Approximate Inference with Amortised MCMC

TL;DR

This paper introduces a new approximate inference method called Amortised MCMC that leverages neural networks to improve sampling efficiency and quality in complex probabilistic models, demonstrated on image generation tasks.

Contribution

The paper presents a generic framework combining MCMC and neural network amortisation for improved approximate inference, capable of handling complex and implicit distributions.

Findings

Generated realistic image samples with deep generative models.

Produced diverse imputations for images with missing regions.

Demonstrated effectiveness on challenging image modelling tasks.

Abstract

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.