Uncertainty quantification of causal effects is crucial for safety-critical applications such as personalized medicine. A powerful approach for this is conformal prediction, which has several practical benefits due to model-agnostic finite-sample guarantees. Yet, existing methods for conformal prediction of causal effects are limited to binary/discrete treatments and make highly restrictive assumptions such as known propensity scores. In this work, we provide a novel conformal prediction method for potential outcomes of continuous treatments. We account for the additional uncertainty introduced through propensity estimation so that our conformal prediction intervals are valid even if the propensity score is unknown. Our contributions are three-fold: (1) We derive finite-sample prediction intervals for potential outcomes of continuous treatments. (2) We provide an algorithm for calculating the derived intervals. (3) We demonstrate the effectiveness of the conformal prediction intervals in experiments on synthetic and real-world datasets. To the best of our knowledge, we are the first to propose conformal prediction for continuous treatments when the propensity score is unknown and must be estimated from data.

翻译：因果效应的不确定性量化对于个性化医疗等安全关键应用至关重要。保形预测为此提供了一种强有力的方法，其具有模型无关的有限样本保证，带来诸多实际优势。然而，现有的因果效应保形预测方法仅限于二元/离散处理，且需依赖已知倾向得分等高度限制性假设。本文提出一种针对连续处理潜在结果的新型保形预测方法。我们考虑了倾向估计引入的额外不确定性，使得即使倾向得分未知，我们的保形预测区间仍然有效。我们的贡献包括三个方面：(1) 推导了连续处理潜在结果的有限样本预测区间。(2) 提供了计算所得区间的算法。(3) 在合成数据集和真实世界数据集的实验中验证了保形预测区间的有效性。据我们所知，我们首次提出了在倾向得分未知且必须从数据中估计的情况下，针对连续处理的保形预测方法。