Existing differentially private (DP) synthetic data generation mechanisms typically assume a single-source table. In practice, data is often distributed across multiple tables with relationships across tables. In this paper, we introduce the first-of-its-kind algorithm that can be combined with any existing DP mechanisms to generate synthetic relational databases. Our algorithm iteratively refines the relationship between individual synthetic tables to minimize their approximation errors in terms of low-order marginal distributions while maintaining referential integrity. This algorithm eliminates the need to flatten a relational database into a master table (saving space), operates efficiently (saving time), and scales effectively to high-dimensional data. We provide both DP and theoretical utility guarantees for our algorithm. Through numerical experiments on real-world datasets, we demonstrate the effectiveness of our method in preserving fidelity to the original data.

An unsolved issue in widely used methods such as Support Vector Data Description (SVDD) and Small Sphere and Large Margin SVM (SSLM) for anomaly detection is their nonconvexity, which hampers the analysis of optimal solutions in a manner similar to SVMs and limits their applicability in large-scale scenarios. In this paper, we introduce a novel convex SSLM formulation which has been demonstrated to revert to a convex quadratic programming problem for hyperparameter values of interest. Leveraging the convexity of our method, we derive numerous results that are unattainable with traditional nonconvex approaches. We conduct a thorough analysis of how hyperparameters influence the optimal solution, pointing out scenarios where optimal solutions can be trivially found and identifying instances of illposedness. Most notably, we establish connections between our method and traditional approaches, providing a clear determination of when the optimal solution is unique-a task unachievable with traditional nonconvex methods. We also derive the $\nu$-property to elucidate the interactions between hyperparameters and the fractions of support vectors and margin errors in both positive and negative classes.