We develop a predictive inference procedure that combines conformal prediction (CP) with unconditional quantile regression (QR) -- a commonly used tool in econometrics that involves regressing the recentered influence function (RIF) of the quantile functional over input covariates. Unlike the more widely-known conditional QR, unconditional QR explicitly captures the impact of changes in covariate distribution on the quantiles of the marginal distribution of outcomes. Leveraging this property, our procedure issues adaptive predictive intervals with localized frequentist coverage guarantees. It operates by fitting a machine learning model for the RIFs using training data, and then applying the CP procedure for any test covariate with respect to a ``hypothetical'' covariate distribution localized around the new instance. Experiments show that our procedure is adaptive to heteroscedasticity, provides transparent coverage guarantees that are relevant to the test instance at hand, and performs competitively with existing methods in terms of efficiency.

翻译：我们开发了一种预测推断程序，将共形预测（CP）与无条件分位数回归（QR）相结合——这是计量经济学中常用的工具，涉及将分位泛函的重新中心化影响函数（RIF）对输入协变量进行回归。与更为人所知的条件分位数回归不同，无条件分位数回归明确捕捉协变量分布变化对结果边际分布分位数的影响。利用这一特性，我们的程序生成具备局部化频率论覆盖保证的自适应预测区间。其运作方式是：首先使用训练数据拟合针对RIF的机器学习模型，然后对任意测试协变量应用CP程序，该程序针对以新实例为中心的“假设性”协变量分布进行。实验表明，我们的程序具有异方差适应性，能为当前测试实例提供透明的覆盖保证，并在效率方面与现有方法相比具有竞争力。