A Neural Network MCMC sampler that maximizes Proposal Entropy
This work addresses a bottleneck in MCMC sampling for machine learning and statistics, offering a novel method to improve efficiency in challenging distributions.
The paper tackles the problem of inefficient sampling from continuous probability distributions with unfavorable geometry by proposing a neural network MCMC sampler that maximizes proposal entropy, achieving significantly higher efficiency than previous neural network methods in various tasks and unbiased sampling with higher entropy in energy-based model training.
Markov Chain Monte Carlo (MCMC) methods sample from unnormalized probability distributions and offer guarantees of exact sampling. However, in the continuous case, unfavorable geometry of the target distribution can greatly limit the efficiency of MCMC methods. Augmenting samplers with neural networks can potentially improve their efficiency. Previous neural network based samplers were trained with objectives that either did not explicitly encourage exploration, or used a L2 jump objective which could only be applied to well structured distributions. Thus it seems promising to instead maximize the proposal entropy for adapting the proposal to distributions of any shape. To allow direct optimization of the proposal entropy, we propose a neural network MCMC sampler that has a flexible and tractable proposal distribution. Specifically, our network architecture utilizes the gradient of the target distribution for generating proposals. Our model achieves significantly higher efficiency than previous neural network MCMC techniques in a variety of sampling tasks. Further, the sampler is applied on training of a convergent energy-based model of natural images. The adaptive sampler achieves unbiased sampling with significantly higher proposal entropy than Langevin dynamics sampler.