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.

翻译：标准共形预测方法虽能保证边缘覆盖度，但常产生效率低下的区间，无法适应局部异方差性；而近期局部化方法则难以在具有不同噪声分布的子群体间维持有效性。为应对这些挑战，我们提出局部化共形多分位数回归（LCMQR），该框架通过融合多分位数信息与基于核的局部化技术，构建高效且自适应的预测区间。理论上，我们通过证明所提出的一致性平均-最大评分机制系统性地产生比先前工作中使用的最大-平均方法更紧凑的区间，解决了共形化复合分位数回归（CCQR）中的不一致性问题。针对异质环境，我们通过分层校准步骤将该框架扩展为组校准LCMQR（GC-LCMQR），确保在离散子组内实现有限样本有效性。在基准数据集和个体处理效应（ITE）任务上的实验表明：LCMQR在标准基准测试中实现了更优的效率，而GC-LCMQR在基线方法失效的混合群体中，能独特地实现对目标子组的组级覆盖保证。