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

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