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Connections between Support Vector Machines, Wasserstein distance and gradient-penalty GANs

arXiv.org Machine Learning

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.


Chiefs' Peters Fined $24,309 for Penalty Flag Toss

U.S. News

During the Jets' go-ahead drive in the fourth quarter, the Chiefs were called for three penalties to prolong the possession. The last of the penalties frustrated Peters, who picked up one of the flags and tossed it into the seats at MetLife Stadium. Peters was penalized for unsportsmanlike conduct, and he headed straight to the locker room thinking he had been ejected.


The biomechanics of a perfect penalty kick

Popular Science

Kicking a stationary ball from the penalty spot was first introduced in 1902 with the ball situated 12 yards from the goal. In 1997 the kick rules were amended to allow goalkeepers to move sideways along the goal line prior to the ball being kicked. The importance of this rule change has been highlighted in kicking research, which shows that if the goalkeeper has a greater opportunity to distract the player--think waving arms--it results in a higher percentage of saved penalties. This is particularly the case in situations that provoke higher levels of anxiety for the penalty shooter, like a World Cup deciding penalty kick.


Israel's new death penalty bill 'targets Palestinians'

Al Jazeera

The Israeli government's proposal to make it easier for judges to hand out the death penalty for "terrorist activity" has been condemned as "fascist" by Palestinian politicians and rights groups, who fear it will give Israel legal cover to target Palestinians.


Penalty to be waived for accidental ball movement on green

U.S. News

Johnson's ruling was the most famous, mainly because of how it was carried out. He was notified on the 12th tee that he might face a penalty and that he could review it with officials after the round. That meant Johnson had to play the final seven holes of the U.S. Open without knowing if he would get a penalty shot. It ultimately didn't matter, though even after his three-shot victory, Johnson did not think he deserved a penalty shot.