Metropolis-Hastings Generative Adversarial Networks

Abstract

We introduce the Metropolis-Hastings generative adversarial network (MH-GAN), which combines aspects of Markov chain Monte Carlo and GANs. The MH-GAN draws samples from the distribution implicitly defined by a GAN's discriminatorgenerator pair, as opposed to standard GANs which draw samples from the distribution defined only by the generator. It uses the discriminator from GAN training to build a wrapper around the generator for improved sampling. With a perfect discriminator, this wrapped generator samples from the true distribution on the data exactly even when the generator is imperfect. We demonstrate the benefits of the improved generator on multiple benchmark datasets, including CIFAR-10 and CelebA, using the DCGAN, WGAN, and progressive GAN.

Discriminator Contrastive Divergence: Semi-Amortized Generative Modeling by Exploring Energy of the Discriminator

“…For GAN models, we take WGAN-GP [13], Spectral Normalization GAN (SNGAN) [25], and Progressiv eGAN [19] for comparison. We also take the aforementioned DRS [3], DOT [33] and MH-GAN [36] into consideration. The choices of EBM and GANs are due to their close relation to our proposed method, as analyzed in Section 4.…”

“…Hence, there is strong motivation to further improve the generated distribution by exploring the remaining information. Two recent advancements are discriminator rejection sampling(DRS) [3] and MH-GANs [36]. DRS conducts rejection sampling on the output of the generator.…”

“…It has been studied both theoretically and empirically in the context of GANs [2,15,17], with the same inductive bias, that learning a discriminative model is more accessible than a generative model. Based on the above fact, the rejection-sampling based methods are proposed to use the estimated density ratio, e.g., x) in original GANs, to conduct rejection sampling [3] or Metropolis-Hastings sampling [36] based on generated distribution p G θ . These methods radically modify the generated distribution p G θ to p * , the improvement in empirical performance as shown in [3,36] demonstrates that we can construct a superior distribution p * to prescribe the empirical distribution p data by involving the remaining information in discriminator.…”

“…Recent work [3,36] has shown that a density ratio can be obtained through the output of discriminator, and a more superior distribution can be acquired by conducting rejection sampling or Metropolis-Hastings sampling with the estimated density ratio based on the original GAN [10].…”

“…The learning objective of GANs usually minimizes some measure discrepancy, e.g., f -divergence (f -GANs [28]) or Integral Probability Metric (Wasserstein GANs [2]). With f -divergence as the objective function, the discriminator essentially estimates the density ratio [37], and the estimated ratio proves useful in further improving the sample quality of the generator [3,36]. However, how to leverage the information contained in the discriminator of Wasserstein GANs (WGAN) [2] is less explored.…”