The Implicit Metropolis-Hastings Algorithm
This work addresses sampling challenges in machine learning for researchers and practitioners using generative models, but it is incremental as it builds on existing GAN-based filtering ideas.
The authors tackled the problem of generating samples from a target distribution using implicit probabilistic models by introducing the implicit Metropolis-Hastings algorithm, which learns a discriminator to estimate density ratios and produces a chain of samples, with theoretical analysis showing the discriminator loss bounds the error and experimental validation on CIFAR-10 and CelebA datasets.
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 and CelebA datasets.