用量子熵改进布尔超立方体上的变分推断，提升精度与效率。
Variational Inference on the Boolean Hypercube with the Quantum Entropy
- 基于量子松弛重构KL散度，构建对数归一化常数上界。
- 提出原对偶优化算法高效计算上界，数值实验优于现有方法。
- 引入类似SOS的层级结构，设计贪心选择策略优化松弛精度。
本文针对布尔超立方体上的成对马尔可夫随机场，基于量子松弛的Kullback-Leibler散度，推导出对数归一化常数的变分推断上界。进一步提出基于原对偶优化的高效算法以计算这些上界。通过引入类似求和平方（SoS）的层级结构，提升上界精度，并设计一种贪心算法用于在不同松弛层级间进行选择。通过大量数值实验，与当前最优方法对比，验证了所提方法的有效性与优越性。
原文摘要 · Abstract (English)
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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