Inference of time-ordered multibody interactions
This addresses the challenge of modeling complex dynamic systems with multiple interacting components over time, which is incremental as it builds on existing Markov chain and interaction frameworks.
The paper tackles the problem of describing complex systems with temporal and multibody dependencies by introducing time-ordered multibody interactions, showing how to decompose multivariate Markov chains into these interactions and presenting an algorithm to extract them from data, with experimental validation demonstrating robustness against statistical errors and efficiency in inferring parsimonious ensembles.
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.