A complete understanding of heterogeneous treatment effects involves characterizing the full conditional distribution of potential outcomes. To this end, we propose the Conditional Counterfactual Mean Embeddings (CCME), a framework that embeds conditional distributions of counterfactual outcomes into a reproducing kernel Hilbert space (RKHS). Under this framework, we develop a two-stage meta-estimator for CCME that accommodates any RKHS-valued regression in each stage. Based on this meta-estimator, we develop three practical CCME estimators: (1) Ridge Regression estimator, (2) Deep Feature estimator that parameterizes the feature map by a neural network, and (3) Neural-Kernel estimator that performs RKHS-valued regression, with the coefficients parameterized by a neural network. We provide finite-sample convergence rates for all estimators, establishing that they possess the double robustness property. Our experiments demonstrate that our estimators accurately recover distributional features including multimodal structure of conditional counterfactual distributions.

翻译：要完全理解异质性处理效应，需要刻画潜在结果的全条件分布。为此，我们提出了条件反事实均值嵌入（CCME）框架，该框架将反事实结果的条件分布嵌入到再生核希尔伯特空间（RKHS）中。在此框架下，我们为CCME开发了一个两阶段元估计器，该估计器允许每个阶段使用任意RKHS值回归方法。基于此元估计器，我们开发了三种实用的CCME估计器：（1）岭回归估计器，（2）通过神经网络参数化特征映射的深度特征估计器，以及（3）执行RKHS值回归且系数由神经网络参数化的神经-核估计器。我们为所有估计器提供了有限样本收敛速率，证明它们具有双重稳健性。实验表明，我们的估计器能够准确恢复条件反事实分布的多峰结构等分布特征。