Fast Instrument Learning with Faster Rates

TL;DR

This paper introduces a novel nonlinear instrumental variable regression method that combines kernelized techniques with adaptive algorithms, achieving faster convergence rates and flexibility in high-dimensional settings.

Contribution

It presents a simple, efficient algorithm that avoids complex optimization, adapts to latent feature dimensions, and enhances uncertainty quantification and model selection in IV regression.

Findings

Faster convergence rates demonstrated in simulations

Flexible integration with machine learning models

Competitive performance in high-dimensional IV regression

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.