Causal effects are usually studied in terms of the means of counterfactual distributions, which may be insufficient in many scenarios. Given a class of densities known up to normalizing constants, we propose to model counterfactual distributions by minimizing kernel Stein discrepancies in a doubly robust manner. This enables the estimation of counterfactuals over large classes of distributions while exploiting the desired double robustness. We present a theoretical analysis of the proposed estimator, providing sufficient conditions for consistency and asymptotic normality, as well as an examination of its empirical performance.

翻译：因果效应通常通过反事实分布的均值进行研究，但在许多场景下这可能不够充分。针对一类已知归一化常数的密度函数，我们提出通过双重稳健方式最小化核斯坦因散度来建模反事实分布。该方法能够在利用期望的双重稳健性质的同时，对大类分布进行反事实估计。我们对该估计量进行了理论分析，给出了其一致性和渐近正态性的充分条件，并检验了其实证表现。