Adversarially Training MCMC with Non-Volume-Preserving Flows.

Area of Science:

• Computational Statistics
• Machine Learning
• Bayesian Inference

Background:

• Neural network-parameterized flow models are increasingly used for efficient Markov chain Monte Carlo (MCMC) transition kernels.
• Existing methods often struggle with multi-modal distributions due to limited gradient information utilization or the use of volume-preserving flows.

Purpose of the Study:

• To develop a novel training scheme for MCMC transition kernels that overcomes limitations of current approaches.
• To improve the efficiency and performance of MCMC sampling, particularly for multi-modal target distributions.

Main Methods:

• A two-stage training process: an exploration stage followed by a training stage for transition kernels.
• Utilizing non-volume-preserving flows for transition kernel construction.
• Employing an adversarial training framework to optimize kernel performance.

Main Results:

• Significant improvements in effective sample size and rapid mixing to the target distribution.
• Achieved low autocorrelation of samples and fast convergence rates.
• Outperformed state-of-the-art parameterized transition kernels on challenging distributions and real-world datasets.

Conclusions:

• The proposed novel training scheme enhances gradient information utilization and deep neural network expressiveness for MCMC.
• The method demonstrates superior performance in sampling efficiency, convergence, and sample quality compared to existing techniques.
• This approach offers a promising advancement for MCMC methods in statistical modeling and machine learning.