This paper introduces Conformal Thresholded Intervals (CTI), a novel conformal regression method that aims to produce the smallest possible prediction set with guaranteed coverage. Unlike existing methods that rely on nested conformal framework and full conditional distribution estimation, CTI estimates the conditional probability density for a new response to fall into each interquantile interval using off-the-shelf multi-output quantile regression. CTI constructs prediction sets by thresholding the estimated conditional interquantile intervals based on their length, which is inversely proportional to the estimated probability density. The threshold is determined using a calibration set to ensure marginal coverage. Experimental results demonstrate that CTI achieves optimal performance across various datasets.

翻译：本文提出了一种新颖的保形回归方法——保形阈值区间（CTI），旨在生成具有保证覆盖度的最小可能预测集。与依赖嵌套保形框架和完整条件分布估计的现有方法不同，CTI利用现成的多输出分位数回归来估计新响应落入每个分位数区间的条件概率密度。CTI通过基于区间长度对估计的条件分位数区间进行阈值处理来构建预测集，该长度与估计的概率密度成反比。阈值使用校准集确定，以确保边际覆盖度。实验结果表明，CTI在多种数据集上均实现了最优性能。