发表机构
Institute of Data Science, University of Hong Kong; School of Computing and Data Science, University of Hong Kong（香港大学数据科学研究所; 香港大学计算与数据科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究将超图重建视为局部信噪比判别问题，提出一种快速算法，可高效重建任意阶数的高阶交互，并给出信息论可检测性边界。
AI 中文摘要
复杂系统通常通过成对网络进行测量和表示，即使底层交互同时涉及两个以上的单元。从成对测量中恢复这种潜在的超图结构是一个基本的逆问题，但随着候选超边空间随系统规模呈指数增长，现有方法无法在任意交互阶数下进行可扩展的超图重建。在这里，我们将超图重建视为一个局部信噪比判别问题，并利用这种局部性构建了一种快速算法，该算法可重建任意交互阶数的超图。在多种合成和真实世界系统中，我们的方法在恢复潜在超图结构方面实现了高精度，同时重建超图的速度比现有方法快数个数量级。我们的方法还提供了一个信息论可检测性边界，该边界能准确预测哪些高阶交互可从成对测量中恢复。
英文摘要
Complex systems are routinely measured and represented through pairwise networks, even when the underlying interactions involve more than two units at once. Recovering this latent hypergraph structure from pairwise measurements is a fundamental inverse problem, but as the space of candidate hyperedges grows exponentially with system size, scalable hypergraph reconstruction at arbitrary interaction orders is out of reach for existing methods. Here we cast hypergraph reconstruction as a local signal-to-noise discrimination problem and use this locality to build a fast algorithm that reconstructs hypergraphs up to any interaction order. Across diverse synthetic and real-world systems our method achieves a high recovery accuracy of latent hypergraph structure while reconstructing hypergraphs up to orders of magnitude more quickly than current approaches. Our approach also yields an information-theoretic detectability boundary that sharply predicts which latent hyperedges are recoverable from pairwise measurements.
Comments27 pages, 5 figures, 6 tables
