  Generative models trained with Differential Privacy (DP) are increasingly
used to produce synthetic data while reducing privacy risks. Navigating their
specific privacy-utility tradeoffs makes it challenging to determine which
models would work best for specific settings/tasks. In this paper, we fill this
gap in the context of tabular data by analyzing how DP generative models
distribute privacy budgets across rows and columns, arguably the main source of
utility degradation. We examine the main factors contributing to how privacy
budgets are spent, including underlying modeling techniques, DP mechanisms, and
data dimensionality.
  Our extensive evaluation of both graphical and deep generative models sheds
light on the distinctive features that render them suitable for different
settings and tasks. We show that graphical models distribute the privacy budget
horizontally and thus cannot handle relatively wide datasets while the
performance on the task they were optimized for monotonically increases with
more data. Deep generative models spend their budget per iteration, so their
behavior is less predictable with varying dataset dimensions but could perform
better if trained on more features. Also, low levels of privacy
($\epsilon\geq100$) could help some models generalize, achieving better results
than without applying DP.
