Networks can describe the structure of a wide variety of complex systems by specifying which pairs of entities in the system are connected. While such pairwise representations are flexible, they are not necessarily appropriate when the fundamental interactions involve more than two entities at the same time. Pairwise representations nonetheless remain ubiquitous, because higher-order interactions are often not recorded explicitly in network data. Here, we introduce a Bayesian approach to reconstruct latent higher-order interactions from ordinary pairwise network data. Our method is based on the principle of parsimony and only includes higher-order structures when there is sufficient statistical evidence for them. We demonstrate its applicability to a wide range of datasets, both synthetic and empirical.

网络可以通过指定系统中连接的实体对来描述各种复杂系统的结构。虽然这种成对表示很灵活，但当基本交互同时涉及两个以上的实体时，它们不一定合适。尽管如此，成对表示仍然无处不在，因为高阶交互通常没有明确记录在网络数据中。在这里，我们引入了一种贝叶斯方法来从普通的成对网络数据重建潜在的高阶交互。我们的方法基于简约原则，只有在有足够的统计证据时才包括高阶结构。我们证明了它对广泛的数据集的适用性，包括合成数据集和经验数据集。