超图上的信息传递:可探测性、相变和高阶信息

IF 2.2 3区 物理与天体物理 Q2 MECHANICS
Nicolò Ruggeri, Alessandro Lonardi and Caterina De Bacco
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引用次数: 0

摘要

超图是研究具有高阶交互作用的系统时广泛采用的工具。尽管最近这些系统中的群落检测方法取得了进步,但我们仍然缺乏对其可检测性极限的理论分析。在这里,我们推导出了超图中群落检测的闭式边界。通过使用消息传递公式,我们证明了可探测性取决于超图的结构属性,如超边大小的分布或它们的同类性。我们的表述能够描述超图的熵与其簇展开的熵的关系,表明当超图在节点对上高度重叠时,群落检测能力会增强。我们开发了一种高效的信息传递算法,用于学习大型系统中的群落和模型参数。此外,我们还设计了一种精确采样程序,以便从概率模型中生成合成数据。利用这些方法,我们对合成数据集中的群落检测边界进行了数值研究,并从真实系统中提取了群落。我们的研究结果拓展了我们对超图中群落检测极限的理解,并为研究具有高阶交互作用的系统引入了灵活的数学工具。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Message-passing on hypergraphs: detectability, phase transitions and higher-order information
Hypergraphs are widely adopted tools to examine systems with higher-order interactions. Despite recent advancements in methods for community detection in these systems, we still lack a theoretical analysis of their detectability limits. Here, we derive closed-form bounds for community detection in hypergraphs. Using a message-passing formulation, we demonstrate that detectability depends on the hypergraphs’ structural properties, such as the distribution of hyperedge sizes or their assortativity. Our formulation enables a characterization of the entropy of a hypergraph in relation to that of its clique expansion, showing that community detection is enhanced when hyperedges highly overlap on pairs of nodes. We develop an efficient message-passing algorithm to learn communities and model parameters on large systems. Additionally, we devise an exact sampling routine to generate synthetic data from our probabilistic model. Using these methods, we numerically investigate the boundaries of community detection in synthetic datasets, and extract communities from real systems. Our results extend our understanding of the limits of community detection in hypergraphs and introduce flexible mathematical tools to study systems with higher-order interactions.
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来源期刊
CiteScore
4.50
自引率
12.50%
发文量
210
审稿时长
1.0 months
期刊介绍: JSTAT is targeted to a broad community interested in different aspects of statistical physics, which are roughly defined by the fields represented in the conferences called ''Statistical Physics''. Submissions from experimentalists working on all the topics which have some ''connection to statistical physics are also strongly encouraged. The journal covers different topics which correspond to the following keyword sections. 1. Quantum statistical physics, condensed matter, integrable systems Scientific Directors: Eduardo Fradkin and Giuseppe Mussardo 2. Classical statistical mechanics, equilibrium and non-equilibrium Scientific Directors: David Mukamel, Matteo Marsili and Giuseppe Mussardo 3. Disordered systems, classical and quantum Scientific Directors: Eduardo Fradkin and Riccardo Zecchina 4. Interdisciplinary statistical mechanics Scientific Directors: Matteo Marsili and Riccardo Zecchina 5. Biological modelling and information Scientific Directors: Matteo Marsili, William Bialek and Riccardo Zecchina
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