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Causal effects are usually studied in terms of the means of counterfactualdistributions, which may be insufficient in many scenarios. Given a class ofdensities known up to normalizing constants, we propose to model counterfactualdistributions by minimizing kernel Stein discrepancies in a doubly robustmanner. This enables the estimation of counterfactuals over large classes ofdistributions while exploiting the desired double robustness. We present atheoretical analysis of the proposed estimator, providing sufficient conditionsfor consistency and asymptotic normality, as well as an examination of itsempirical performance.

Counterfactual Density Estimation using Kernel Stein Discrepancies