We propose a conformal prediction method for constructing tight simultaneous prediction intervals for multiple, potentially related, numerical outputs given a single input. This method can be combined with any multi-target regression model and guarantees finite-sample coverage. It is computationally efficient and yields informative prediction intervals even with limited data. The core idea is a novel \emph{coordinate-wise} standardization procedure that makes residuals across output dimensions directly comparable, estimating suitable scaling parameters using the calibration data themselves. This does not require modeling of cross-output dependence nor auxiliary sample splitting. Implementing this idea requires overcoming technical challenges associated with transductive or full conformal prediction. Experiments on simulated and real data demonstrate this method can produce tighter prediction intervals than existing baselines while maintaining valid simultaneous coverage.

翻译：本文提出一种共形预测方法，用于在给定单一输入时，为多个可能相关的数值输出构建紧密的同步预测区间。该方法可与任意多目标回归模型结合，并保证有限样本覆盖性。其计算效率高，即使在有限数据条件下仍能生成信息量丰富的预测区间。核心创新在于一种新颖的坐标标准化过程，该过程通过校准数据自身估计合适的缩放参数，使不同输出维度的残差可直接比较。该方法无需对输出间依赖关系进行建模，也无需辅助样本分割。实现这一思路需克服与转导或完全共形预测相关的技术挑战。在模拟和真实数据上的实验表明，本方法能在保持有效同步覆盖的同时，生成比现有基线更紧凑的预测区间。