Reproduce “Kernel Instrumental Variable Regression” on OpenResearch

About this paper

Rahul Singh, Maneesh Sahani, Arthur Gretton

KIV addresses causal demand estimation when prices and sales are confounded. It uses instrumental variables and replaces linear two-stage least squares with two kernel regressions: stage one learns a conditional mean embedding of inputs given the instrument, and stage two predicts outcomes from those embeddings. In simulations, KIV leads runnable methods at 5,000 and 10,000 observations, but not uniformly.

Key insights

• The RKHS formulation of the IV problem, particularly for estimating conditional mean embeddings, allows for direct, closed-form solutions in both stages, avoiding complex density estimation or sampling.
• KIV can achieve the minimax optimal convergence rate for its end-to-end estimator, a rate theoretically equivalent to optimal single-stage regression in unconfounded settings, demonstrating its statistical efficiency.
• An asymmetric sample splitting strategy, allocating more samples to Stage 1 (n) than Stage 2 (m), is crucial for achieving minimax optimality, providing a novel theoretical prescription for two-stage IV methods.

Summary by alphaXiv.