Conformalized Quantile Regression (CQR) is a recently proposed method for constructing prediction intervals for a response $Y$ given covariates $X$, without making distributional assumptions. However, existing constructions of CQR can be ineffective for problems where the quantile regressors perform better in certain parts of the feature space than others. The reason is that the prediction intervals of CQR do not distinguish between two forms of uncertainty: first, the variability of the conditional distribution of $Y$ given $X$ (i.e., aleatoric uncertainty), and second, our uncertainty in estimating this conditional distribution (i.e., epistemic uncertainty). This can lead to intervals that are overly narrow in regions where epistemic uncertainty is high. To address this, we propose a new variant of the CQR methodology, Uncertainty-Aware CQR (UACQR), that explicitly separates these two sources of uncertainty to adjust quantile regressors differentially across the feature space. Compared to CQR, our methods enjoy the same distribution-free theoretical coverage guarantees, while demonstrating in our experiments stronger conditional coverage properties in simulated settings and real-world data sets alike.

翻译：共形分位数回归（CQR）是一种近期提出的方法，用于在给定协变量 $X$ 的情况下构建响应 $Y$ 的预测区间，且无需做出分布假设。然而，当分位数回归器在特征空间的某些部分表现优于其他部分时，现有的CQR构建方法可能无效。原因在于CQR的预测区间无法区分两种形式的不确定性：首先，给定 $X$ 后 $Y$ 的条件分布的变异性（即偶然不确定性）；其次，我们估计此条件分布时的不确定性（即认知不确定性）。这可能导致在认知不确定性较高的区域中预测区间过于狭窄。为解决此问题，我们提出了一种新的CQR变体——不确定性感知共形分位数回归（UACQR），它明确分离了这两种不确定性来源，以便在特征空间中不同区域对分位数回归器进行差异化调整。与CQR相比，本方法享有相同的无分布理论覆盖保证，同时在模拟环境和真实数据集的实验中展现出更强的条件覆盖特性。