The Gaussianity assumption has been pointed out as the main limitation of the Variational AutoEncoder (VAE) in spite of its usefulness in computation. To improve the distributional capacity (i.e., expressive power of distributional family) of the VAE, we propose a new VAE learning method with a nonparametric distributional assumption on its generative model. By estimating an infinite number of conditional quantiles, our proposed VAE model directly estimates the conditional cumulative distribution function, and we call this approach distributional learning of the VAE. Furthermore, by adopting the continuous ranked probability score (CRPS) loss, our proposed learning method becomes computationally tractable. To evaluate how well the underlying distribution of the dataset is captured, we apply our model for synthetic data generation based on inverse transform sampling. Numerical results with real tabular datasets corroborate our arguments.

翻译：高斯性假设尽管在计算上具有实用性，但已被指出是变分自编码器（VAE）的主要局限性。为提升VAE的分布容量（即分布族的表达能力），我们提出了一种新的VAE学习方法，该方法在其生成模型上采用非参数分布假设。通过估计无穷多个条件分位数，我们提出的VAE模型直接估计条件累积分布函数，并将此方法称为VAE的分布学习。此外，通过采用连续排序概率评分（CRPS）损失，我们提出的学习方法在计算上变得易于处理。为评估数据集潜在分布被捕捉的程度，我们基于逆变换采样将模型应用于合成数据生成。基于真实表格数据的数值结果证实了我们的论点。