  Non-discrimination is a recognized objective in algorithmic decision making.
In this paper, we introduce a novel probabilistic formulation of data
pre-processing for reducing discrimination. We propose a convex optimization
for learning a data transformation with three goals: controlling
discrimination, limiting distortion in individual data samples, and preserving
utility. We characterize the impact of limited sample size in accomplishing
this objective, and apply two instances of the proposed optimization to
datasets, including one on real-world criminal recidivism. The results
demonstrate that all three criteria can be simultaneously achieved and also
reveal interesting patterns of bias in American society.
