Enhanced localized conformal prediction with imperfect auxiliary information
提出增强局部共形预测方法，利用辅助数据改善校准数据稀疏区域的预测集可靠性，保持有限样本边际覆盖保证，理论证明和模拟显示其局部覆盖优于标准方法。
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 compared to standard LCP, highlighting its effectiveness in settings with limited calibration data but available auxiliary information from related tasks.