Quasi-Bayesian Dual Instrumental Variable Regression

TL;DR

This paper introduces a quasi-Bayesian approach for instrumental variable regression that provides uncertainty quantification, leveraging kernelized models and dual formulations, with theoretical guarantees and scalable algorithms for high-dimensional data.

Contribution

It develops a novel quasi-Bayesian IV regression method with minimax optimal contraction rates and extends to neural networks, addressing the lack of uncertainty quantification in machine learning-based IV methods.

Findings

Achieves minimax optimal contraction rates in $L_2$ and Sobolev norms.

Provides valid credible balls with frequentist guarantees.

Demonstrates effective uncertainty estimation on high-dimensional problems.

Abstract

Recent years have witnessed an upsurge of interest in employing flexible machine learning models for instrumental variable (IV) regression, but the development of uncertainty quantification methodology is still lacking. In this work we present a novel quasi-Bayesian procedure for IV regression, building upon the recently developed kernelized IV models and the dual/minimax formulation of IV regression. We analyze the frequentist behavior of the proposed method, by establishing minimax optimal contraction rates in $L_2$ and Sobolev norms, and discussing the frequentist validity of credible balls. We further derive a scalable inference algorithm which can be extended to work with wide neural network models. Empirical evaluation shows that our method produces informative uncertainty estimates on complex high-dimensional problems.