Ai-sampler: Adversarial Learning of Markov kernels with involutive maps

Evgenii Egorov, Riccardo Valperga, Stratis Gavves
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:12304-12317, 2024.

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 this Paper

BibTeX
@InProceedings{pmlr-v235-egorov24a, title = {Ai-sampler: Adversarial Learning of {M}arkov kernels with involutive maps}, author = {Egorov, Evgenii and Valperga, Riccardo and Gavves, Stratis}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {12304--12317}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/egorov24a/egorov24a.pdf}, url = {https://proceedings.mlr.press/v235/egorov24a.html}, 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.} }
Endnote
%0 Conference Paper %T Ai-sampler: Adversarial Learning of Markov kernels with involutive maps %A Evgenii Egorov %A Riccardo Valperga %A Stratis Gavves %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-egorov24a %I PMLR %P 12304--12317 %U https://proceedings.mlr.press/v235/egorov24a.html %V 235 %X 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.
APA
Egorov, E., Valperga, R. & Gavves, S.. (2024). Ai-sampler: Adversarial Learning of Markov kernels with involutive maps. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:12304-12317 Available from https://proceedings.mlr.press/v235/egorov24a.html.

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