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

arXiv: https://arxiv.org/abs/2111.03950 · HTML: https://mlsanity.com/paper/2111.03950/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 87 references that are in the map.
- First posted on arXiv 6 Nov 2021.

## Builds on (most cited first, 22 of 22)

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm](https://mlsanity.com/paper/1702.07254/) (2017)
- [External Validity: From Do-Calculus to Transportability Across Populations](https://mlsanity.com/paper/1503.01603/) (2015)
- [Nonparametric methods for doubly robust estimation of continuous treatment effects](https://mlsanity.com/paper/1507.00747/) (2015)
- [Generalized Optimal Matching Methods for Causal Inference](https://mlsanity.com/paper/1612.08321/) (2016)
- [Metrizing Weak Convergence with Maximum Mean Discrepancies](https://mlsanity.com/paper/2006.09268/) (2020)
- [Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves](https://mlsanity.com/paper/2010.04855/) (2020)
- [Covariate Balancing Propensity Score by Tailored Loss Functions](https://mlsanity.com/paper/1601.05890/) (2016)
- [Counterfactual Mean Embeddings](https://mlsanity.com/paper/1805.08845/) (2018)
- [Double/Debiased Machine Learning for Dynamic Treatment Effects via g-Estimation](https://mlsanity.com/paper/2002.07285/) (2020)
- [A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects](https://mlsanity.com/paper/1903.03662/) (2019)
- [Structural Nested Models and G-estimation: The Partially Realized Promise](https://mlsanity.com/paper/1503.01589/) (2015)
- [Minimax Linear Estimation of the Retargeted Mean](https://mlsanity.com/paper/1901.10296/) (2019)
- [Evaluating (weighted) dynamic treatment effects by double machine learning](https://mlsanity.com/paper/2012.00370/) (2020)
- [Sequential Double Robustness in Right-Censored Longitudinal Models](https://mlsanity.com/paper/1705.02459/) (2017)
- [An Interventionist Approach to Mediation Analysis](https://mlsanity.com/paper/2008.06019/) (2020)
- [On the multiply robust estimation of the mean of the g-functional](https://mlsanity.com/paper/1705.08582/) (2017)
- [Multiply Robust Causal Mediation Analysis with Continuous Treatments](https://mlsanity.com/paper/2105.09254/) (2021)

## Built on by (most cited first, 5 of 5)

- [Kernel methods for long term dose response curves](https://mlsanity.com/paper/2201.05139/) (2022)
- [Supervised Kernel Thinning](https://mlsanity.com/paper/2410.13749/) (2024)
- [Double Debiased Machine Learning for Mediation Analysis with Continuous Treatments](https://mlsanity.com/paper/2503.06156/) (2025)
- [ActiveCQ: Active Estimation of Causal Quantities](https://mlsanity.com/paper/2509.24293/) (2025)
- [Distributional Causal Mediation via Conditional Generative Modeling](https://mlsanity.com/paper/2605.01765/) (2026)

## Abstract (arXiv)

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.