Paper ID: 2411.03759 • Published Nov 6, 2024
Variational Inference on the Boolean Hypercube with the Quantum Entropy
Eliot Beyler (SIERRA), Francis Bach (SIERRA)
TL;DR
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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.