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 for complex causal estimands. 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.

翻译：我们提出基于核岭回归的简单非参数估计量，用于估计中介和时变剂量反应曲线。通过将Pearl的中介公式和Robins的g-公式嵌入核方法中，我们允许处理变量、中介变量和协变量在一般空间中连续取值，并允许处理变量与混杂因子之间存在非线性反馈。我们的核心创新是一种称为序列核嵌入的再生核希尔伯特空间技术，利用该技术可构建复杂因果估计量的简单估计量。所提出的估计量在保持经典识别框架通用性的同时，实现了非渐近一致收敛速率。在包含大量协变量的非线性模拟中，我们展示了其优越性能。我们利用该方法估计了美国职业培训计划的中介和时变剂量反应曲线，并提供了可作为未来研究基准的清洁数据。我们将结果拓展至中介和时变处理效应及反事实分布，验证了半参数有效性和弱收敛性。