Conformal Prediction for Regression with Clipped Outcomes

2026-07-22

AI Summary

This work addresses the challenge of conformal prediction in regression settings where the response variable is subject to two-sided truncation. Existing methods struggle to simultaneously achieve marginal and conditional coverage, often failing to provide valid conditional coverage—particularly on easily predictable instances. To overcome this limitation, the authors introduce a novel nonconformity score tailored to truncated data and propose two calibration strategies: one ensuring tight marginal coverage, and another employing a two-stage mechanism that prioritizes conditional coverage, thereby exposing the inherent limitations of marginal coverage in truncation scenarios. Within the conformal prediction framework, the proposed score leverages the structure of truncated observations to deliver finite-sample theoretical coverage guarantees and, under model consistency, attains oracle-like asymptotic performance, substantially outperforming naive adaptations of existing methods.

Abstract

We study conformal prediction for regression using calibration data with outcomes that are doubly censored (clipped) at known fixed thresholds. We show that existing methods are unsatisfactory in this setting, as they yield intervals that may have higher marginal coverage than desired and yet lose conditional coverage precisely for the easier-to-predict cases whose outcomes are typically fully observed. This reveals that marginal coverage, the usual target of conformal prediction, may not be the ideal goal under clipping. We address this challenge by introducing a new nonconformity score and calibration methods at both ends of this trade-off: one for tight marginal coverage, and a two-step method that prioritizes conditional coverage. We characterize their finite-sample coverage and oracle-like asymptotic behavior under suitable consistency of the underlying model, and we compare them to more direct adaptations of existing approaches.

Problem

• conformal prediction
• regression
• clipped outcomes
• marginal coverage
• conditional coverage

Innovation

• Conformal Prediction
• Clipped Outcomes
• Conditional Coverage
• Nonconformity Score
• Regression