Partially adaptive regularized multiple regression analysis for estimating linear causal effects
Hisayoshi Nanmo, Manabu Kuroki
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.
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.}
}