提出新方法生成更精准的预测区间，适配不同数据分布。
Localized Conformal Multi-Quantile Regression
- 融合多分位数与核函数定位，自适应调整预测范围。
- 在基准数据集上预测区间更紧致，效率优于现有方法。
- 适合需要分组准确覆盖的场景，如个性化治疗效果评估。
标准置信推断方法虽保证整体覆盖率，但常产生效率低下的预测区间，难以适应局部异方差性；近期局部化方法又常在具有不同噪声特征的子群体间丧失有效性。为此，我们提出局部化置信多分位数回归（LCMQR），通过融合多分位数信息与基于核的局部化策略，构建高效且自适应的预测区间。理论上，我们纠正了之前工作在共轭复合分位数回归（CCQR）中的不一致性，证明所提出的先平均后取最大值的评分机制始终生成比先取最大后平均更紧致的区间。针对异质环境，我们进一步引入分组校准的LCMQR（GC-LCMQR），通过分层校准步骤，在有限样本下确保不同子群体内的覆盖率。在基准数据集及个体处理效应（ITE）任务上的实验表明，LCMQR在标准基准上表现更优，而GC-LCMQR在混合群体中首次实现目标子群体的组级覆盖率，而基线方法则失败。
原文摘要 · Abstract (English)
Standard conformal prediction methods guarantee marginal coverage but often produce inefficient intervals that fail to adapt to local heteroscedasticity, while recent localized approaches often struggle to maintain validity across distinct subpopulations with varying noise profiles. To address these challenges, we introduce Localized Conformal Multi-Quantile Regression (LCMQR), a novel framework that synergizes multi-quantile information with kernel-based localization to construct efficient and adaptive prediction intervals. Theoretically, we resolve an inconsistency in Conformalized Composite Quantile Regression (CCQR) by proving that our consistent Average-then-Max scoring mechanism systematically yields tighter intervals than the Max-then-Average approach used in prior work. For heterogeneous environments, we extend this framework to Group-Calibrated LCMQR (GC-LCMQR) via a stratified calibration step that guarantees finite-sample validity within distinct subgroups. Experiments on benchmark datasets and an Individual Treatment Effect (ITE) task demonstrate that LCMQR achieves superior efficiency on standard benchmarks, while GC-LCMQR uniquely achieves group-level coverage for target subgroups in mixture populations where baselines fail.
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