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We propose simple nonparametric estimators for mediated and time-varying doseresponse curves based on kernel ridge regression. By embedding Pearl'smediation formula and Robins' g-formula with kernels, we allow treatments,mediators, and covariates to be continuous in general spaces, and also allowfor nonlinear treatment-confounder feedback. Our key innovation is areproducing kernel Hilbert space technique called sequential kernel embedding,which we use to construct simple estimators for complex causal estimands. Ourestimators preserve the generality of classic identification while alsoachieving nonasymptotic uniform rates. In nonlinear simulations with manycovariates, we demonstrate strong performance. We estimate mediated andtime-varying dose response curves of the US Job Corps, and clean data that mayserve as a benchmark in future work. We extend our results to mediated andtime-varying treatment effects and counterfactual distributions, verifyingsemiparametric efficiency and weak convergence.

Sequential Kernel Embedding for Mediated and Time-Varying Dose Response Curves