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arXiv · 2411.03759

Variational Inference on the Boolean Hypercube with the Quantum Entropy

Eliot Beyler·Francis Bach
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Abstract

In this paper, we derive variational inference upper-bounds on the log-partition function of pairwise 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.

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Eliot Beyler, Francis Bach. 2024-11-06. Variational Inference on the Boolean Hypercube with the Quantum Entropy. https://arxiv.org/abs/2411.03759

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