Variational Inference on the Boolean Hypercube with the Quantum Entropy

Eliot Beyler, Francis Bach
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:1153-1161, 2025.

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 this Paper

BibTeX
@InProceedings{pmlr-v258-beyler25a, 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}, pages = {1153--1161}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/beyler25a/beyler25a.pdf}, url = {https://proceedings.mlr.press/v258/beyler25a.html}, 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.} }
Endnote
%0 Conference Paper %T Variational Inference on the Boolean Hypercube with the Quantum Entropy %A Eliot Beyler %A Francis Bach %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-beyler25a %I PMLR %P 1153--1161 %U https://proceedings.mlr.press/v258/beyler25a.html %V 258 %X 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.
APA
Beyler, E. & Bach, F.. (2025). Variational Inference on the Boolean Hypercube with the Quantum Entropy. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:1153-1161 Available from https://proceedings.mlr.press/v258/beyler25a.html.

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