Kernel Methods For Causal Inference
37Rahul Singh (MIT)
https://simons.berkeley.edu/talks/kernel-methods-causal-inference
Algorithmic Aspects of Causal Inference
We propose a family of estimators based on kernel ridge regression for nonparametric dose response curves and semiparametric treatment effects. Treatment and covariates may be discrete or continuous, and low, high, or infinite dimensional. We reduce causal estimation and inference to combinations of kernel ridge regressions, which have closed form solutions and are easily computed by matrix operations, unlike other machine learning paradigms. This computational simplicity allows us to extend the framework to several settings: (i) heterogeneous effects and distribution shift; (ii) instruments and proxies; (iii) mediation and dynamic effects; (iv) sample selection and data fusion. For dose responses, we prove uniform consistency with finite sample rates. For treatment effects, we prove root-n consistency, Gaussian approximation, and semiparametric efficiency with a new double spectral robustness property.