Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to characterize the structural organization of hypergraphs. The method allows to infer missing hyperedges of any size in a principled way, and to jointly detect overlapping communities in presence of higher-order interactions. Furthermore, our model has an efficient numerical implementation, and it runs faster than dyadic algorithms on pairwise records projected from higher-order data. We apply our method to a variety of real-world systems, showing strong performance in hyperedge prediction tasks, detecting communities well aligned with the information carried by interactions, and robustness against addition of noisy hyperedges. Our approach illustrates the fundamental advantages of a hypergraph probabilistic model when modeling relational systems with higher-order interactions.

翻译：测谎仪是所有系统单元之间结构化的编码,最近证明这是描述许多真实世界生物和社会网络的成功工具。 我们在此提出一个基于统计推论的框架,以描述高光学结构结构的特征。 这种方法可以以有原则的方式推断出任何大小的缺失高屏,并共同发现存在较高级相互作用的重叠社区。 此外,我们的模型具有高效的数字实施,其运行速度比从较高级数据预测的对称记录上的双轨算法要快。 我们将我们的方法应用于各种真实世界系统,显示超尖端预测任务方面的强效,探测社区与互动所传播的信息非常吻合,并有力地防止噪音高屏障的增加。 我们的方法说明了在模拟具有较高级相互作用的关系系统时,高光谱概率模型的根本优点。