ρ-GNF : A Novel Sensitivity Analysis Approach Under Unobserved Confounders
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We propose a new sensitivity analysis model that combines copulas and normalizing flows for causal inference under unobserved confounding. We refer to the new model as ρ-GNF (ρ-Graphical Normalizing Flow), where ρ∈[-1,+1] is a bounded sensitivity parameter representing the backdoor non-causal association due to unobserved confounding modeled using the most well studied and widely popular Gaussian copula. Specifically, ρ-GNF enables us to estimate and analyse the frontdoor causal effect or average causal effect (ACE) as a function of ρ. We call this the ρ_curve. The ρ_curve enables us to specify the confounding strength required to nullify the ACE. We call this the ρ_value. Further, the ρ_curve also enables us to provide bounds for the ACE given an interval of ρ values. We illustrate the benefits of ρ-GNF with experiments on simulated and real-world data in terms of our empirical ACE bounds being narrower than other popular ACE bounds.
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