An Introduction to Deep Generative Modeling
- URL: http://arxiv.org/abs/2103.05180v1
- Date: Tue, 9 Mar 2021 02:19:06 GMT
- Title: An Introduction to Deep Generative Modeling
- Authors: Lars Ruthotto and Eldad Haber
- Abstract summary: Deep generative models (DGM) are neural networks with many hidden layers trained to approximate complicated, high-dimensional probability distributions.
We provide an introduction to DGMs and a framework for modeling the three most popular approaches.
Our goal is to enable and motivate the reader to contribute to this proliferating research area.
- Score: 8.909115457491522
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Deep generative models (DGM) are neural networks with many hidden layers
trained to approximate complicated, high-dimensional probability distributions
using a large number of samples. When trained successfully, we can use the DGMs
to estimate the likelihood of each observation and to create new samples from
the underlying distribution. Developing DGMs has become one of the most hotly
researched fields in artificial intelligence in recent years. The literature on
DGMs has become vast and is growing rapidly. Some advances have even reached
the public sphere, for example, the recent successes in generating
realistic-looking images, voices, or movies; so-called deep fakes. Despite
these successes, several mathematical and practical issues limit the broader
use of DGMs: given a specific dataset, it remains challenging to design and
train a DGM and even more challenging to find out why a particular model is or
is not effective. To help advance the theoretical understanding of DGMs, we
provide an introduction to DGMs and provide a concise mathematical framework
for modeling the three most popular approaches: normalizing flows (NF),
variational autoencoders (VAE), and generative adversarial networks (GAN). We
illustrate the advantages and disadvantages of these basic approaches using
numerical experiments. Our goal is to enable and motivate the reader to
contribute to this proliferating research area. Our presentation also
emphasizes relations between generative modeling and optimal transport.
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