Amortized Variational Inference via Nosé-Hoover Thermostat Hamiltonian Monte Carlo

Abstract

Sampling latents from the posterior distribution efficiently and accurately is a fundamental problem for posterior inference. Markov chain Monte Carlo (MCMC) is such a useful tool to do that but at the cost of computational burden since it needs many transition steps to converge to the stationary distribution for each datapoint. Amortized variational inference within the framework of MCMC is thus proposed where the learned parameters of the model are shared by all observations. Langevin autoencoder is a newly proposed method that amortizes inference in parameter space. This paper generalizes the Langevin autoencoder by utilizing the stochastic gradient Nosé-Hoover Thermostat Hamiltonian Monte Carlo to conduct amortized updating of the parameters of the inference distribution. The proposed method improves variational inference accuracy for the latent by subtly dealing with the noise introduced by stochastic gradient without estimating that noise explicitly. Experiments benchmarking our method against baseline generative methods highlight the effectiveness of our proposed method.