Rahul Singh, Hannah Zhou
arXiv 13 Jan 2022 · Econometrics · 2 citations (OpenAlex)
arXiv:2201.05139 · PDF · DOI · OpenAlex · Extracted main text
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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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 | Fischer, S. and Steinwart, I (2020) Sobolev norm learning rates for regularized least-squares algorithms | 0.941 | 6 | 4 | 83% |
| 2 | Berlinet, A. and Thomas-Agnan, C (2011) Reproducing Kernel Hilbert Spaces in Probability and Statistics | 0.928 | 4 | 3 | 100% |
| 3 | Athey, S., Chetty, R., and Imbens, G (2020) Combining experimental and observational data to estimate treatment effects on long term outcomes | 0.874 | 6 | 4 | 67% |
| 4 | Athey, S., Chetty, R., Imbens, G., and Kang, H (2020) Estimating treatment effects using multiple surrogates: The role of the surrogate score and the surrogate index | 0.843 | 4 | 3 | 75% |
| 5 | Prentice, R. L (1989) Surrogate endpoints in clinical trials: definition and operational criteria | 0.737 | 3 | 3 | 67% |
| 6 | Caponnetto, A. and De Vito, E (2007) Optimal rates for the regularized least-squares algorithm | 0.737 | 3 | 2 | 100% |
| 7 | Kallus, N. and Mao, X (2020) On the role of surrogates in the efficient estimation of treatment effects with limited outcome data | 0.737 | 3 | 2 | 100% |
| 8 | Singh, R., Xu, L., and Gretton, A (2024) Kernel methods for causal functions: Dose, heterogeneous, and incremental response curves self | 0.721 | 8 | 6 | 38% |
| 9 | Carrasco, M., Florens, J.-P., and Renault, E (2007) Linear inverse problems in structural econometrics estimation based on spectral decomposition and regularization | 0.644 | 2 | 2 | 100% |
| 10 | Newey, W. K (1994) The asymptotic variance of semiparametric estimators | 0.644 | 2 | 2 | 100% |
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