Instrumental Variable Regression with Confounder Balancing

Anpeng Wu, Kun Kuang, Bo Li, Fei Wu
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:24056-24075, 2022.

Abstract

This paper considers the challenge of estimating treatment effects from observational data in the presence of unmeasured confounders. A popular way to address this challenge is to utilize an instrumental variable (IV) for two-stage regression, i.e., 2SLS and variants, but limited to the linear setting. Recently, many nonlinear IV regression variants were proposed to overcome it by regressing the treatment with IVs and observed confounders in stage 1, leading to the imbalance of the observed confounders in stage 2. In this paper, we propose a Confounder Balanced IV Regression (CB-IV) algorithm to jointly remove the bias from the unmeasured confounders and balance the observed confounders. To the best of our knowledge, this is the first work to combine confounder balancing in IV regression for treatment effect estimation. Theoretically, we re-define and solve the inverse problems for the response-outcome function. Experiments show that our algorithm outperforms the existing approaches.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-wu22e, title = {Instrumental Variable Regression with Confounder Balancing}, author = {Wu, Anpeng and Kuang, Kun and Li, Bo and Wu, Fei}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {24056--24075}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/wu22e/wu22e.pdf}, url = {https://proceedings.mlr.press/v162/wu22e.html}, abstract = {This paper considers the challenge of estimating treatment effects from observational data in the presence of unmeasured confounders. A popular way to address this challenge is to utilize an instrumental variable (IV) for two-stage regression, i.e., 2SLS and variants, but limited to the linear setting. Recently, many nonlinear IV regression variants were proposed to overcome it by regressing the treatment with IVs and observed confounders in stage 1, leading to the imbalance of the observed confounders in stage 2. In this paper, we propose a Confounder Balanced IV Regression (CB-IV) algorithm to jointly remove the bias from the unmeasured confounders and balance the observed confounders. To the best of our knowledge, this is the first work to combine confounder balancing in IV regression for treatment effect estimation. Theoretically, we re-define and solve the inverse problems for the response-outcome function. Experiments show that our algorithm outperforms the existing approaches.} }
Endnote
%0 Conference Paper %T Instrumental Variable Regression with Confounder Balancing %A Anpeng Wu %A Kun Kuang %A Bo Li %A Fei Wu %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-wu22e %I PMLR %P 24056--24075 %U https://proceedings.mlr.press/v162/wu22e.html %V 162 %X This paper considers the challenge of estimating treatment effects from observational data in the presence of unmeasured confounders. A popular way to address this challenge is to utilize an instrumental variable (IV) for two-stage regression, i.e., 2SLS and variants, but limited to the linear setting. Recently, many nonlinear IV regression variants were proposed to overcome it by regressing the treatment with IVs and observed confounders in stage 1, leading to the imbalance of the observed confounders in stage 2. In this paper, we propose a Confounder Balanced IV Regression (CB-IV) algorithm to jointly remove the bias from the unmeasured confounders and balance the observed confounders. To the best of our knowledge, this is the first work to combine confounder balancing in IV regression for treatment effect estimation. Theoretically, we re-define and solve the inverse problems for the response-outcome function. Experiments show that our algorithm outperforms the existing approaches.
APA
Wu, A., Kuang, K., Li, B. & Wu, F.. (2022). Instrumental Variable Regression with Confounder Balancing. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:24056-24075 Available from https://proceedings.mlr.press/v162/wu22e.html.

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