We generalize the concept of maximum-margin classifiers (MMCs) to arbitrary
norms and non-linear functions. Support Vector Machines (SVMs) are a special
case of MMC. We find that MMCs can be formulated as Integral Probability
Metrics (IPMs) or classifiers with some form of gradient norm penalty. This
implies a direct link to a class of Generative adversarial networks (GANs)
which penalize a gradient norm. We show that the Discriminator in Wasserstein,
Standard, Least-Squares, and Hinge GAN with Gradient Penalty is an MMC. We
explain why maximizing a margin may be helpful in GANs. We hypothesize and
confirm experimentally that $L^ınfty$-norm penalties with Hinge loss produce
better GANs than $L^2$-norm penalties (based on common evaluation metrics). We
derive the margins of Relativistic paired (Rp) and average (Ra) GANs.
Description
[1910.06922] Connections between Support Vector Machines, Wasserstein distance and gradient-penalty GANs
%0 Journal Article
%1 jolicoeurmartineau2019connections
%A Jolicoeur-Martineau, Alexia
%A Mitliagkas, Ioannis
%D 2019
%K generative-models optimization regularisation
%T Connections between Support Vector Machines, Wasserstein distance and
gradient-penalty GANs
%U http://arxiv.org/abs/1910.06922
%X We generalize the concept of maximum-margin classifiers (MMCs) to arbitrary
norms and non-linear functions. Support Vector Machines (SVMs) are a special
case of MMC. We find that MMCs can be formulated as Integral Probability
Metrics (IPMs) or classifiers with some form of gradient norm penalty. This
implies a direct link to a class of Generative adversarial networks (GANs)
which penalize a gradient norm. We show that the Discriminator in Wasserstein,
Standard, Least-Squares, and Hinge GAN with Gradient Penalty is an MMC. We
explain why maximizing a margin may be helpful in GANs. We hypothesize and
confirm experimentally that $L^ınfty$-norm penalties with Hinge loss produce
better GANs than $L^2$-norm penalties (based on common evaluation metrics). We
derive the margins of Relativistic paired (Rp) and average (Ra) GANs.
@article{jolicoeurmartineau2019connections,
abstract = {We generalize the concept of maximum-margin classifiers (MMCs) to arbitrary
norms and non-linear functions. Support Vector Machines (SVMs) are a special
case of MMC. We find that MMCs can be formulated as Integral Probability
Metrics (IPMs) or classifiers with some form of gradient norm penalty. This
implies a direct link to a class of Generative adversarial networks (GANs)
which penalize a gradient norm. We show that the Discriminator in Wasserstein,
Standard, Least-Squares, and Hinge GAN with Gradient Penalty is an MMC. We
explain why maximizing a margin may be helpful in GANs. We hypothesize and
confirm experimentally that $L^\infty$-norm penalties with Hinge loss produce
better GANs than $L^2$-norm penalties (based on common evaluation metrics). We
derive the margins of Relativistic paired (Rp) and average (Ra) GANs.},
added-at = {2019-10-16T16:23:51.000+0200},
author = {Jolicoeur-Martineau, Alexia and Mitliagkas, Ioannis},
biburl = {https://www.bibsonomy.org/bibtex/255d512d550d5842fcc370aa03c1e9853/kirk86},
description = {[1910.06922] Connections between Support Vector Machines, Wasserstein distance and gradient-penalty GANs},
interhash = {7e0485ebe7fe3a9e09133c3bbeacf2b6},
intrahash = {55d512d550d5842fcc370aa03c1e9853},
keywords = {generative-models optimization regularisation},
note = {cite arxiv:1910.06922Comment: Code at https://github.com/AlexiaJM/MaximumMarginGANs},
timestamp = {2019-10-16T16:23:51.000+0200},
title = {Connections between Support Vector Machines, Wasserstein distance and
gradient-penalty GANs},
url = {http://arxiv.org/abs/1910.06922},
year = 2019
}