Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction
Afsaneh Mastouri, Yuchen Zhu, Limor Gultchin, Anna Korba, Ricardo Silva, Matt Kusner, Arthur Gretton, Krikamol Muandet
Abstract
We address the problem of causal effect estima-tion in the presence of unobserved confounding,but where proxies for the latent confounder(s) areobserved. We propose two kernel-based meth-ods for nonlinear causal effect estimation in thissetting: (a) a two-stage regression approach, and(b) a maximum moment restriction approach. Wefocus on the proximal causal learning setting, butour methods can be used to solve a wider classof inverse problems characterised by a Fredholmintegral equation. In particular, we provide a uni-fying view of two-stage and moment restrictionapproaches for solving this problem in a nonlin-ear setting. We provide consistency guaranteesfor each algorithm, and demonstrate that these ap-proaches achieve competitive results on syntheticdata and data simulating a real-world task. In par-ticular, our approach outperforms earlier methodsthat are not suited to leveraging proxy variables.
BibTeX
@InProceedings{pmlr-v139-mastouri21a,
title = {Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction},
author = {Mastouri, Afsaneh and Zhu, Yuchen and Gultchin, Limor and Korba, Anna and Silva, Ricardo and Kusner, Matt and Gretton, Arthur and Muandet, Krikamol},
booktitle = {Proceedings of the 38th International Conference on Machine Learning},
pages = {7512--7523},
year = {2021},
editor = {Meila, Marina and Zhang, Tong},
volume = {139},
series = {Proceedings of Machine Learning Research},
month = {18--24 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v139/mastouri21a/mastouri21a.pdf},
url = {https://proceedings.mlr.press/v139/mastouri21a.html},
abstract = {We address the problem of causal effect estima-tion in the presence of unobserved confounding,but where proxies for the latent confounder(s) areobserved. We propose two kernel-based meth-ods for nonlinear causal effect estimation in thissetting: (a) a two-stage regression approach, and(b) a maximum moment restriction approach. Wefocus on the proximal causal learning setting, butour methods can be used to solve a wider classof inverse problems characterised by a Fredholmintegral equation. In particular, we provide a uni-fying view of two-stage and moment restrictionapproaches for solving this problem in a nonlin-ear setting. We provide consistency guaranteesfor each algorithm, and demonstrate that these ap-proaches achieve competitive results on syntheticdata and data simulating a real-world task. In par-ticular, our approach outperforms earlier methodsthat are not suited to leveraging proxy variables.}
}