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

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  • Rahul Singh
  • Liyuan Xu
  • Arthur Gretton

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 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.

Suggested Citation

  • Rahul Singh & Liyuan Xu & Arthur Gretton, 2021. "Sequential Kernel Embedding for Mediated and Time-Varying Dose Response Curves," Papers 2111.03950, arXiv.org, revised Jul 2023.
    • Handle: RePEc:arx:papers:2111.03950
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    Cited by:

    1. Rahul Singh, 2021. "Generalized Kernel Ridge Regression for Causal Inference with Missing-at-Random Sample Selection," Papers 2111.05277, arXiv.org.
    2. Rahul Singh, 2022. "Generalized Kernel Ridge Regression for Long Term Causal Inference: Treatment Effects, Dose Responses, and Counterfactual Distributions," Papers 2201.05139, arXiv.org.
    3. Isaac Meza & Rahul Singh, 2021. "Nested Nonparametric Instrumental Variable Regression: Long Term, Mediated, and Time Varying Treatment Effects," Papers 2112.14249, arXiv.org, revised Mar 2024.

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