Year: 2021
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Wang, Ziyu, Zhou, Yuhao, Ren, Tongzheng, Zhu, Jun
Institutions: Tsinghua University, The University of Texas at Austin
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3210058712