Inference of time-ordered multibody interactions

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 combined interactions from data 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 obtaining simple interaction ensembles.