$ρ$-GNF : A Novel Sensitivity Analysis Approach Under Unobserved Confounders

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 $\rho$-GNF ($\rho$-Graphical Normalizing Flow), where $\rho{\in}[-1,+1]$ 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, $\rho$-GNF enables us to estimate and analyse the frontdoor causal effect or average causal effect (ACE) as a function of $\rho$. We call this the $\rho_{curve}$. The $\rho_{curve}$ enables us to specify the confounding strength required to nullify the ACE. We call this the $\rho_{value}$. Further, the $\rho_{curve}$ also enables us to provide bounds for the ACE given an interval of $\rho$ values. We illustrate the benefits of $\rho$-GNF with experiments on simulated and real-world data in terms of our empirical ACE bounds being narrower than other popular ACE bounds.