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.
STARK denoises spatial transcriptomics images via adaptive regularization
Department of Mathematics, University of British Columbia（数学系，不列颠哥伦比亚大学）；Department of Computer Science, University of British Columbia（计算机科学系，不列颠哥伦比亚大学）；Department of Mathematics and Mathematical Statistics, Umeå University（数学与统计学系，乌梅大学）；Premium Research Institute for Human Metaverse Medicine (WPI-PRIMe), The University of Osaka（人类元宇宙医学研究学院（WPI-PRIMe），大阪大学）
