  Generative adversarial networks (GANs) are a powerful approach to
unsupervised learning. They have achieved state-of-the-art performance in the
image domain. However, GANs are limited in two ways. They often learn
distributions with low support---a phenomenon known as mode collapse---and they
do not guarantee the existence of a probability density, which makes evaluating
generalization using predictive log-likelihood impossible. In this paper, we
develop the prescribed GAN (PresGAN) to address these shortcomings. PresGANs
add noise to the output of a density network and optimize an
entropy-regularized adversarial loss. The added noise renders tractable
approximations of the predictive log-likelihood and stabilizes the training
procedure. The entropy regularizer encourages PresGANs to capture all the modes
of the data distribution. Fitting PresGANs involves computing the intractable
gradients of the entropy regularization term; PresGANs sidestep this
intractability using unbiased stochastic estimates. We evaluate PresGANs on
several datasets and found they mitigate mode collapse and generate samples
with high perceptual quality. We further found that PresGANs reduce the gap in
performance in terms of predictive log-likelihood between traditional GANs and
variational autoencoders (VAEs).
