# Kernel methods for long term dose response curves

arXiv: https://arxiv.org/abs/2201.05139 · HTML: https://mlsanity.com/paper/2201.05139/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 52 references that are in the map.
- First posted on arXiv 13 Jan 2022.

## Builds on (most cited first, 17 of 17)

- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [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)
- [On the role of surrogates in the efficient estimation of treatment effects with limited outcome data](https://mlsanity.com/paper/2003.12408/) (2020)
- [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)
- [Combining Observational and Experimental Datasets Using Shrinkage Estimators](https://mlsanity.com/paper/2002.06708/) (2020)
- [Using Experiments to Correct for Selection in Observational Studies](https://mlsanity.com/paper/2006.09676/) (2020)
- [Estimating Treatment Effects using Multiple Surrogates: The Role of the Surrogate Score and the Surrogate Index](https://mlsanity.com/paper/1603.09326/) (2016)
- [Propensity Score Methods for Merging Observational and Experimental Datasets](https://mlsanity.com/paper/1804.07863/) (2018)
- [Estimating the Long-Term Effects of Novel Treatments](https://mlsanity.com/paper/2103.08390/) (2021)
- [Sequential Kernel Embedding for Mediated and Time-Varying Dose Response Curves](https://mlsanity.com/paper/2111.03950/) (2021)
- [Nested Nonparametric Instrumental Variable Regression](https://mlsanity.com/paper/2112.14249/) (2021)
- [Generalized Kernel Ridge Regression for Causal Inference with Missing-at-Random Sample Selection](https://mlsanity.com/paper/2111.05277/) (2021)

## Built on by (most cited first, 4 of 4)

- [Long-term Causal Inference Under Persistent Confounding via Data Combination](https://mlsanity.com/paper/2202.07234/) (2022)
- [Continuous Treatment Effects with Surrogate Outcomes](https://mlsanity.com/paper/2402.00168/) (2024)
- [Regression-Based Estimation of Causal Effects in the Presence of Selection Bias and Confounding](https://mlsanity.com/paper/2503.20546/) (2025)
- [Orthogonal Learner for Estimating Heterogeneous Long-Term Treatment Effects](https://mlsanity.com/paper/2604.00915/) (2026)

## Abstract (arXiv)

A core challenge in causal inference is how to extrapolate long term effects, of possibly continuous actions, from short term experimental data. It arises in artificial intelligence: the long term consequences of continuous actions may be of interest, yet only short term rewards may be collected in exploration. For this estimand, called the long term dose response curve, we propose a simple nonparametric estimator based on kernel ridge regression. By embedding the distribution of the short term experimental data with kernels, we derive interpretable weights for extrapolating long term effects. Our method allows actions, short term rewards, and long term rewards to be continuous in general spaces. It also allows for nonlinearity and heterogeneity in the link between short term effects and long term effects. We prove uniform consistency, with nonasymptotic error bounds reflecting the effective dimension of the data. As an application, we estimate the long term dose response curve of Project STAR, a social program which randomly assigned students to various class sizes. We extend our results to long term counterfactual distributions, proving weak convergence.