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.

翻译：本文基于Kullback-Leibler散度的量子松弛形式，推导了布尔超立方体上成对马尔可夫随机场对数配分函数的变分推断上界。随后提出一种基于原始-对偶优化的高效算法来计算这些上界。通过引入与平方和（SoS）层次结构类似的"层次化"方法改进了这些界，并提出一种贪心算法来筛选这些松弛形式。我们开展了大量数值实验，并与该推断问题的最先进方法进行了比较。