  A significant part of MCMC methods can be considered as the
Metropolis-Hastings (MH) algorithm with different proposal distributions. From
this point of view, the problem of constructing a sampler can be reduced to the
question - how to choose a proposal for the MH algorithm? To address this
question, we propose to learn an independent sampler that maximizes the
acceptance rate of the MH algorithm, which, as we demonstrate, is highly
related to the conventional variational inference. For Bayesian inference, the
proposed method compares favorably against alternatives to sample from the
posterior distribution. Under the same approach, we step beyond the scope of
classical MCMC methods and deduce the Generative Adversarial Networks (GANs)
framework from scratch, treating the generator as the proposal and the
discriminator as the acceptance test. On real-world datasets, we improve
Frechet Inception Distance and Inception Score, using different GANs as a
proposal distribution for the MH algorithm. In particular, we demonstrate
improvements of recently proposed BigGAN model on ImageNet.
