Variational Inference on the Boolean Hypercube with the Quantum Entropy

Fuente: arXiv
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Main Authors: Beyler, Eliot, Bach, Francis
Format: Preprint
Published: 2024
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author Beyler, Eliot
Bach, Francis
author_facet Beyler, Eliot
Bach, Francis
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2411_03759
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Variational Inference on the Boolean Hypercube with the Quantum Entropy
Beyler, Eliot
Bach, Francis
Information Theory
Machine Learning
Optimization and Control
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.
title Variational Inference on the Boolean Hypercube with the Quantum Entropy
topic Information Theory
Machine Learning
Optimization and Control
url https://arxiv.org/abs/2411.03759