Concise network models of memory dynamics reveal explainable patterns in path data

TL;DR

This paper introduces a method to build concise, interpretable network models from path data that capture higher-order dependencies, revealing memory effects in complex systems more efficiently than traditional models.

Contribution

The authors develop a novel approach to construct simplified second-order network models that balance interpretability, size, and accuracy, capturing memory effects in path data.

Findings

Reveals large-scale memory patterns in synthetic and real-world data

Constructs concise networks that outperform first-order models in insight and size

Achieves similar accuracy to second-order models with fewer parameters

Abstract

Networks are a powerful tool to model the structure and dynamics of complex systems across scales. Direct connections between system components are often represented as edges, while paths and walks capture indirect interactions. This approach assumes that flows in the system are sequences of independent transitions. Path data from real-world systems often have higher-order dependencies, which require more sophisticated models. In this work, we propose a method to construct concise networks from path data that interpolate between first and second-order models. We prioritise simplicity and interpretability by creating state nodes that capture latent modes of second-order effects and introducing an interpretable measure to balance model size and accuracy. In both synthetic and real-world applications, our method reveals large-scale memory patterns and constructs concise networks that provide insights beyond the first-order model at the fraction of the size of a second-order model.