  Machine learning (ML) models can underperform on certain population groups
due to choices made during model development and bias inherent in the data. We
categorize sources of discrimination in the ML pipeline into two classes:
aleatoric discrimination, which is inherent in the data distribution, and
epistemic discrimination, which is due to decisions made during model
development. We quantify aleatoric discrimination by determining the
performance limits of a model under fairness constraints, assuming perfect
knowledge of the data distribution. We demonstrate how to characterize
aleatoric discrimination by applying Blackwell's results on comparing
statistical experiments. We then quantify epistemic discrimination as the gap
between a model's accuracy when fairness constraints are applied and the limit
posed by aleatoric discrimination. We apply this approach to benchmark existing
fairness interventions and investigate fairness risks in data with missing
values. Our results indicate that state-of-the-art fairness interventions are
effective at removing epistemic discrimination on standard (overused) tabular
datasets. However, when data has missing values, there is still significant
room for improvement in handling aleatoric discrimination.
