Papers › Quasi-Bayesian Dual Instrumental Variable Regression

Quasi-Bayesian Dual Instrumental Variable Regression

16 Jun 2021NeurIPS 2021 12arXiv:2106.08750archive 2025-07-28

Ziyu Wang, Yuhao Zhou, Tongzheng Ren, Jun Zhu

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 L₂ 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.

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