Fast Instrument Learning with Faster Rates

Ziyu Wang, Yuhao Zhou, Jun Zhu

Keywords: causal inference, kernel method, gaussian process

Abstract: We investigate nonlinear instrumental variable (IV) regression given high-dimensional instruments. We propose a simple algorithm which combines kernelized IV methods and an arbitrary, adaptive regression algorithm, accessed as a black box. Our algorithm enjoys faster-rate convergence and adapts to the dimensionality of informative latent features, while avoiding an expensive minimax optimization procedure, which has been necessary to establish similar guarantees. It further brings the benefit of flexible machine learning models to quasi-Bayesian uncertainty quantification, likelihood-based model selection, and model averaging. Simulation studies demonstrate the competitive performance of our method.

TL;DR: Fast and provably adaptive instrument learning, through kernel learning with black-box ML models.

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:2205.10772/code)