Inference of time-ordered multibody interactions

TL;DR

This paper introduces a new framework for modeling complex systems with temporal and multibody dependencies, providing algorithms to extract and analyze these interactions from data.

Contribution

It presents a novel concept of time-ordered multibody interactions and an algorithm to infer them from data, advancing the understanding of complex system dynamics.

Findings

Algorithm accurately infers interaction ensembles from data.

Method is robust against statistical errors.

Efficiently captures system-level dynamics.

Abstract

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.