We introduce time-ordered multibody interactions to describe complex systems manifesting temporal as well as multibody dependencies. First, we show how the dynamics of multivariate Markov chains can be decomposed in ensembles of time-ordered multibody interactions. Then, we present an algorithm to extract those interactions from data capturing the system-level dynamics of node states and a measure to characterize the complexity of interaction ensembles. Finally, we experimentally validate the robustness of our algorithm against statistical errors and its efficiency at inferring parsimonious interaction ensembles.

翻译：我们引入时序多体相互作用来描述同时呈现时间依赖与多体依赖的复杂系统。首先，我们展示了多元马尔可夫链的动力学如何被分解为时序多体相互作用的集合。随后，我们提出了一种算法，用于从捕捉节点状态系统级动态的数据中提取这些相互作用，并给出一种衡量相互作用集合复杂性的指标。最后，我们通过实验验证了该算法对统计误差的鲁棒性，以及在推断简约相互作用集合方面的效率。