  Self-learning Monte Carlo (SLMC) methods are recently proposed to accelerate
Markov chain Monte Carlo (MCMC) methods using a machine learning model. With
latent generative models, 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. To solve the limitation, we propose parallel adaptive annealing, which
makes SLMC methods directly apply to multimodal distributions with a gradually
trained proposal while annealing target distribution. Parallel adaptive
annealing is based on (i) sequential learning with annealing to inherit and
update the model parameters, (ii) adaptive annealing to automatically detect
under-learning, and (iii) parallel annealing to mitigate mode collapse of
proposal models. We also propose VAE-SLMC method which utilizes a variational
autoencoder (VAE) as a proposal of SLMC to make efficient parallel proposals
independent of any previous state using recently clarified quantitative
properties of VAE. Experiments validate that our method can proficiently obtain
accurate samples from multiple multimodal toy distributions and practical
multimodal posterior distributions, which is difficult to achieve with the
existing SLMC methods.
