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Kernel methods for long term dose response curves

Rahul Singh, Hannah Zhou

arXiv 13 Jan 2022 · Econometrics · 2 citations (OpenAlex)

arXiv:2201.05139 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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.

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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Fischer, S. and Steinwart, I (2020) Sobolev norm learning rates for regularized least-squares algorithms0.9416483%
2Berlinet, A. and Thomas-Agnan, C (2011) Reproducing Kernel Hilbert Spaces in Probability and Statistics0.92843100%
3Athey, S., Chetty, R., and Imbens, G (2020) Combining experimental and observational data to estimate treatment effects on long term outcomes0.8746467%
4Athey, S., Chetty, R., Imbens, G., and Kang, H (2020) Estimating treatment effects using multiple surrogates: The role of the surrogate score and the surrogate index0.8434375%
5Prentice, R. L (1989) Surrogate endpoints in clinical trials: definition and operational criteria0.7373367%
6Caponnetto, A. and De Vito, E (2007) Optimal rates for the regularized least-squares algorithm0.73732100%
7Kallus, N. and Mao, X (2020) On the role of surrogates in the efficient estimation of treatment effects with limited outcome data0.73732100%
8Singh, R., Xu, L., and Gretton, A (2024) Kernel methods for causal functions: Dose, heterogeneous, and incremental response curves self0.7218638%
9Carrasco, M., Florens, J.-P., and Renault, E (2007) Linear inverse problems in structural econometrics estimation based on spectral decomposition and regularization0.64422100%
10Newey, W. K (1994) The asymptotic variance of semiparametric estimators0.64422100%

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