Sensitivity Analysis to Unobserved Confounding with Copula-based Normalizing Flows
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918122968055808 |
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| author | Balgi, Sourabh Braun, Marc Peña, Jose M. Daoud, Adel |
| author_facet | Balgi, Sourabh Braun, Marc Peña, Jose M. Daoud, Adel |
| contents | We propose a novel method for sensitivity analysis to unobserved confounding in causal inference. The method builds on a copula-based causal graphical normalizing flow that we term $ρ$-GNF, where $ρ\in [-1,+1]$ is the sensitivity parameter. The parameter represents the non-causal association between exposure and outcome due to unobserved confounding, which is modeled as a Gaussian copula. In other words, the $ρ$-GNF enables scholars to estimate the average causal effect (ACE) as a function of $ρ$, accounting for various confounding strengths. The output of the $ρ$-GNF is what we term the $ρ_{curve}$, which provides the bounds for the ACE given an interval of assumed $ρ$ values. The $ρ_{curve}$ also enables scholars to identify the confounding strength required to nullify the ACE. We also propose a Bayesian version of our sensitivity analysis method. Assuming a prior over the sensitivity parameter $ρ$ enables us to derive the posterior distribution over the ACE, which enables us to derive credible intervals. Finally, leveraging on experiments from simulated and real-world data, we show the benefits of our sensitivity analysis method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08752 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sensitivity Analysis to Unobserved Confounding with Copula-based Normalizing Flows Balgi, Sourabh Braun, Marc Peña, Jose M. Daoud, Adel Methodology Machine Learning We propose a novel method for sensitivity analysis to unobserved confounding in causal inference. The method builds on a copula-based causal graphical normalizing flow that we term $ρ$-GNF, where $ρ\in [-1,+1]$ is the sensitivity parameter. The parameter represents the non-causal association between exposure and outcome due to unobserved confounding, which is modeled as a Gaussian copula. In other words, the $ρ$-GNF enables scholars to estimate the average causal effect (ACE) as a function of $ρ$, accounting for various confounding strengths. The output of the $ρ$-GNF is what we term the $ρ_{curve}$, which provides the bounds for the ACE given an interval of assumed $ρ$ values. The $ρ_{curve}$ also enables scholars to identify the confounding strength required to nullify the ACE. We also propose a Bayesian version of our sensitivity analysis method. Assuming a prior over the sensitivity parameter $ρ$ enables us to derive the posterior distribution over the ACE, which enables us to derive credible intervals. Finally, leveraging on experiments from simulated and real-world data, we show the benefits of our sensitivity analysis method. |
| title | Sensitivity Analysis to Unobserved Confounding with Copula-based Normalizing Flows |
| topic | Methodology Machine Learning |
| url | https://arxiv.org/abs/2508.08752 |