$ρ$-GNF: A Copula-based Sensitivity Analysis to Unobserved Confounding Using Normalizing Flows

Sourabh Balgi, Jose M. Peña, Adel Daoud
Proceedings of The 12th International Conference on Probabilistic Graphical Models, PMLR 246:20-37, 2024.

Abstract

We propose a novel sensitivity analysis to unobserved confounding in observational studies using copulas and normalizing flows. Using the idea of interventional equivalence of structural causal models, we develop $\rho$-GNF ($\rho$-graphical normalizing flow), where $\rho{\in}[-1,+1]$ is a bounded sensitivity parameter. This parameter represents the back-door non-causal association due to unobserved confounding, and which is encoded with a Gaussian copula. In other words, the $\rho$-GNF enables scholars to estimate the average causal effect (ACE) as a function of $\rho$, while accounting for various assumed strengths of the unobserved confounding. The output of the $\rho$-GNF is what we denote as the $\rho_{curve}$ that provides the bounds for the ACE given an interval of assumed $\rho$ values. In particular, the $\rho_{curve}$ enables scholars to identify the confounding strength required to nullify the ACE, similar to other sensitivity analysis methods (e.g., the E-value). Leveraging on experiments from simulated and real-world data, we show the benefits of $\rho$-GNF. One benefit is that the $\rho$-GNF uses a Gaussian copula to encode the distribution of the unobserved causes, which is commonly used in many applied settings. This distributional assumption produces narrower ACE bounds compared to other popular sensitivity analysis methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v246-balgi24a, title = {$ρ$-GNF: A Copula-based Sensitivity Analysis to Unobserved Confounding Using Normalizing Flows}, author = {Balgi, Sourabh and Pe\~na, Jose M. and Daoud, Adel}, booktitle = {Proceedings of The 12th International Conference on Probabilistic Graphical Models}, pages = {20--37}, year = {2024}, editor = {Kwisthout, Johan and Renooij, Silja}, volume = {246}, series = {Proceedings of Machine Learning Research}, month = {11--13 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v246/main/assets/balgi24a/balgi24a.pdf}, url = {https://proceedings.mlr.press/v246/balgi24a.html}, abstract = {We propose a novel sensitivity analysis to unobserved confounding in observational studies using copulas and normalizing flows. Using the idea of interventional equivalence of structural causal models, we develop $\rho$-GNF ($\rho$-graphical normalizing flow), where $\rho{\in}[-1,+1]$ is a bounded sensitivity parameter. This parameter represents the back-door non-causal association due to unobserved confounding, and which is encoded with a Gaussian copula. In other words, the $\rho$-GNF enables scholars to estimate the average causal effect (ACE) as a function of $\rho$, while accounting for various assumed strengths of the unobserved confounding. The output of the $\rho$-GNF is what we denote as the $\rho_{curve}$ that provides the bounds for the ACE given an interval of assumed $\rho$ values. In particular, the $\rho_{curve}$ enables scholars to identify the confounding strength required to nullify the ACE, similar to other sensitivity analysis methods (e.g., the E-value). Leveraging on experiments from simulated and real-world data, we show the benefits of $\rho$-GNF. One benefit is that the $\rho$-GNF uses a Gaussian copula to encode the distribution of the unobserved causes, which is commonly used in many applied settings. This distributional assumption produces narrower ACE bounds compared to other popular sensitivity analysis methods.} }
Endnote
%0 Conference Paper %T $ρ$-GNF: A Copula-based Sensitivity Analysis to Unobserved Confounding Using Normalizing Flows %A Sourabh Balgi %A Jose M. Peña %A Adel Daoud %B Proceedings of The 12th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2024 %E Johan Kwisthout %E Silja Renooij %F pmlr-v246-balgi24a %I PMLR %P 20--37 %U https://proceedings.mlr.press/v246/balgi24a.html %V 246 %X We propose a novel sensitivity analysis to unobserved confounding in observational studies using copulas and normalizing flows. Using the idea of interventional equivalence of structural causal models, we develop $\rho$-GNF ($\rho$-graphical normalizing flow), where $\rho{\in}[-1,+1]$ is a bounded sensitivity parameter. This parameter represents the back-door non-causal association due to unobserved confounding, and which is encoded with a Gaussian copula. In other words, the $\rho$-GNF enables scholars to estimate the average causal effect (ACE) as a function of $\rho$, while accounting for various assumed strengths of the unobserved confounding. The output of the $\rho$-GNF is what we denote as the $\rho_{curve}$ that provides the bounds for the ACE given an interval of assumed $\rho$ values. In particular, the $\rho_{curve}$ enables scholars to identify the confounding strength required to nullify the ACE, similar to other sensitivity analysis methods (e.g., the E-value). Leveraging on experiments from simulated and real-world data, we show the benefits of $\rho$-GNF. One benefit is that the $\rho$-GNF uses a Gaussian copula to encode the distribution of the unobserved causes, which is commonly used in many applied settings. This distributional assumption produces narrower ACE bounds compared to other popular sensitivity analysis methods.
APA
Balgi, S., Peña, J.M. & Daoud, A.. (2024). $ρ$-GNF: A Copula-based Sensitivity Analysis to Unobserved Confounding Using Normalizing Flows. Proceedings of The 12th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 246:20-37 Available from https://proceedings.mlr.press/v246/balgi24a.html.

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