Balanced Marginal and Joint Distributional Learning for Tabular Data Synthesis via Mixture Cramer–Wold Distance

In recent times, slicing methods have yielded a successful outcome in generative models for image, sound, and text data, primarily focusing on joint distributional learning. However, we have identified a critical limitation of the slicing approach for tabular data: it struggles to capture marginal distributional patterns, which are significant for effective tabular data synthesis. To tackle this problem, we introduce a new measure of discrepancy, the mixture Cramer–Wold distance. This measure enables us to capture both marginal and joint distributional patterns simultaneously, striking a balance between the two aspects, and we provide theoretical foundations for its application. Leveraging the power of the mixture Cramer–Wold distance, we present CWDAE (Cramer–Wold Distributional AutoEncoder), a generative model that demonstrates notable performance in generating synthetic tabular data. Furthermore, our model offers the flexibility to adjust the level of data privacy to meet specific needs easily.