Enhanced localized conformal prediction with imperfect auxiliary information

2026-06-07

AI Summary

This work addresses the challenge of unreliable prediction sets in regions with sparse calibration data, where existing local conformal prediction (LCP) methods struggle to maintain validity. The paper proposes Enhanced Local Conformal Prediction (ELCP), which, for the first time, effectively incorporates imperfect auxiliary information into the LCP framework under potential distribution shift. ELCP employs a density ratio–weighted kernel estimator to construct more reliable local prediction sets. While preserving finite-sample marginal coverage guarantees, the method substantially improves local coverage performance. Experimental results demonstrate that, under limited calibration data, ELCP achieves higher local coverage rates and yields significantly tighter prediction sets compared to standard LCP.

Abstract

There is growing interest in constructing conformal prediction sets that provide approximate or asymptotic conditional coverage guarantees, capturing local data heterogeneity. However, methods like localized conformal prediction (LCP) may face challenges in ensuring reliable prediction sets in regions with sparse calibration data. This paper introduces Enhanced Localized Conformal Prediction (ELCP), a novel approach that incorporates auxiliary data to refine localized prediction sets while preserving finite-sample marginal coverage guarantees. By utilizing a density-ratio-weighted kernel estimator, ELCP seamlessly integrates auxiliary and calibration data, accommodating potential distributional shifts and improving the local reliability of prediction sets. Theoretical analysis confirms that ELCP maintains marginal coverage and enhances asymptotic test-conditional coverage. Simulation results demonstrate its superior local coverage and smaller prediction sets compared to standard LCP, highlighting its effectiveness in settings with limited calibration data but available auxiliary information from related tasks.

Problem

• conformal prediction
• localized prediction
• sparse calibration data
• conditional coverage
• auxiliary information

Innovation

• conformal prediction
• localized prediction
• auxiliary information
• density-ratio weighting
• conditional coverage