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The Implicit Metropolis-Hastings Algorithm
Kirill Neklyudov · Evgenii Egorov · Dmitry Vetrov

Wed Dec 11 05:00 PM -- 07:00 PM (PST) @ East Exhibition Hall B + C #183

Recent works propose using the discriminator of a GAN to filter out unrealistic samples of the generator. We generalize these ideas by introducing the implicit Metropolis-Hastings algorithm. For any implicit probabilistic model and a target distribution represented by a set of samples, implicit Metropolis-Hastings operates by learning a discriminator to estimate the density-ratio and then generating a chain of samples. Since the approximation of density ratio introduces an error on every step of the chain, it is crucial to analyze the stationary distribution of such chain. For that purpose, we present a theoretical result stating that the discriminator loss upper bounds the total variation distance between the target distribution and the stationary distribution. Finally, we validate the proposed algorithm both for independent and Markov proposals on CIFAR-10, CelebA, ImageNet datasets.

Author Information

Kirill Neklyudov (Samsung AI Center, Moscow)
Evgenii Egorov (Skolkovo Institute of Science and Technology)
Dmitry Vetrov (Higher School of Economics, Samsung AI Center, Moscow)

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