Rahul Singh, Liyuan Xu, Arthur Gretton
arXiv 6 Nov 2021 · Statistics — Methodology · publishedBernoulli (2025) · 2 citations (OpenAlex)
arXiv:2111.03950 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Singh, R., Xu, L., and Gretton, A (2024) Supplement to “sequential kernel embedding for mediated and time-varying dose response curves” self | 1.000 | 26 | 6 | 100% |
| 2 | Robins, J. M (1986) A new approach to causal inference in mortality studies with a sustained exposure period—application to control of the healthy w… | 1.000 | 6 | 3 | 100% |
| 3 | Huber, M., Hsu, Y.-C., Lee, Y.-Y., and Lettry, L (2020) Direct and indirect effects of continuous treatments based on generalized propensity score weighting | 0.920 | 9 | 4 | 78% |
| 4 | Fischer, S. and Steinwart, I (2020) Sobolev norm learning rates for regularized least-squares algorithms | 0.874 | 9 | 6 | 67% |
| 5 | Robins, J. M. and Greenland, S (1992) Identifiability and exchangeability for direct and indirect effects | 0.874 | 5 | 2 | 100% |
| 6 | Schochet, P. Z., Burghardt, J., and McConnell, S (2008) Does Job Corps work? Impact findings from the national Job Corps study | 0.843 | 4 | 4 | 75% |
| 7 | Caponnetto, A. and De Vito, E (2007) Optimal rates for the regularized least-squares algorithm | 0.843 | 4 | 3 | 75% |
| 8 | Lewis, G. and Syrgkanis, V (2021) Double/debiased machine learning for dynamic treatment effects | 0.843 | 5 | 3 | 60% |
| 9 | Newey, W. K (1994) The asymptotic variance of semiparametric estimators | 0.843 | 3 | 3 | 100% |
| 10 | Vanvan der Vaart, A (1991) On differentiable functionals | 0.843 | 3 | 3 | 100% |
Showing the top 10 of 76 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Kernel methods for long term dose response curves | 0.405 | 1 | 1 |