Measuring Model Fairness under Noisy Covariates: A Theoretical Perspective
In this work we study the problem of measuring the fairness of a machine learning model under noisy information. In many applications, evaluating a model according to a well-specified metric such as the FPR requires access to variables that cannot be jointly observed in a given practical setting. A standard workaround is to then use proxies for one or more of these variables. These proxies are either obtained using domain expertise or by training another machine learning model. Prior works have demonstrated the dangers of using such an approach, and strong independence assumptions are needed to provide guarantees on the accuracy of the noisy estimates via proxies. In contrast, in this work we present a general theoretical framework that aims to characterize weaker conditions under which accurate model auditing is possible via the above approach. Furthermore, our theory identifies potential sources of errors and decouples them into two interpretable parts Epsilon_c and Epsilon_g. The first part depends on natural properties of the proxy such as precision and recall, whereas the second part captures correlations between different variables of interest. We show that in many scenarios the error in the estimates is dominated by the Epsilon_c via a linear dependence, whereas the dependence on the correlations only constitutes a lower order term. As a result we expand the understanding of scenarios where model auditing via proxies can be an effective approach. Finally, we compare via simulations the theoretical upper-bounds to the distribution of simulated estimation errors and show that both theoretical guarantees and empirical results significantly improve as we progressively enforce structure along the conditions highlighted by the theory.