Measuring Model Fairness under Noisy Covariates: A Theoretical Perspective

TL;DR

This paper provides a theoretical analysis of measuring machine learning model fairness using noisy covariate proxies, identifying conditions under which accurate fairness evaluation is feasible and analyzing sources of estimation errors.

Contribution

It introduces a weaker set of conditions for accurate fairness measurement with proxies and decouples error sources into interpretable components, expanding understanding of proxy-based fairness evaluation.

Findings

Error dominated by proxy performance metrics like precision and recall

Correlation effects between variables are lower order error contributors

Structured data assumptions improve theoretical and empirical accuracy

Abstract

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 $\gamma$ and $\epsilon$. The first part $\gamma$ depends solely on the performance of the proxy such as precision and recall, whereas the second part $\epsilon$ captures correlations between all the variables of interest. We show that in many scenarios the error in the estimates is dominated by $\gamma$ via a linear dependence, whereas the dependence on the correlations $\epsilon$ 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.