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Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments

Rahul Singh

arXiv 18 Dec 2020 · Statistics — Machine Learning · 7 citations (OpenAlex)

arXiv:2012.10315 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Negative control is a strategy for learning the causal relationship between treatment and outcome in the presence of unmeasured confounding. The treatment effect can nonetheless be identified if two auxiliary variables are available: a negative control treatment (which has no effect on the actual outcome), and a negative control outcome (which is not affected by the actual treatment). These auxiliary variables can also be viewed as proxies for a traditional set of control variables, and they bear resemblance to instrumental variables. I propose a family of algorithms based on kernel ridge regression for learning nonparametric treatment effects with negative controls. Examples include dose response curves, dose response curves with distribution shift, and heterogeneous treatment effects. Data may be discrete or continuous, and low, high, or infinite dimensional. I prove uniform consistency and provide finite sample rates of convergence. I estimate the dose response curve of cigarette smoking on infant birth weight adjusting for unobserved confounding due to household income, using a data set of singleton births in the state of Pennsylvania between 1989 and 1991.

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61
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190
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61
distinct cited
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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
1Mastouri, A., Zhu, Y., Gultchin, L., Korba, A., Silva, R., Kusner, M… (2021) Proximal causal learning with kernels: Two-stage estimation and moment restriction1.00094100%
2Miao, W. and Tchetgen Tchetgen, E. J (2018) A confounding bridge approach for double negative control inference on causal effects0.92843100%
3Tchetgen Tchetgen, E. J., Ying, A., Cui, Y., Shi, X., and Miao, W (2020) An introduction to proximal causal learning0.92843100%
4Deaner, B (2018) Proxy controls and panel data0.81711555%
5Fischer, S. and Steinwart, I (2020) Sobolev norm learning rates for regularized least-squares algorithms0.79410450%
6Ghassami, A., Ying, A., Shpitser, I., and Tchetgen Tchetgen, E. J (2021) Minimax kernel machine learning for a class of doubly robust functionals0.7375440%
7Kallus, N., Mao, X., and Uehara, M (2021) Causal inference under unmeasured confounding with negative controls: A minimax learning approach0.7375440%
8Caponnetto, A. and De Vito, E (2007) Optimal rates for the regularized least-squares algorithm0.7375340%
9Carrasco, M., Florens, J.-P., and Renault, E (2007) Linear inverse problems in structural econometrics estimation based on spectral decomposition and regularization0.7374350%
10Smale, S. and Zhou, D.-X (2007) Learning theory estimates via integral operators and their approximations0.7373367%

Showing the top 10 of 61 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Inference on Strongly Identified Functionals of Weakly Identified Functions0.73732
2A Kernelization-Based Approach to Nonparametric Binary Choice Models0.64422
3Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference0.51131
4Proxy Controls and Panel Data0.40511
5Controlling for Unmeasured Confounding in Panel Data Using Minimal Bridge Functions: From Two-Way Fixed Effects to Factor Models0.40511
6Many Proxy Controls0.40511
7Generalized Kernel Ridge Regression for Causal Inference with Missing-at-Random Sample Selection0.40511
8Long-term Causal Inference Under Persistent Confounding via Data Combination0.40511
9Controlling for Latent Confounding with Triple Proxies0.40511
10Instrumented Common Confounding0.40511