Measuring Model Fairness under Noisy Covariates: A Theoretical Perspective
This work addresses the challenge of fairness assessment in machine learning under practical data limitations, offering theoretical insights for scenarios where noisy covariates are common, though it is incremental in building on prior proxy-based methods.
The paper tackles the problem of measuring model fairness when covariates are noisy, focusing on group fairness metrics and using proxies for covariates instead of sensitive attributes. It presents a theoretical analysis showing that under weaker conditions, accurate fairness evaluation is possible, with error dominated by proxy performance rather than correlations, and validates this with simulations.
In this work we study the problem of measuring the fairness of a machine learning model under noisy information. Focusing on group fairness metrics, we investigate the particular but common situation when the evaluation requires controlling for the confounding effect of covariate variables. In a practical setting, we might not be able to jointly observe the covariate and group information, and a standard workaround is to then use proxies for one or more of these variables. Prior works have demonstrated the challenges with using a proxy for sensitive attributes, and strong independence assumptions are needed to provide guarantees on the accuracy of the noisy estimates. In contrast, in this work we study using a proxy for the covariate variable and present a theoretical analysis that aims to characterize weaker conditions under which accurate fairness evaluation is possible. Furthermore, our theory identifies potential sources of errors and decouples them into two interpretable parts $γ$ and $ε$. The first part $γ$ depends solely on the performance of the proxy such as precision and recall, whereas the second part $ε$ captures correlations between all the variables of interest. We show that in many scenarios the error in the estimates is dominated by $γ$ via a linear dependence, whereas the dependence on the correlations $ε$ only constitutes a lower order term. As a result we expand the understanding of scenarios where measuring model fairness 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 assuming some structure on the data, even weak, is key to significantly improve both theoretical guarantees and empirical results.