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Generative models trained with Differential Privacy (DP) can producesynthetic data while reducing privacy risks. However, navigating theirprivacy-utility tradeoffs makes finding the best models for specificsettings/tasks challenging. This paper bridges this gap by profiling how DPgenerative models for tabular data distribute privacy budgets across rows andcolumns, which is one of the primary sources of utility degradation. We comparegraphical and deep generative models, focusing on the key factors contributingto how privacy budgets are spent, i.e., underlying modeling techniques, DPmechanisms, and data dimensionality.  Through our measurement study, we shed light on the characteristics that makedifferent models suitable for various settings and tasks. For instance, we findthat graphical models distribute privacy budgets horizontally and thus cannothandle relatively wide datasets for a fixed training time; also, theperformance on the task they were optimized for monotonically increases withmore data but could also overfit. Deep generative models spend their budgetsper iteration, so their behavior is less predictable with varying datasetdimensions, but are more flexible as they could perform better if trained onmore features. Moreover, low levels of privacy ($\epsilon\geq100$) could helpsome models generalize, achieving better results than without applying DP. Webelieve our work will aid the deployment of DP synthetic data techniques bynavigating through the best candidate models vis-a-vis the dataset features,desired privacy levels, and downstream tasks.

Graphical vs. Deep Generative Models: Measuring the Impact of Differentially Private Mechanisms and Budgets on Utility