Distributional Learning of Variational AutoEncoder: Application to Synthetic Data Generation

TL;DR

This paper introduces a novel VAE model with an infinite mixture of asymmetric Laplace distributions, enhancing distributional flexibility for synthetic data generation while maintaining computational efficiency.

Contribution

It proposes a nonparametric VAE decoder using an infinite mixture of asymmetric Laplace distributions, expanding model capacity without losing efficiency.

Findings

Superior synthetic data generation performance

Enhanced data privacy adjustment capabilities

Theoretical link to quantile estimation

Abstract

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.