To Split or not to Split: The Impact of Disparate Treatment in Classification

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Abstract
Disparate treatment occurs when a machine learning model produces different decisions for individuals based on a legally protected or sensitive attribute (e.g., age, sex). In domains where prediction accuracy is paramount, it could potentially be acceptable to fit a model which exhibits disparate treatment. To evaluate the effect of disparate treatment, we compare the performance of split classifiers (i.e., classifiers trained and deployed separately on each group) with group-blind classifiers (i.e., classifiers which do not use a sensitive attribute). We introduce the benefit-of-splitting for quantifying the performance improvement by splitting classifiers. Computing the benefit-of-splitting directly from its definition could be intractable since it involves solving optimization problems over an infinite-dimensional functional space. Under different performance measures, we (i) prove an equivalent expression for the benefit-of-splitting which can be efficiently computed by solving small-scale convex programs; (ii) provide sharp upper and lower bounds for the benefit-of-splitting which reveal precise conditions where a group-blind classifier will always suffer from a non-trivial performance gap from the split classifiers. In the finite sample regime, splitting is not necessarily beneficial and we provide data-dependent bounds to understand this effect. Finally, we validate our theoretical results through numerical experiments on both synthetic and real-world datasets.
Funding Information
  • National Science Foundation (CIF 1900750, CAREER 1845852, IIS 1926925)
  • Amazon Research Award
  • Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica (IA101021)

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