Joint Distributional Learning via Cramer-Wold Distance

Abstract: The assumption of conditional independence among observed variables, primarily used in the Variational Autoencoder (VAE) decoder modeling, has limitations when dealing with high-dimensional datasets or complex correlation structures among observed variables. To address this issue, we introduced the Cramer-Wold distance regularization, which can be computed in a closed-form, to facilitate joint distributional learning for high-dimensional datasets. Additionally, we introduced a two-step learning method to enable flexible prior modeling and improve the alignment between the aggregated posterior and the prior distribution. Furthermore, we provide theoretical distinctions from existing methods within this category. To evaluate the synthetic data generation performance of our proposed approach, we conducted experiments on high-dimensional datasets with multiple categorical variables. Given that many readily available datasets and data science applications involve such datasets, our experiments demonstrate the effectiveness of our proposed methodology.