Approximate Inference with Amortised MCMC
This provides a new generic framework for approximate inference in machine learning, particularly useful for handling complex models with intractable densities, though it appears incremental as it builds on existing MCMC and amortization techniques.
The paper tackles the problem of approximate inference by introducing a framework that amortizes MCMC dynamics to approximate target distributions, enabling the use of complex, intractable approximation families like deep neural networks. The method was tested on image modeling with deep generative models, producing realistic samples and diverse imputations for images with missing pixels.
We propose a novel approximate inference algorithm that approximates a target distribution by amortising the dynamics of a user-selected MCMC sampler. The idea is to initialise MCMC using samples from an approximation network, apply the MCMC operator to improve these samples, and finally use the samples to update the approximation network thereby improving its quality. This provides a new generic framework for approximate inference, allowing us to deploy highly complex, or implicitly defined approximation families with intractable densities, including approximations produced by warping a source of randomness through a deep neural network. Experiments consider image modelling with deep generative models as a challenging test for the method. Deep models trained using amortised MCMC are shown to generate realistic looking samples as well as producing diverse imputations for images with regions of missing pixels.