We adapt Gaussian processes for estimating the average dose-response function in observational settings, introducing a powerful complement to treatment effect estimation for understanding heterogeneous effects. We incorporate samples from a Gaussian process posterior for the propensity score into a Gaussian process response model using Girard's approach to integrating over uncertainty in training data. We show Girard's method admits a positive-definite kernel, and provide theoretical justification by identifying it with an inner product of kernel mean embeddings. We demonstrate double robustness of our approach under a misspecified response function or propensity score. We characterize and mitigate regularization-induced confounding in Gaussian process response models. We show improvement over other methods for average dose-response function estimation in terms of coverage of the dose-response function and estimation bias, with less sensitivity to misspecification across experiments.

翻译：本文通过将高斯过程应用于观测性研究中的平均剂量-响应函数估计，为理解异质性效应提供了一种强大的处理效应估计补充方法。我们采用吉拉尔方法，将倾向得分高斯过程后验的样本整合到高斯过程响应模型中，从而实现对训练数据不确定性的积分。我们证明吉拉尔方法允许使用正定核，并通过将其与核均值嵌入的内积相关联提供了理论依据。我们展示了在响应函数或倾向得分设定错误情况下本方法的双重稳健性。我们刻画并缓解了高斯过程响应模型中正则化引起的混杂偏倚。实验表明，在剂量-响应函数的覆盖范围和估计偏差方面，本方法优于其他平均剂量-响应函数估计方法，且在不同实验中对模型设定错误的敏感性更低。