# Learning Nonparametric High-Dimensional Generative Models: The Empirical-Beta-Copula Autoencoder

arXiv: https://arxiv.org/abs/2309.09916 · HTML: https://mlsanity.com/paper/2309.09916/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 42 of its 81 references that are in the map.
- First posted on arXiv 18 Sep 2023.

## Builds on (most cited first, 30 of 42)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [A note on the evaluation of generative models](https://mlsanity.com/paper/1511.01844/) (2015)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [DRAW: A Recurrent Neural Network For Image Generation](https://mlsanity.com/paper/1502.04623/) (2015)
- [From Variational to Deterministic Autoencoders](https://mlsanity.com/paper/1903.12436/) (2019)
- [Inference Suboptimality in Variational Autoencoders](https://mlsanity.com/paper/1801.03558/) (2018)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [Generative Adversarial Transformers](https://mlsanity.com/paper/2103.01209/) (2021)
- [Flows for simultaneous manifold learning and density estimation](https://mlsanity.com/paper/2003.13913/) (2020)
- [BIVA: A Very Deep Hierarchy of Latent Variables for Generative Modeling](https://mlsanity.com/paper/1902.02102/) (2019)
- [Iterative Amortized Inference](https://mlsanity.com/paper/1807.09356/) (2018)
- [Understanding and Improving Interpolation in Autoencoders via an Adversarial Regularizer](https://mlsanity.com/paper/1807.07543/) (2018)
- [An empirical study on evaluation metrics of generative adversarial networks](https://mlsanity.com/paper/1806.07755/) (2018)
- [Hierarchical VAEs Know What They Don't Know](https://mlsanity.com/paper/2102.08248/) (2021)
- [Copula-based conformal prediction for Multi-Target Regression](https://mlsanity.com/paper/2101.12002/) (2021)
- [Variational Autoencoder with Implicit Optimal Priors](https://mlsanity.com/paper/1809.05284/) (2018)
- [The Thermodynamic Variational Objective](https://mlsanity.com/paper/1907.00031/) (2019)

## Abstract (arXiv)

By sampling from the latent space of an autoencoder and decoding the latent space samples to the original data space, any autoencoder can simply be turned into a generative model. For this to work, it is necessary to model the autoencoder's latent space with a distribution from which samples can be obtained. Several simple possibilities (kernel density estimates, Gaussian distribution) and more sophisticated ones (Gaussian mixture models, copula models, normalization flows) can be thought of and have been tried recently. This study aims to discuss, assess, and compare various techniques that can be used to capture the latent space so that an autoencoder can become a generative model while striving for simplicity. Among them, a new copula-based method, the Empirical Beta Copula Autoencoder, is considered. Furthermore, we provide insights into further aspects of these methods, such as targeted sampling or synthesizing new data with specific features.