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A significant part of MCMC methods can be considered as theMetropolis-Hastings (MH) algorithm with different proposal distributions. Fromthis point of view, the problem of constructing a sampler can be reduced to thequestion - how to choose a proposal for the MH algorithm? To address thisquestion, we propose to learn an independent sampler that maximizes theacceptance rate of the MH algorithm, which, as we demonstrate, is highlyrelated to the conventional variational inference. For Bayesian inference, theproposed method compares favorably against alternatives to sample from theposterior distribution. Under the same approach, we step beyond the scope ofclassical MCMC methods and deduce the Generative Adversarial Networks (GANs)framework from scratch, treating the generator as the proposal and thediscriminator as the acceptance test. On real-world datasets, we improveFrechet Inception Distance and Inception Score, using different GANs as aproposal distribution for the MH algorithm. In particular, we demonstrateimprovements of recently proposed BigGAN model on ImageNet.

Metropolis-Hastings view on variational inference and adversarial training