Variational Inference on the Boolean Hypercube with the Quantum Entropy

Eliot Beyler, Francis Bach
11/6/2024
cs.ITcs.LGmath.OC

No official code found. Best implementation: ebeyler/variational_inference_quatum_entropy (0 stars, MIT, last commit 2025-04-29).

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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Cite this paper

@article{beyler2024variational,
  title  = {Variational Inference on the Boolean Hypercube with the Quantum Entropy},
  author = {Eliot Beyler and Francis Bach},
  year   = {2024},
  eprint = {2411.03759},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2411.03759v2}
}

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