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 those interactions from data capturing the system-level dynamics of node states and a measure to characterize the complexity of interaction ensembles.

Bayesian inference of transition matrices from incomplete graph data with a topological prior.

Many network analysis and graph learning techniques are based on discrete- or continuous-time models of random walks. To apply these methods, it is necessary to infer transition matrices that formalize the underlying stochastic process in an observed graph. For weighted graphs, where weighted edges capture observations of repeated interactions between nodes, it is common to estimate the entries of such transition matrices based on the (relative) weights of edges.