# Distributional Learning of Variational AutoEncoder: Application to Synthetic Data Generation

arXiv: https://arxiv.org/abs/2302.11294 · HTML: https://mlsanity.com/paper/2302.11294/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 68 references that are in the map.
- First posted on arXiv 22 Feb 2023.

## Builds on (most cited first, 30 of 34)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [A General and Adaptive Robust Loss Function](https://mlsanity.com/paper/1701.03077/) (2017)
- [Stochastic Latent Actor-Critic: Deep Reinforcement Learning with a Latent Variable Model](https://mlsanity.com/paper/1907.00953/) (2019)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Focal Frequency Loss for Image Reconstruction and Synthesis](https://mlsanity.com/paper/2012.12821/) (2020)
- [Generating Multi-label Discrete Patient Records using Generative Adversarial Networks](https://mlsanity.com/paper/1703.06490/) (2017)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [Data Synthesis based on Generative Adversarial Networks](https://mlsanity.com/paper/1806.03384/) (2018)
- [CTAB-GAN: Effective Table Data Synthesizing](https://mlsanity.com/paper/2102.08369/) (2021)
- [Don't Blame the ELBO! A Linear VAE Perspective on Posterior Collapse](https://mlsanity.com/paper/1911.02469/) (2019)
- [Improved Conditional VRNNs for Video Prediction](https://mlsanity.com/paper/1904.12165/) (2019)
- [Reliable training and estimation of variance networks](https://mlsanity.com/paper/1906.03260/) (2019)
- [Variational Approaches for Auto-Encoding Generative Adversarial Networks](https://mlsanity.com/paper/1706.04987/) (2017)
- [Topic-Guided Variational Autoencoders for Text Generation](https://mlsanity.com/paper/1903.07137/) (2019)
- [A Loss Function for Generative Neural Networks Based on Watson's Perceptual Model](https://mlsanity.com/paper/2006.15057/) (2020)
- [Copula Flows for Synthetic Data Generation](https://mlsanity.com/paper/2101.00598/) (2021)
- [On Implicit Regularization in β-VAEs](https://mlsanity.com/paper/2002.00041/) (2020)
- [Causal-TGAN: Generating Tabular Data Using Causal Generative Adversarial Networks](https://mlsanity.com/paper/2104.10680/) (2021)

## Built on by (most cited first, 9 of 9)

- [Distributional MIPLIB: a Multi-Domain Library for Advancing ML-Guided MILP Methods](https://mlsanity.com/paper/2406.06954/) (2024)
- [MALLM-GAN: Multi-Agent Large Language Model as Generative Adversarial Network for Synthesizing Tabular Data](https://mlsanity.com/paper/2406.10521/) (2024)
- [Privacy Measurement in Tabular Synthetic Data: State of the Art and Future Research Directions](https://mlsanity.com/paper/2311.17453/) (2023)
- [Probabilistic bias adjustment of seasonal predictions of Arctic Sea Ice Concentration](https://mlsanity.com/paper/2510.09891/) (2025)
- [Masked Language Modeling Becomes Conditional Density Estimation for Tabular Data Synthesis](https://mlsanity.com/paper/2405.20602/) (2024)
- [Toward generative machine learning for boosting ensembles of climate simulations](https://mlsanity.com/paper/2602.06287/) (2026)
- [Joint Distributional Learning via Cramer-Wold Distance](https://mlsanity.com/paper/2310.16374/) (2023)
- [Balanced Marginal and Joint Distributional Learning via Mixture Cramer-Wold Distance](https://mlsanity.com/paper/2312.03307/) (2023)
- [Likelihood-Free Variational Autoencoders](https://mlsanity.com/paper/2504.17622/) (2025)

## Abstract (arXiv)

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.