A Neural Network MCMC sampler that maximizes Proposal Entropy

Abstract

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.

arXiv commentconference submission preprint

References in corpus (15)

• NICE: Non-linear Independent Components Estimation
• Normalizing Flows: An Introduction and Review of Current Methods
• Density estimation using Real NVP
• Markov Chain Monte Carlo and Variational Inference: Bridging the Gap
• Implicit Generation and Generalization in Energy-Based Models
• A-NICE-MC: Adversarial Training for MCMC
• NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport
• Modified Hamiltonian Monte Carlo for Bayesian inference
• Hamiltonian Monte Carlo Without Detailed Balance
• Understanding the Limitations of Variational Mutual Information Estimators
• Gradient-based Adaptive Markov Chain Monte Carlo
• Metropolis-Hastings view on variational inference and adversarial training
• Deep Involutive Generative Models for Neural MCMC
• Ergodic Inference: Accelerate Convergence by Optimisation
• A Condition Number for Hamiltonian Monte Carlo

Cited by in corpus (3)

• Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models
• Path Integral Sampler: a stochastic control approach for sampling
• Entropy-based adaptive Hamiltonian Monte Carlo