Kernel Methods for Multistage Causal Inference: Mediation Analysis and Dynamic Treatment Effects

Rahul Singh, Liyuan Xu, Arthur Gretton

Abstract: We propose simple estimators for mediation analysis and dynamic treatment effects over short horizons based on kernel ridge regression. We study both nonparametric response curves and semiparametric treatment effects, allowing treatments, mediators, and covariates to be continuous or discrete in general spaces. Our key innovation is a new RKHS technique called sequential mean embedding, which facilitates the construction of simple estimators for complex causal estimands, including new estimands without existing alternatives. In particular, we propose machine learning estimators of dynamic dose response curves and dynamic counterfactual distributions without restrictive linearity, Markov, or no-effect-modification assumptions. Our simple estimators preserve the generality of classic identification while also achieving nonasymptotic uniform rates for causal functions and semiparametric efficiency for causal scalars. In nonlinear simulations with many covariates, we demonstrate state-of-the-art performance. We estimate mediated and dynamic response curves of the US Job Corps program for disadvantaged youth, and share a data set that may serve as a benchmark in future work.