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.

通过引入 Cramer-Wold 距离正则化和两步骤学习方法，本研究在处理高维数据集或观测变量间的复杂相关结构时，改进了变分自编码器 (Variational Autoencoder) 解码模型中存在的条件独立性假设限制，以实现高维数据的联合分布学习；实验结果表明所提出的方法在合成数据生成方面具有较高的性能。