  Despite several works that succeed in generating synthetic data with
differential privacy (DP) guarantees, they are inadequate for generating
high-quality synthetic data when the input data has missing values. In this
work, we formalize the problems of DP synthetic data with missing values and
propose three effective adaptive strategies that significantly improve the
utility of the synthetic data on four real-world datasets with different types
and levels of missing data and privacy requirements. We also identify the
relationship between privacy impact for the complete ground truth data and
incomplete data for these DP synthetic data generation algorithms. We model the
missing mechanisms as a sampling process to obtain tighter upper bounds for the
privacy guarantees to the ground truth data. Overall, this study contributes to
a better understanding of the challenges and opportunities for using private
synthetic data generation algorithms in the presence of missing data.
