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Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves

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  • Rahul Singh
  • Liyuan Xu
  • Arthur Gretton

Abstract

We propose estimators based on kernel ridge regression for nonparametric causal functions such as dose, heterogeneous, and incremental response curves. Treatment and covariates may be discrete or continuous in general spaces. Due to a decomposition property specific to the RKHS, our estimators have simple closed form solutions. We prove uniform consistency with finite sample rates via original analysis of generalized kernel ridge regression. We extend our main results to counterfactual distributions and to causal functions identified by front and back door criteria. We achieve state-of-the-art performance in nonlinear simulations with many covariates, and conduct a policy evaluation of the US Job Corps training program for disadvantaged youths.

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  • Rahul Singh & Liyuan Xu & Arthur Gretton, 2020. "Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves," Papers 2010.04855, arXiv.org, revised Oct 2022.
  • Handle: RePEc:arx:papers:2010.04855
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    Cited by:

    1. Rahul Singh, 2021. "Kernel Ridge Riesz Representers: Generalization, Mis-specification, and the Counterfactual Effective Dimension," Papers 2102.11076, arXiv.org, revised Jul 2024.
    2. Keith Battocchi & Eleanor Dillon & Maggie Hei & Greg Lewis & Miruna Oprescu & Vasilis Syrgkanis, 2021. "Estimating the Long-Term Effects of Novel Treatments," Papers 2103.08390, arXiv.org, revised Feb 2022.
    3. AmirEmad Ghassami & Andrew Ying & Ilya Shpitser & Eric Tchetgen Tchetgen, 2021. "Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference," Papers 2104.02929, arXiv.org, revised Mar 2022.
    4. Victor Chernozhukov & Whitney Newey & Rahul Singh & Vasilis Syrgkanis, 2020. "Adversarial Estimation of Riesz Representers," Papers 2101.00009, arXiv.org, revised Apr 2024.
    5. Rahul Singh, 2020. "Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments," Papers 2012.10315, arXiv.org, revised Mar 2023.

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