision: Conformal Prediction with Limited False Discoveries. Abstract: In this paper, we develop a new approach to conformal prediction in which we aim to output a precise set of promising prediction candidates that is guaranteed to contain a limited number of incorrect answers. Standard conformal prediction provides the ability to adapt to model uncertainty by constructing a calibrated candidate set in place of a single prediction, with guarantees that the set contains the correct answer with high probability. In order to obey this coverage property, however, conformal sets can often become inundated with noisy candidates---which can render them unhelpful in practice. This is particularly relevant to large-scale settings where the cost (monetary or otherwise) of false positives is substantial, such as for in-silico screening for drug discovery, where any positively identified molecular compound is then manufactured and tested. We propose to trade coverage for precision by enforcing that the presence of incorrect candidates in the predicted conformal sets (i.e., the total number of false discoveries) is bounded according to a user-specified tolerance. Subject to this constraint, our algorithm then optimizes for a generalized notion of set coverage (i.e., the true discovery rate) that allows for any number of true answers for a given query (including zero). We demonstrate the effectiveness of this approach across a number of classification tasks in natural language processing, computer vision, and computational chemistry.
