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.

翻译：近年来，构建能够提供近似或渐近条件覆盖保证、捕捉局部数据异质性的共形预测集引起了广泛关注。然而，局部化共形预测（LCP）等方法在校准数据稀疏的区域可能难以确保可靠的预测集。本文提出增强型局部化共形预测（ELCP）——一种创新方法，通过引入辅助数据来优化局部预测集，同时保持有限样本边际覆盖保证。ELCP采用密度比加权核估计器，无缝整合辅助数据与校准数据，适应潜在分布偏移并提升预测集的局部可靠性。理论分析证实，ELCP可维持边际覆盖并增强渐近检验条件覆盖。模拟结果显示，与标准LCP相比，该方法在局部覆盖率和预测集规模上均具有优势，尤其适用于校准数据有限但具有相关任务辅助信息的场景。