Kernel Instrumental Variable Regression
This work addresses causal inference in observational data for researchers and practitioners, offering a novel nonparametric method that improves over existing approaches.
The authors tackled the problem of learning causal relationships from observational data with confounding by proposing kernel instrumental variable regression (KIV), a nonparametric generalization of two-stage least squares. They proved its consistency and optimal convergence rates, and in experiments, it outperformed state-of-the-art alternatives for nonparametric IV regression.
Instrumental variable (IV) regression is a strategy for learning causal relationships in observational data. If measurements of input X and output Y are confounded, the causal relationship can nonetheless be identified if an instrumental variable Z is available that influences X directly, but is conditionally independent of Y given X and the unmeasured confounder. The classic two-stage least squares algorithm (2SLS) simplifies the estimation problem by modeling all relationships as linear functions. We propose kernel instrumental variable regression (KIV), a nonparametric generalization of 2SLS, modeling relations among X, Y, and Z as nonlinear functions in reproducing kernel Hilbert spaces (RKHSs). We prove the consistency of KIV under mild assumptions, and derive conditions under which convergence occurs at the minimax optimal rate for unconfounded, single-stage RKHS regression. In doing so, we obtain an efficient ratio between training sample sizes used in the algorithm's first and second stages. In experiments, KIV outperforms state of the art alternatives for nonparametric IV regression.