The Gaussianity assumption has been consistently criticized as a main limitation of the Variational Autoencoder (VAE) despite its efficiency in computational modeling. In this paper, we propose a new approach that expands the model capacity (i.e., expressive power of distributional family) without sacrificing the computational advantages of the VAE framework. Our VAE model's decoder is composed of an infinite mixture of asymmetric Laplace distribution, which possesses general distribution fitting capabilities for continuous variables. Our model is represented by a special form of a nonparametric M-estimator for estimating general quantile functions, and we theoretically establish the relevance between the proposed model and quantile estimation. We apply the proposed model to synthetic data generation, and particularly, our model demonstrates superiority in easily adjusting the level of data privacy.

翻译：高斯性假设一直被认为是变分自编码器（VAE）在计算建模中高效性的主要局限，尽管其效率显著。本文提出了一种新方法，在保持VAE框架计算优势的同时，扩展了模型容量（即分布族的表达能力）。我们的VAE模型的解码器由无限混合的非对称拉普拉斯分布组成，具备对连续变量的一般分布拟合能力。该模型表现为一种用于估计一般分位函数的非参数M估计量的特殊形式，我们从理论上建立了所提模型与分位估计之间的相关性。我们将所提模型应用于合成数据生成，特别地，该模型在灵活调整数据隐私水平方面展现出优越性。