Kernel Ridge Riesz Representers: Generalization, Mis-specification, and the Counterfactual Effective Dimension
This work addresses methodological gaps in causal inference for researchers and practitioners, offering a more robust framework for estimating treatment effects with uncertainty quantification, though it builds incrementally on existing kernel methods.
The paper tackles limitations in kernel balancing weights for causal inference by introducing kernel ridge Riesz representers (KRRR), which provide generalization error bounds and relax model specification assumptions, enabling confidence intervals for heterogeneous treatment effects with application to 401(k) eligibility effects on assets by age.
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.