Variational Inference on the Boolean Hypercube with the Quantum Entropy

• URL: http://arxiv.org/abs/2411.03759v2
• Date: Fri, 14 Feb 2025 08:25:32 GMT
• Title: Variational Inference on the Boolean Hypercube with the Quantum Entropy
• Authors: Eliot Beyler, Francis Bach,
• Abstract summary: We derive variational inference upper-bounds on the log-partition function of pairwise Markov random fields on the Boolean hypercube.<n>We then propose an efficient algorithm to compute these bounds based on primal-dual optimization.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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