Ai-Sampler: Adversarial Learning of Markov kernels with involutive maps
This work addresses a bottleneck in statistics and machine learning for researchers and practitioners needing efficient MCMC methods, though it appears incremental as it builds on existing reversible neural network techniques.
The authors tackled the problem of inefficient sampling from complex probability distributions by proposing a method to train Markov chain transition kernels using adversarial learning with involutive maps, achieving improved mixing and sampling efficiency.
Markov chain Monte Carlo methods have become popular in statistics as versatile techniques to sample from complicated probability distributions. In this work, we propose a method to parameterize and train transition kernels of Markov chains to achieve efficient sampling and good mixing. This training procedure minimizes the total variation distance between the stationary distribution of the chain and the empirical distribution of the data. Our approach leverages involutive Metropolis-Hastings kernels constructed from reversible neural networks that ensure detailed balance by construction. We find that reversibility also implies $C_2$-equivariance of the discriminator function which can be used to restrict its function space.