High-fidelity (HF) data are often expensive to collect and therefore scarce, making conditional quantiles difficult to estimate accurately. We propose a two-stage, model-agnostic method for multi-fidelity quantile regression. The central idea is a local quantile link: at each covariate value, the HF quantile is represented as a low-fidelity (LF) quantile evaluated at a covariate-dependent level. This reformulation reduces the problem to estimating the level function, which can be smoother than the HF quantile itself when the LF and HF conditional distributions have similar shapes. We also study the complementary regime in which this advantage weakens and introduce a correction step to improve robustness. Our theory characterizes when the proposed estimator converges faster than direct quantile regression using HF data alone and when the correction step provides further improvement. Experiments on synthetic and real data show that our method yields more accurate quantile estimates and tighter conformal prediction intervals.

翻译：高保真数据通常收集成本高昂且因而稀缺，这使得条件分位数的精确估计变得困难。我们提出了一种与模型无关的两阶段多保真分位数回归方法。核心思想是局部分位数链接：在每个协变量取值处，高保真分位数被表示为协变量依赖水平上评估的低保真分位数。这一重新表述将问题简化为估计水平函数，当低保真和高保真条件分布形状相似时，该函数可能比高保真分位数本身更平滑。我们还研究了这一优势减弱的互补情形，并引入校正步骤以提升鲁棒性。我们的理论刻画了所提估计量何时比仅使用高保真数据的直接分位数回归收敛更快，以及校正步骤何时能提供进一步改进。在合成数据和真实数据上的实验表明，我们的方法能产生更精确的分位数估计和更紧的共形预测区间。