%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 }