Self-learning Monte Carlo (SLMC) methods are recently proposed to accelerate
Markov chain Monte Carlo (MCMC) methods by using a machine learning model.With
generative models having latent variables, SLMC methods realize efficient Monte
Carlo updates with less autocorrelation. However, SLMC methods are difficult to
directly apply to multimodal distributions for which training data are
difficult to obtain. In this paper, we propose a novel SLMC method called the
``annealing VAE-SLMC" to drastically expand the range of applications. Our
VAE-SLMC utilizes a variational autoencoder (VAE) as a generative model to make
efficient parallel proposals independent of any previous state by applying the
theoretically derived implicit isometricity of the VAE. We combine an adaptive
annealing process to the VAE-SLMC, making our method applicable to the cases
where obtaining unbiased training data is difficult in practical sense due to
slow mixing. We also propose a parallel annealing process and an exchange
process between chains to make the annealing operation more precise and
efficient. Experiments validate that our method can proficiently obtain
unbiased samples from multiple multimodal toy distributions and practical
multimodal posterior distributions, which is difficult to achieve with the
existing SLMC methods.Comment: 24 pages,12 figure