We develop a skew-adaptive extension of split conformal prediction for regression. The method starts from an asymmetric interval family centered at a point prediction and uses the gauge approach to deduce the conformity score induced by this family. The inverse hyperbolic sine transform of signed scaled residuals provides the training target for an additional predictive model, whose role is to learn how predictive uncertainty should tilt across the feature space. The resulting procedure preserves the finite-sample marginal validity of split conformal prediction under exchangeability, while producing intervals that adapt to both local scale and local skewness. We also develop a calibration-sample-based estimator for comparing the expected relative future width of the skew-adaptive and classical scaled-score intervals. Experiments on a variety of datasets indicate gains in prediction interval efficiency over the scaled-score construction and conformalized quantile regression, and show that the proposed estimator closely matches the corresponding average width ratio observed on the test sample.

翻译：我们针对回归问题提出了一种偏态自适应的拆分共形预测扩展方法。该方法以围绕点预测的非对称区间族为出发点，采用规范方法推导该区间族诱导的一致性评分机制。通过对带符号标准化残差进行反双曲正弦变换，我们为额外预测模型生成训练目标，该模型的功能是学习预测不确定性如何随特征空间变化而产生倾斜。所提过程在保持交换性假设下拆分共形预测的有限样本边际有效性的同时，能够生成同时适应局部尺度与局部偏态特性的预测区间。我们还开发了一种基于校准样本的估计器，用于比较偏态自适应区间与经典得分尺度区间的期望相对未来宽度。在多个数据集上的实验表明，相较于得分尺度构造方法和共形分位数回归，该方法在预测区间效率上取得显著提升，且所提估计器与测试样本上观测到的对应平均宽度比率高度吻合。