  Intersectionality is a framework that analyzes how interlocking systems of
power and oppression affect individuals along overlapping dimensions including
race, gender, sexual orientation, class, and disability. Intersectionality
theory therefore implies it is important that fairness in artificial
intelligence systems be protected with regard to multi-dimensional protected
attributes. However, the measurement of fairness becomes statistically
challenging in the multi-dimensional setting due to data sparsity, which
increases rapidly in the number of dimensions, and in the values per dimension.
We present a Bayesian probabilistic modeling approach for the reliable,
data-efficient estimation of fairness with multi-dimensional protected
attributes, which we apply to two existing intersectional fairness metrics.
Experimental results on census data and the COMPAS criminal justice recidivism
dataset demonstrate the utility of our methodology, and show that Bayesian
methods are valuable for the modeling and measurement of fairness in an
intersectional context.
