🤖 AI Summary
This paper addresses causal inference under nonlinear dynamic feedback among continuous treatments, mediators, and confounders—a setting where identification and consistent estimation of mediation effects and time-varying dose–response curves are fundamentally challenging. Methodologically, it introduces the first identifiable framework with non-asymptotic uniform convergence rates, unifying Pearl’s mediation formula and Robins’ g-formula via kernelization and developing a novel sequential kernel embedding technique in reproducing kernel Hilbert spaces for functional causal modeling. The approach integrates kernel ridge regression, semiparametric efficient estimation, and weak convergence analysis. Empirically, it demonstrates robustness and reliability in high-dimensional nonlinear simulations and delivers actionable insights from the U.S. Job Corps program, yielding a reproducible benchmark dataset. Furthermore, the framework extends to counterfactual distribution estimation, broadening its applicability to complex longitudinal causal questions.
📝 Abstract
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.
