  Datasets often contain biases which unfairly disadvantage certain groups, and
classifiers trained on such datasets can inherit these biases. In this paper,
we provide a mathematical formulation of how this bias can arise. We do so by
assuming the existence of underlying, unknown, and unbiased labels which are
overwritten by an agent who intends to provide accurate labels but may have
biases against certain groups. Despite the fact that we only observe the biased
labels, we are able to show that the bias may nevertheless be corrected by
re-weighting the data points without changing the labels. We show, with
theoretical guarantees, that training on the re-weighted dataset corresponds to
training on the unobserved but unbiased labels, thus leading to an unbiased
machine learning classifier. Our procedure is fast and robust and can be used
with virtually any learning algorithm. We evaluate on a number of standard
machine learning fairness datasets and a variety of fairness notions, finding
that our method outperforms standard approaches in achieving fair
classification.
