  The vast majority of techniques to train fair models require access to the
protected attribute (e.g., race, gender), either at train time or in
production. However, in many important applications this protected attribute is
largely unavailable. In this paper, we develop methods for measuring and
reducing fairness violations in a setting with limited access to protected
attribute labels. Specifically, we assume access to protected attribute labels
on a small subset of the dataset of interest, but only probabilistic estimates
of protected attribute labels (e.g., via Bayesian Improved Surname Geocoding)
for the rest of the dataset. With this setting in mind, we propose a method to
estimate bounds on common fairness metrics for an existing model, as well as a
method for training a model to limit fairness violations by solving a
constrained non-convex optimization problem. Unlike similar existing
approaches, our methods take advantage of contextual information --
specifically, the relationships between a model's predictions and the
probabilistic prediction of protected attributes, given the true protected
attribute, and vice versa -- to provide tighter bounds on the true disparity.
We provide an empirical illustration of our methods using voting data. First,
we show our measurement method can bound the true disparity up to 5.5x tighter
than previous methods in these applications. Then, we demonstrate that our
training technique effectively reduces disparity while incurring lesser
fairness-accuracy trade-offs than other fair optimization methods with limited
access to protected attributes.
