A New Paradigm for Generative Adversarial Networks based on Randomized Decision Rules Article Swipe

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Sehwan Kim , Qifan Song , Faming Liang · YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2306.13641

The Generative Adversarial Network (GAN) was recently introduced in the literature as a novel machine learning method for training generative models. It has many applications in statistics such as nonparametric clustering and nonparametric conditional independence tests. However, training the GAN is notoriously difficult due to the issue of mode collapse, which refers to the lack of diversity among generated data. In this paper, we identify the reasons why the GAN suffers from this issue, and to address it, we propose a new formulation for the GAN based on randomized decision rules. In the new formulation, the discriminator converges to a fixed point while the generator converges to a distribution at the Nash equilibrium. We propose to train the GAN by an empirical Bayes-like method by treating the discriminator as a hyper-parameter of the posterior distribution of the generator. Specifically, we simulate generators from its posterior distribution conditioned on the discriminator using a stochastic gradient Markov chain Monte Carlo (MCMC) algorithm, and update the discriminator using stochastic gradient descent along with simulations of the generators. We establish convergence of the proposed method to the Nash equilibrium. Apart from image generation, we apply the proposed method to nonparametric clustering and nonparametric conditional independence tests. A portion of the numerical results is presented in the supplementary material.

Type

preprint

Language

en

Landing Page

http://arxiv.org/abs/2306.13641

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https://arxiv.org/pdf/2306.13641

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green

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10

OpenAlex ID

https://openalex.org/W4382173626

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OpenAlex ID

https://openalex.org/W4382173626

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DOI

https://doi.org/10.48550/arxiv.2306.13641

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Title

A New Paradigm for Generative Adversarial Networks based on Randomized Decision Rules

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Type

preprint

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Language

en

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Publication year

2023

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Publication date

2023-06-23

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Authors

Sehwan Kim, Qifan Song, Faming Liang

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Landing page

https://arxiv.org/abs/2306.13641

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https://arxiv.org/pdf/2306.13641

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Yes

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green

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https://arxiv.org/pdf/2306.13641

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Concepts

Discriminator, Nonparametric statistics, Computer science, Markov chain Monte Carlo, Posterior probability, Independence (probability theory), Cluster analysis, Bayes' theorem, Mathematical optimization, Artificial intelligence, Machine learning, Algorithm, Mathematics, Bayesian probability, Econometrics, Statistics, Detector, Telecommunications

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0

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Related works (count)

10

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