Generative Adversarial Networks (GANs) have shown impressive performance in generating photo-realistic images. They fit generative models by minimizing certain distance measure between the real image distribution and the generated data distribution. Several distance measures have been used, such as Jensen-Shannon divergence, @math -divergence, and Wasserstein distance, and choosing an appropriate distance measure is very important for training the generative network. In this paper, we choose to use the maximum mean discrepancy (MMD) as the distance metric, which has several nice theoretical guarantees. In fact, generative moment matching network (GMMN) (Li, Swersky, and Zemel 2015) is such a generative model which contains only one generator network @math trained by directly minimizing MMD between the real and generated distributions. However, it fails to generate meaningful samples on challenging benchmark datasets, such as CIFAR-10 and LSUN. To improve on GMMN, we propose to add an extra network @math , called mapper. @math maps both real data distribution and generated data distribution from the original data space to a feature representation space @math , and it is trained to maximize MMD between the two mapped distributions in @math , while the generator @math tries to minimize the MMD. We call the new model generative adversarial mapping networks (GAMNs). We demonstrate that the adversarial mapper @math can help @math to better capture the underlying data distribution. We also show that GAMN significantly outperforms GMMN, and is also superior to or comparable with other state-of-the-art GAN based methods on MNIST, CIFAR-10 and LSUN-Bedrooms datasets.
More related to our method, generative moment matching networks GMMNs @cite_6 @cite_19 optimize MMD between distributions to learn generative models from data. The original GMMN only includes a single generator. To boost the performance of GMMN, li2015generative introduce an auto-encoder to a GMMN and name it GMMN+AE. They first use an auto-encoder to produce the code representations of data and then minimize MMD between data code distribution and generated code distribution. The functionality of the auto-encoder here is similar to that of the mapper in GAMN to some extent: both of them map the data distribution from the real data space to another code (representation) space and can reduce the dimension of high-dimensional images. However, the mapper in GAMN is entirely different from the auto-encoder in GMMN+AE. The most different part is that the mapper is a dynamic network which always changes during training process to be a good adversary for the generator, while the auto-encoder is a static network which is trained in the beginning and then keeps fixed all the time. We believe this difference makes the mapper much powerful than the auto-encoder, thus enhancing the generator in GAMN considerably. Our experiments also demonstrate this.
@cite_19 @cite_6
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We consider training a deep neural network to generate samples from an unknown distribution given i.i.d. data. We frame learning as an optimization minimizing a two-sample test statistic---informally speaking, a good generator network produces samples that cause a two-sample test to fail to reject the null hypothesis. As our two-sample test statistic, we use an unbiased estimate of the maximum mean discrepancy, which is the centerpiece of the nonparametric kernel two-sample test proposed by (2012). We compare to the adversarial nets framework introduced by (2014), in which learning is a two-player game between a generator network and an adversarial discriminator network, both trained to outwit the other. From this perspective, the MMD statistic plays the role of the discriminator. In addition to empirical comparisons, we prove bounds on the generalization error incurred by optimizing the empirical MMD. We consider the problem of learning deep generative models from data. We formulate a method that generates an independent sample via a single feedforward pass through a multilayer perceptron, as in the recently proposed generative adversarial networks (, 2014). Training a generative adversarial network, however, requires careful optimization of a difficult minimax program. Instead, we utilize a technique from statistical hypothesis testing known as maximum mean discrepancy (MMD), which leads to a simple objective that can be interpreted as matching all orders of statistics between a dataset and samples from the model, and can be trained by backpropagation. We further boost the performance of this approach by combining our generative network with an auto-encoder network, using MMD to learn to generate codes that can then be decoded to produce samples. We show that the combination of these techniques yields excellent generative models compared to baseline approaches as measured on MNIST and the Toronto Face Database.