  It is of critical importance to be aware of the historical discrimination
embedded in the data and to consider a fairness measure to reduce bias
throughout the predictive modeling pipeline. Given various notions of fairness
defined in the literature, investigating the correlation and interaction among
metrics is vital for addressing unfairness. Practitioners and data scientists
should be able to comprehend each metric and examine their impact on one
another given the context, use case, and regulations. Exploring the
combinatorial space of different metrics for such examination is burdensome. To
alleviate the burden of selecting fairness notions for consideration, we
propose a framework that estimates the correlation among fairness notions. Our
framework consequently identifies a set of diverse and semantically distinct
metrics as representative for a given context. We propose a Monte-Carlo
sampling technique for computing the correlations between fairness metrics by
indirect and efficient perturbation in the model space. Using the estimated
correlations, we then find a subset of representative metrics. The paper
proposes a generic method that can be generalized to any arbitrary set of
fairness metrics. We showcase the validity of the proposal using comprehensive
experiments on real-world benchmark datasets.
