Quasi-Bayesian Dual Instrumental Variable Regression
This provides uncertainty estimates for instrumental variable regression in high-dimensional settings, which is incremental as it builds on existing kernelized and dual formulations.
The authors tackled the lack of uncertainty quantification in instrumental variable regression with flexible machine learning models by proposing a quasi-Bayesian procedure, achieving minimax optimal contraction rates and scalable inference that works with neural networks.
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.