Multi-Group Fairness Evaluation via Conditional Value-at-Risk Testing
Lucas Monteiro Paes Ananda Theertha Suresh Alex Beutel Flavio P. Calmon Ahmad Beirami
Machine learning (ML) models used in prediction and classification tasks may
display performance disparities across population groups determined by
sensitive attributes (e.g., race, sex, age). We consider the problem of
evaluating the performance of a fixed ML model across population groups defined
by multiple sensitive attributes (e.g., race and sex and age). Here, the sample
complexity for estimating the worst-case performance gap across groups (e.g.,
the largest difference in error rates) increases exponentially with the number
of group-denoting sensitive attributes. To address this issue, we propose an
approach to test for performance disparities based on Conditional Value-at-Risk
(CVaR). By allowing a small probabilistic slack on the groups over which a
model has approximately equal performance, we show that the sample complexity
required for discovering performance violations is reduced exponentially to be
at most upper bounded by the square root of the number of groups. As a
byproduct of our analysis, when the groups are weighted by a specific prior
distribution, we show that R\'enyi entropy of order $2/3$ of the prior
distribution captures the sample complexity of the proposed CVaR test
algorithm. Finally, we also show that there exists a non-i.i.d. data collection
strategy that results in a sample complexity independent of the number of
groups.