PCM Selector: Penalized Covariate-Mediator Selection Operator for Evaluating Linear Causal Effects
Hisayoshi Nanmo, Manabu Kuroki
Abstract
For a data-generating process for random variables that can be described with a linear structural equation model, we consider a situation in which (i) a set of covariates satisfying the back-door criterion cannot be observed or (ii) such a set can be observed, but standard statistical estimation methods cannot be applied to estimate causal effects because of multicollinearity/high-dimensional data problems. We propose a novel two-stage penalized regression approach, the penalized covariate-mediator selection operator (PCM Selector), to estimate the causal effects in such scenarios. Unlike existing penalized regression analyses, when a set of intermediate variables is available, PCM Selector provides a consistent or less biased estimator of the causal effect. In addition, PCM Selector provides a variable selection procedure for intermediate variables to obtain better estimation accuracy of the causal effects than does the back-door criterion.
BibTeX
@article{Nanmo_Kuroki_2025, title={PCM Selector: Penalized Covariate-Mediator Selection Operator for Evaluating Linear Causal Effects}, volume={39}, url={https://ojs.aaai.org/index.php/AAAI/article/view/34889}, DOI={10.1609/aaai.v39i25.34889}, abstractNote={For a data-generating process for random variables that can be described with a linear structural equation model, we consider a situation in which (i) a set of covariates satisfying the back-door criterion cannot be observed or (ii) such a set can be observed, but standard statistical estimation methods cannot be applied to estimate causal effects because of multicollinearity/high-dimensional data problems. We propose a novel two-stage penalized regression approach, the penalized covariate-mediator selection operator (PCM Selector), to estimate the causal effects in such scenarios. Unlike existing penalized regression analyses, when a set of intermediate variables is available, PCM Selector provides a consistent or less biased estimator of the causal effect. In addition, PCM Selector provides a variable selection procedure for intermediate variables to obtain better estimation accuracy of the causal effects than does the back-door criterion.}, number={25}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Nanmo, Hisayoshi and Kuroki, Manabu}, year={2025}, month={Apr.}, pages={26851-26858} }