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

arXiv: https://arxiv.org/abs/2002.04788 · HTML: https://mlsanity.com/paper/2002.04788/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2020.

## Built on by (most cited first, 14 of 14)

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- [When Personalization Harms: Reconsidering the Use of Group Attributes in Prediction](https://mlsanity.com/paper/2206.02058/) (2022)
- [Impact of Data Processing on Fairness in Supervised Learning](https://mlsanity.com/paper/2102.01867/) (2021)
- [Differentially Private Fair Binary Classifications](https://mlsanity.com/paper/2402.15603/) (2024)
- [Quantifying Feature Contributions to Overall Disparity Using Information Theory](https://mlsanity.com/paper/2206.08454/) (2022)
- [To Pool or Not To Pool: Analyzing the Regularizing Effects of Group-Fair Training on Shared Models](https://mlsanity.com/paper/2402.18803/) (2024)
- [Does Privacy Always Harm Fairness? Data-Dependent Trade-offs via Chernoff Information Neural Estimation](https://mlsanity.com/paper/2601.13698/) (2026)

## Abstract (arXiv)

Disparate treatment occurs when a machine learning model yields different decisions for individuals based on a 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.