Scalable Quasi-Bayesian Inference for Instrumental Variable Regression

Ziyu Wang, Yuhao Zhou, Tongzheng Ren, Jun Zhu

Keywords: probabilistic methods, causal inference, uncertainty quantification, instrumental variable, approximate inference

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 scalable quasi-Bayesian procedure for IV regression, building upon the recently developed kernelized IV models. Contrary to Bayesian modeling for IV, our approach does not require additional assumptions on the data generating process, and leads to a scalable approximate inference algorithm with time cost comparable to the corresponding point estimation methods. Our algorithm can be further extended to work with neural network models. We analyze the theoretical properties of the proposed quasi-posterior, and demonstrate through empirical evaluation the competitive performance of our method.

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TL;DR: A scalable uncertainty quantification procedure for kernelized and NN-based IV models.

Code: https://github.com/meta-inf/qbdiv

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2106.08750/code)