Reliable uncertainty quantification for causal effects is crucial in various applications, but remains difficult in nonparametric models, particularly for continuous treatments. We introduce IMPspec, a Gaussian process (GP) framework for modeling uncertainty over interventional causal functions under continuous treatments, which can be represented using reproducing Kernel Hilbert Spaces (RKHSs). By using principled function class expansions and a spectral representation of RKHS features, IMPspec yields tractable training and inference, a spectral algorithm to calibrate posterior credible intervals, and avoids the underfitting and variance collapse pathologies of earlier GP-on-RKHS methods. Across synthetic benchmarks and an application in healthcare, IMPspec delivers state-of-the-art performance in causal uncertainty quantification and downstream causal Bayesian optimization tasks.

翻译：在各类应用中，可靠的因果效应不确定性量化至关重要，但在非参数模型中仍存在困难，特别是对于连续处理情形。本文提出IMPspec——一种用于连续处理下干预因果函数不确定性建模的高斯过程框架，该框架可利用再生核希尔伯特空间进行表示。通过采用基于原理的函数类展开与RKHS特征的谱表示，IMPspec实现了可处理的训练与推断过程，提供了校准后验可信区间的谱算法，并避免了早期基于RKHS的高斯过程方法中存在的欠拟合与方差塌缩问题。在合成基准测试及医疗健康领域的应用中，IMPspec在因果不确定性量化及下游因果贝叶斯优化任务中均展现出最先进的性能。