# Confounder Balancing for Instrumental Variable Regression with Latent Variable

arXiv: https://arxiv.org/abs/2211.10008 · HTML: https://mlsanity.com/paper/2211.10008/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 58 references that are in the map.
- First posted on arXiv 18 Nov 2022.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [CLUB: A Contrastive Log-ratio Upper Bound of Mutual Information](https://mlsanity.com/paper/2006.12013/) (2020)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [Learning Deep Features in Instrumental Variable Regression](https://mlsanity.com/paper/2010.07154/) (2020)
- [Treatment effect estimation with disentangled latent factors](https://mlsanity.com/paper/2001.10652/) (2020)
- [Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions](https://mlsanity.com/paper/1604.07125/) (2016)
- [Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variables](https://mlsanity.com/paper/1908.03932/) (2019)
- [Optimal Sup-norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV Regression](https://mlsanity.com/paper/1508.03365/) (2015)
- [A Critical Look at the Consistency of Causal Estimation With Deep Latent Variable Models](https://mlsanity.com/paper/2102.06648/) (2021)
- [Ivy: Instrumental Variable Synthesis for Causal Inference](https://mlsanity.com/paper/2004.05316/) (2020)
- [Efficient Online Estimation of Causal Effects by Deciding What to Observe](https://mlsanity.com/paper/2108.09265/) (2021)
- [Average causal effect estimation via instrumental variables: the no simultaneous heterogeneity assumption](https://mlsanity.com/paper/2010.10017/) (2020)
- [Homogeneity in the instrument-treatment association is not sufficient for the Wald estimand to equal the average causal effect for a binary instrument and a continuous exposure](https://mlsanity.com/paper/2107.01070/) (2021)

## Built on by (most cited first, 1 of 1)

- [Causal Inference with Complex Treatments: A Survey](https://mlsanity.com/paper/2407.14022/) (2024)

## Abstract (arXiv)

This paper studies the confounding effects from the unmeasured confounders and the imbalance of observed confounders in IV regression and aims at unbiased causal effect estimation. Recently, nonlinear IV estimators were proposed to allow for nonlinear model in both stages. However, the observed confounders may be imbalanced in stage 2, which could still lead to biased treatment effect estimation in certain cases. To this end, we propose a Confounder Balanced IV Regression (CB-IV) algorithm to jointly remove the bias from the unmeasured confounders and the imbalance of observed confounders. Theoretically, by redefining and solving an inverse problem for potential outcome function, we show that our CB-IV algorithm can unbiasedly estimate treatment effects and achieve lower variance. The IV methods have a major disadvantage in that little prior or theory is currently available to pre-define a valid IV in real-world scenarios. Thus, we study two more challenging settings without pre-defined valid IVs: (1) indistinguishable IVs implicitly present in observations, i.e., mixed-variable challenge, and (2) latent IVs don't appear in observations, i.e., latent-variable challenge. To address these two challenges, we extend our CB-IV by a latent-variable module, namely CB-IV-L algorithm. Extensive experiments demonstrate that our CB-IV(-L) outperforms the existing approaches.