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Causal approaches to fairness have seen substantial recent interest, bothfrom the machine learning community and from wider parties interested inethical prediction algorithms. In no small part, this has been due to the factthat causal models allow one to simultaneously leverage data and expertknowledge to remove discriminatory effects from predictions. However, one ofthe primary assumptions in causal modeling is that you know the causal graph.This introduces a new opportunity for bias, caused by misspecifying the causalmodel. One common way for misspecification to occur is via unmeasuredconfounding: the true causal effect between variables is partially described byunobserved quantities. In this work we design tools to assess the sensitivityof fairness measures to this confounding for the popular class of non-linearadditive noise models (ANMs). Specifically, we give a procedure for computingthe maximum difference between two counterfactually fair predictors, where onehas become biased due to confounding. For the case of bivariate confounding ourtechnique can be swiftly computed via a sequence of closed-form updates. Formultivariate confounding we give an algorithm that can be efficiently solvedvia automatic differentiation. We demonstrate our new sensitivity analysistools in real-world fairness scenarios to assess the bias arising fromconfounding.

The Sensitivity of Counterfactual Fairness to Unmeasured Confounding