Isotonic Conformal Inference

Abstract

A predictor with small overall bias can still exhibit systematic bias conditional on its predicted value, limiting its reliability for downstream uncertainty quantification and candidate screening. We propose Isotonic Conformal Inference, a unified framework for prediction and multiple testing that separates calibration from inference and exploits the level set structure of an isotonic predictor. This structure enables the computation of localized conformal quantiles and $p$-values while avoiding repeated isotonic refitting across candidate responses. For prediction, we introduce Split Isotonic Conformal Prediction (sICP) and Transductive Isotonic Conformal Prediction (tICP), establish prediction-conditional coverage guarantees for both methods, and characterize their finite-sample and asymptotic self-calibration properties. For selection, we introduce Isotonic Conformal Selection (ICS), which provides finite-sample stratum-conditional false discovery rate control. Experiments on simulated regression problems, a healthcare-utilization dataset, and a high-throughput ADMET drug discovery dataset demonstrate the practical performance of the framework and substantially lower computational costs relative to full transductive baselines.