# Quasi-Bayesian Dual Instrumental Variable Regression

arXiv: https://arxiv.org/abs/2106.08750 · HTML: https://mlsanity.com/paper/2106.08750/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 71 references that are in the map.
- First posted on arXiv 16 Jun 2021.

## Builds on (most cited first, 14 of 14)

- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Randomized Prior Functions for Deep Reinforcement Learning](https://mlsanity.com/paper/1806.03335/) (2018)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm](https://mlsanity.com/paper/1702.07254/) (2017)
- [Uncertainty in Neural Networks: Approximately Bayesian Ensembling](https://mlsanity.com/paper/1810.05546/) (2018)
- [Deep Generalized Method of Moments for Instrumental Variable Analysis](https://mlsanity.com/paper/1905.12495/) (2019)
- [Minimax Estimation of Conditional Moment Models](https://mlsanity.com/paper/2006.07201/) (2020)
- [Mat'ern Gaussian processes on Riemannian manifolds](https://mlsanity.com/paper/2006.10160/) (2020)
- [Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction](https://mlsanity.com/paper/2105.04544/) (2021)
- [Adversarial Generalized Method of Moments](https://mlsanity.com/paper/1803.07164/) (2018)
- [Optimal Sup-norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV Regression](https://mlsanity.com/paper/1508.03365/) (2015)
- [The Variational Method of Moments](https://mlsanity.com/paper/2012.09422/) (2020)
- [Frequentist coverage and sup-norm convergence rate in Gaussian process regression](https://mlsanity.com/paper/1708.04753/) (2017)

## Built on by (most cited first, 3 of 3)

- [Spectral Representation Learning for Conditional Moment Models](https://mlsanity.com/paper/2210.16525/) (2022)
- [Fast Instrument Learning with Faster Rates](https://mlsanity.com/paper/2205.10772/) (2022)
- [Generalized Bayes for Causal Inference](https://mlsanity.com/paper/2603.03035/) (2026)

## Abstract (arXiv)

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.