# Difference between revisions of "stat946w18/IMPROVING GANS USING OPTIMAL TRANSPORT"

## Introduction

Generative Adversarial Networks (GANs) are powerful generative models. A GAN model consists of a generator and a discriminator or critic. The generator is a neural network which is trained to generate data having a distribution matched with the distribution of the real data. The critic is also a neural network, which is trained to separate the generated data from the real data. A loss function that measures the distribution distance between the generated data and the real one is important to train the generator.

Optimal transport theory evaluates the distribution distance based on metric, which provides another method for generator training. The main advantage of optimal transport theory over the distance measurement in GAN is its closed form solution for having a tractable training process. But the theory might also result in inconsistency in statistical estimation due to the given biased gradients if the mini-batches method is applied.

This paper presents a variant GANs named OT-GAN, which incorporates a discriminative metric called 'MIni-batch Energy Distance' into its critic in order to overcome the issue of biased gradients.

## GANs and Optimal Transport

where $\prod (p,g)$ is the set of all joint distributions $\gamma (x,y)$ with marginals $p(x), g(y)$ and $c(x,y)$ is a cost function which takes to be the Euclidean distance. Consider that solving the Wasserstein distance is usually not possible, the proposed Wasserstein GAN (W-GAN) provides an estimated solution by switching the optimal transport problem into dual formulation using a set of Lipschitz functions. A neural network can then be used to obtain an estimation.