We introduce Conformal Interquantile Regression (CIR), a conformal regression method that efficiently constructs near-minimal prediction intervals with guaranteed coverage. CIR leverages black-box machine learning models to estimate outcome distributions through interquantile ranges, transforming these estimates into compact prediction intervals while achieving approximate conditional coverage. We further propose CIR+ (Conditional Interquantile Regression with More Comparison), which enhances CIR by incorporating a width-based selection rule for interquantile intervals. This refinement yields narrower prediction intervals while maintaining comparable coverage, though at the cost of slightly increased computational time. Both methods address key limitations of existing distributional conformal prediction approaches: they handle skewed distributions more effectively than Conformalized Quantile Regression, and they achieve substantially higher computational efficiency than Conformal Histogram Regression by eliminating the need for histogram construction. Extensive experiments on synthetic and real-world datasets demonstrate that our methods optimally balance predictive accuracy and computational efficiency compared to existing approaches.

翻译：本文提出保形分位数回归（Conformal Interquantile Regression，CIR），这是一种能够高效构建具有覆盖保证的近似最小预测区间的保形回归方法。CIR利用黑盒机器学习模型通过分位数间距估计结果分布，将这些估计转化为紧凑的预测区间，同时实现近似条件覆盖。我们进一步提出CIR+（带更多比较的条件分位数回归），该方法通过引入基于宽度的分位数区间选择规则来增强CIR。这种改进在保持相当覆盖水平的同时产生更窄的预测区间，但代价是计算时间略有增加。两种方法均解决了现有分布型保形预测方法的关键局限：相较于保形分位数回归（Conformalized Quantile Regression），它们能更有效地处理偏态分布；通过消除直方图构建需求，相比保形直方图回归（Conformal Histogram Regression）显著提升了计算效率。在合成与真实数据集上的大量实验表明，相较于现有方法，我们的方法在预测精度与计算效率之间实现了最优平衡。