Sequential Kernel Embedding for Mediated and Time-Varying Dose Response Curves
This work addresses causal inference challenges in fields like economics or policy analysis by enabling more flexible modeling of complex feedback, though it appears incremental as it builds on existing formulas with kernel embeddings.
The authors tackled the problem of estimating mediated and time-varying dose response curves with continuous treatments and nonlinear feedback by proposing nonparametric estimators based on kernel ridge regression, achieving nonasymptotic uniform rates and demonstrating strong performance in simulations with many covariates.
We propose simple nonparametric estimators for mediated and time-varying dose response curves based on kernel ridge regression. By embedding Pearl's mediation formula and Robins' g-formula with kernels, we allow treatments, mediators, and covariates to be continuous in general spaces, and also allow for nonlinear treatment-confounder feedback. Our key innovation is a reproducing kernel Hilbert space technique called sequential kernel embedding, which we use to construct simple estimators that account for complex feedback. Our estimators preserve the generality of classic identification while also achieving nonasymptotic uniform rates. In nonlinear simulations with many covariates, we demonstrate strong performance. We estimate mediated and time-varying dose response curves of the US Job Corps, and clean data that may serve as a benchmark in future work. We extend our results to mediated and time-varying treatment effects and counterfactual distributions, verifying semiparametric efficiency and weak convergence.