Variational Inference on the Boolean Hypercube with the Quantum Entropy
Information Theory
2025-02-17 v2 Machine Learning
math.IT
Optimization and Control
Machine Learning
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.
Cite
@article{arxiv.2411.03759,
title = {Variational Inference on the Boolean Hypercube with the Quantum Entropy},
author = {Eliot Beyler and Francis Bach},
journal= {arXiv preprint arXiv:2411.03759},
year = {2025}
}