  How can we control for latent discrimination in predictive models? How can we
provably remove it? Such questions are at the heart of algorithmic fairness and
its impacts on society. In this paper, we define a new operational fairness
criteria, inspired by the well-understood notion of omitted variable-bias in
statistics and econometrics. Our notion of fairness effectively controls for
sensitive features and provides diagnostics for deviations from fair decision
making. We then establish analytical and algorithmic results about the
existence of a fair classifier in the context of supervised learning. Our
results readily imply a simple, but rather counter-intuitive, strategy for
eliminating latent discrimination. In order to prevent other features proxying
for sensitive features, we need to include sensitive features in the training
phase, but exclude them in the test/evaluation phase while controlling for
their effects. We evaluate the performance of our algorithm on several
real-world datasets and show how fairness for these datasets can be improved
with a very small loss in accuracy.
