Ai-Sampler: Adversarial Learning of Markov Kernels with Involutive Maps
Abstract
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.
Cite
Text
Egorov et al. "Ai-Sampler: Adversarial Learning of Markov Kernels with Involutive Maps." International Conference on Machine Learning, 2024.Markdown
[Egorov et al. "Ai-Sampler: Adversarial Learning of Markov Kernels with Involutive Maps." International Conference on Machine Learning, 2024.](https://mlanthology.org/icml/2024/egorov2024icml-aisampler/)BibTeX
@inproceedings{egorov2024icml-aisampler,
title = {{Ai-Sampler: Adversarial Learning of Markov Kernels with Involutive Maps}},
author = {Egorov, Evgenii and Valperga, Riccardo and Gavves, Stratis},
booktitle = {International Conference on Machine Learning},
year = {2024},
pages = {12304-12317},
volume = {235},
url = {https://mlanthology.org/icml/2024/egorov2024icml-aisampler/}
}