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Generative models trained with Differential Privacy (DP) can be used togenerate synthetic data while minimizing privacy risks. We analyze the impactof DP on these models vis-a-vis underrepresented classes/subgroups of data,specifically, studying: 1) the size of classes/subgroups in the synthetic data,and 2) the accuracy of classification tasks run on them. We also evaluate theeffect of various levels of imbalance and privacy budgets. Our analysis usesthree state-of-the-art DP models (PrivBayes, DP-WGAN, and PATE-GAN) and showsthat DP yields opposite size distributions in the generated synthetic data. Itaffects the gap between the majority and minority classes/subgroups; in somecases by reducing it (a "Robin Hood" effect) and, in others, by increasing it(a "Matthew" effect). Either way, this leads to (similar) disparate impacts onthe accuracy of classification tasks on the synthetic data, affectingdisproportionately more the underrepresented subparts of the data.Consequently, when training models on synthetic data, one might incur the riskof treating different subpopulations unevenly, leading to unreliable or unfairconclusions.

Robin Hood and Matthew Effects: Differential Privacy Has Disparate Impact on Synthetic Data