Kernel Methods for Causal Inference

Explore kernel methods for causal inference in this 30-minute lecture by Rahul Singh from MIT, part of the Algorithmic Aspects of Causal Inference series at the Simons Institute. Delve into a proposed family of estimators based on kernel ridge regression for nonparametric dose response curves and semiparametric treatment effects. Learn how these methods handle discrete or continuous treatments and covariates in low, high, or infinite dimensional spaces. Discover how causal estimation and inference are reduced to combinations of kernel ridge regressions, offering closed-form solutions and easy computation through matrix operations. Examine the framework's extensions to heterogeneous effects, distribution shift, instruments and proxies, mediation, dynamic effects, sample selection, and data fusion. Gain insights into the theoretical foundations, including uniform consistency with finite sample rates for dose responses, and root-n consistency, Gaussian approximation, and semiparametric efficiency with double spectral robustness for treatment effects. Follow the lecture's structure from introduction and motivation through Project STAR, main ideas, data setting, identification, RKHS algorithms, tuning, assumptions, and uniform consistency.