提出自适应偏度的预测区间方法，提升回归预测精度。
Skew-adaptive conformal prediction
- 基于符号缩放残差的反双曲正弦变换构建新预测模型，学习不确定性倾斜模式。
- 在多个数据集上，预测区间效率优于传统方法，且宽度更优。
- 适合需要精准置信区间、关注预测不确定性的研究者使用。
我们提出一种针对回归任务的偏度自适应分割信赖区间方法。该方法从以点预测为中心的非对称区间族出发，利用量规法推导出对应的符合性得分。通过反双曲正弦变换对带符号缩放残差进行处理，作为额外预测模型的训练目标，该模型学习预测不确定性在特征空间中的倾斜趋势。所提方法在可交换性假设下保持了分割信赖区间的有限样本边际有效性，同时生成的区间能适应局部尺度与局部偏度。我们还提出基于校准样本的估计器，用于比较未来预期相对宽度，实验表明其估计值与测试集上观察到的平均宽度比高度一致。在多种数据集上的实验显示，该方法在预测区间效率上优于经典缩分得分构造和共形化分位数回归。
原文摘要 · Abstract (English)
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.
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