Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference

Amiremad Ghassami, Andrew Ying, Ilya Shpitser, Eric Tchetgen Tchetgen
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:7210-7239, 2022.

Abstract

Robins et al. (2008) introduced a class of influence functions (IFs) which could be used to obtain doubly robust moment functions for the corresponding parameters. However, that class does not include the IF of parameters for which the nuisance functions are solutions to integral equations. Such parameters are particularly important in the field of causal inference, specifically in the recently proposed proximal causal inference framework of Tchetgen Tchetgen et al. (2020), which allows for estimating the causal effect in the presence of latent confounders. In this paper, we first extend the class of Robins et al. to include doubly robust IFs in which the nuisance functions are solutions to integral equations. Then we demonstrate that the double robustness property of these IFs can be leveraged to construct estimating equations for the nuisance functions, which enables us to solve the integral equations without resorting to parametric models. We frame the estimation of the nuisance functions as a minimax optimization problem. We provide convergence rates for the nuisance functions and conditions required for asymptotic linearity of the estimator of the parameter of interest. The experiment results demonstrate that our proposed methodology leads to robust and high-performance estimators for average causal effect in the proximal causal inference framework.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-ghassami22a, title = { Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference }, author = {Ghassami, Amiremad and Ying, Andrew and Shpitser, Ilya and Tchetgen Tchetgen, Eric}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {7210--7239}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/ghassami22a/ghassami22a.pdf}, url = {https://proceedings.mlr.press/v151/ghassami22a.html}, abstract = { Robins et al. (2008) introduced a class of influence functions (IFs) which could be used to obtain doubly robust moment functions for the corresponding parameters. However, that class does not include the IF of parameters for which the nuisance functions are solutions to integral equations. Such parameters are particularly important in the field of causal inference, specifically in the recently proposed proximal causal inference framework of Tchetgen Tchetgen et al. (2020), which allows for estimating the causal effect in the presence of latent confounders. In this paper, we first extend the class of Robins et al. to include doubly robust IFs in which the nuisance functions are solutions to integral equations. Then we demonstrate that the double robustness property of these IFs can be leveraged to construct estimating equations for the nuisance functions, which enables us to solve the integral equations without resorting to parametric models. We frame the estimation of the nuisance functions as a minimax optimization problem. We provide convergence rates for the nuisance functions and conditions required for asymptotic linearity of the estimator of the parameter of interest. The experiment results demonstrate that our proposed methodology leads to robust and high-performance estimators for average causal effect in the proximal causal inference framework. } }
Endnote
%0 Conference Paper %T Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference %A Amiremad Ghassami %A Andrew Ying %A Ilya Shpitser %A Eric Tchetgen Tchetgen %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-ghassami22a %I PMLR %P 7210--7239 %U https://proceedings.mlr.press/v151/ghassami22a.html %V 151 %X Robins et al. (2008) introduced a class of influence functions (IFs) which could be used to obtain doubly robust moment functions for the corresponding parameters. However, that class does not include the IF of parameters for which the nuisance functions are solutions to integral equations. Such parameters are particularly important in the field of causal inference, specifically in the recently proposed proximal causal inference framework of Tchetgen Tchetgen et al. (2020), which allows for estimating the causal effect in the presence of latent confounders. In this paper, we first extend the class of Robins et al. to include doubly robust IFs in which the nuisance functions are solutions to integral equations. Then we demonstrate that the double robustness property of these IFs can be leveraged to construct estimating equations for the nuisance functions, which enables us to solve the integral equations without resorting to parametric models. We frame the estimation of the nuisance functions as a minimax optimization problem. We provide convergence rates for the nuisance functions and conditions required for asymptotic linearity of the estimator of the parameter of interest. The experiment results demonstrate that our proposed methodology leads to robust and high-performance estimators for average causal effect in the proximal causal inference framework.
APA
Ghassami, A., Ying, A., Shpitser, I. & Tchetgen Tchetgen, E.. (2022). Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:7210-7239 Available from https://proceedings.mlr.press/v151/ghassami22a.html.

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