Variational Inference on the Boolean Hypercube with the Quantum Entropy
Abstract
In this paper, we derive variational inference upper-bounds on the log-partition function of a pairwize Markov random fields on the Boolean hypercube, based on quantum relaxations of the Kullback-Leibler divergence. We then propose an efficient algorithm to compute these bounds based on primal-dual optimization. An improvement of these bounds through the use of "hierarchies", similar to sum-of-squares (SoS) hierarchies is proposed, and we present a greedy algorithm to select among these relaxations. We carry extensive numerical experiments and compare with state-of-the-art methods for this inference problem.
Cite
Text
Beyler and Bach. "Variational Inference on the Boolean Hypercube with the Quantum Entropy." Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, 2025.Markdown
[Beyler and Bach. "Variational Inference on the Boolean Hypercube with the Quantum Entropy." Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, 2025.](https://mlanthology.org/aistats/2025/beyler2025aistats-variational/)BibTeX
@inproceedings{beyler2025aistats-variational,
title = {{Variational Inference on the Boolean Hypercube with the Quantum Entropy}},
author = {Beyler, Eliot and Bach, Francis},
booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics},
year = {2025},
pages = {1153-1161},
volume = {258},
url = {https://mlanthology.org/aistats/2025/beyler2025aistats-variational/}
}