  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.
