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Kernel Ridge Riesz Representers: Generalization, Mis-specification, and the Counterfactual Effective Dimension

Rahul Singh

arXiv 22 Feb 2021 · Statistics — Machine Learning · 2 citations (OpenAlex)

arXiv:2102.11076 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Kernel balancing weights provide confidence intervals for average treatment effects, based on the idea of balancing covariates for the treated group and untreated group in feature space, often with ridge regularization. Previous works on the classical kernel ridge balancing weights have certain limitations: (i) not articulating generalization error for the balancing weights, (ii) typically requiring correct specification of features, and (iii) justifying Gaussian approximation for only average effects. I interpret kernel balancing weights as kernel ridge Riesz representers (KRRR) and address these limitations via a new characterization of the counterfactual effective dimension. KRRR is an exact generalization of kernel ridge regression and kernel ridge balancing weights. I prove strong properties similar to kernel ridge regression: population $L_2$ rates controlling generalization error, and a standalone closed form solution that can interpolate. The framework relaxes the stringent assumption that the underlying regression model is correctly specified by the features. It extends Gaussian approximation beyond average effects to heterogeneous effects, justifying confidence sets for causal functions. I use KRRR to quantify uncertainty for heterogeneous treatment effects, by age, of 401(k) eligibility on assets.

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52
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156
in-text mentions
52
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
1Hirshberg, D. A. and Wager, S (2021) Augmented minimax linear estimation1.000123100%
2Hirshberg, D. A., Maleki, A., and Zubizarreta, J. R (2019) Minimax linear estimation of the retargeted mean1.000123100%
3Chernozhukov, V., Newey, W. K., and Singh, R (2022) Debiased machine learning of global and local parameters using regularized Riesz representers self1.00064100%
4Fischer, S. and Steinwart, I (2020) Sobolev norm learning rates for regularized least-squares algorithms1.00064100%
5Kallus, N (2020) Generalized optimal matching methods for causal inference1.00063100%
6Chernozhukov, V., Newey, W. K., Singh, R., and Syrgkanis, V (2020) Adversarial estimation of Riesz representers self0.96510590%
7Chernozhukov, V., Newey, W. K., and Singh, R (2022) Automatic debiased machine learning of causal and structural effects self0.9507586%
8Bruns-Smith, D., Dukes, O., Feller, A., and Ogburn, E. L (2023) Augmented balancing weights as linear regression0.9285480%
9Speckman, P (1979) Minimax estimates of linear functionals in a Hilbert space0.92843100%
10Wong, R. K. W. and Chan, K. C. G (2018) Kernel-based covariate functional balancing for observational studies0.92843100%

Showing the top 10 of 52 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
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