Partially adaptive regularized multiple regression analysis for estimating linear causal effects

Hisayoshi Nanmo, Manabu Kuroki
Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, PMLR 180:1456-1465, 2022.

Abstract

This paper assumes that cause-effect relationships among variables can be described with a linear structural equation model. Then, a situation is considered where a set of observed covariates satisfies the back-door criterion but the ordinary least squares method cannot be applied to estimate linear causal effects because of multicollinearity/high-dimensional data problems. In this situation, we propose a novel regression approach, the “partially adaptive L$_p$-regularized multiple regression analysis” (PAL$_p$MA) method for estimating the total effects. Different from standard regularized regression analysis, PAL$_p$MA provides a consistent or less-biased estimator of the linear causal effect. PAL$_p$MA is also applicable to evaluating direct effects through the single-door criterion. Given space constraints, the proofs, some numerical experiments, and an industrial case study on setting up painting conditions of car bodies are provided in the Supplementary Material.

Cite this Paper

BibTeX
@InProceedings{pmlr-v180-nanmo22a, title = {Partially adaptive regularized multiple regression analysis for estimating linear causal effects}, author = {Nanmo, Hisayoshi and Kuroki, Manabu}, booktitle = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence}, pages = {1456--1465}, year = {2022}, editor = {Cussens, James and Zhang, Kun}, volume = {180}, series = {Proceedings of Machine Learning Research}, month = {01--05 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v180/nanmo22a/nanmo22a.pdf}, url = {https://proceedings.mlr.press/v180/nanmo22a.html}, abstract = {This paper assumes that cause-effect relationships among variables can be described with a linear structural equation model. Then, a situation is considered where a set of observed covariates satisfies the back-door criterion but the ordinary least squares method cannot be applied to estimate linear causal effects because of multicollinearity/high-dimensional data problems. In this situation, we propose a novel regression approach, the “partially adaptive L$_p$-regularized multiple regression analysis” (PAL$_p$MA) method for estimating the total effects. Different from standard regularized regression analysis, PAL$_p$MA provides a consistent or less-biased estimator of the linear causal effect. PAL$_p$MA is also applicable to evaluating direct effects through the single-door criterion. Given space constraints, the proofs, some numerical experiments, and an industrial case study on setting up painting conditions of car bodies are provided in the Supplementary Material.} }
Endnote
%0 Conference Paper %T Partially adaptive regularized multiple regression analysis for estimating linear causal effects %A Hisayoshi Nanmo %A Manabu Kuroki %B Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2022 %E James Cussens %E Kun Zhang %F pmlr-v180-nanmo22a %I PMLR %P 1456--1465 %U https://proceedings.mlr.press/v180/nanmo22a.html %V 180 %X This paper assumes that cause-effect relationships among variables can be described with a linear structural equation model. Then, a situation is considered where a set of observed covariates satisfies the back-door criterion but the ordinary least squares method cannot be applied to estimate linear causal effects because of multicollinearity/high-dimensional data problems. In this situation, we propose a novel regression approach, the “partially adaptive L$_p$-regularized multiple regression analysis” (PAL$_p$MA) method for estimating the total effects. Different from standard regularized regression analysis, PAL$_p$MA provides a consistent or less-biased estimator of the linear causal effect. PAL$_p$MA is also applicable to evaluating direct effects through the single-door criterion. Given space constraints, the proofs, some numerical experiments, and an industrial case study on setting up painting conditions of car bodies are provided in the Supplementary Material.
APA
Nanmo, H. & Kuroki, M.. (2022). Partially adaptive regularized multiple regression analysis for estimating linear causal effects. Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 180:1456-1465 Available from https://proceedings.mlr.press/v180/nanmo22a.html.

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