Berlin 2018 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 37: Networks: From Topology to Dynamics (joint session SOE/DY/BP) (joint session SOE/CPP/BP/DY)

DY 37.4: Vortrag

Mittwoch, 14. März 2018, 10:15–10:30, MA 001

When is a network a network? Multi-order graphical model selection in time series data on networks — •Ingo Scholtes — Chair of Systems Design, ETH Zürich, Zürich, Switzerland

We introduce a novel framework for the modeling of time series data on networks. Such data are important, e.g., when studying click streams of users in the Web, travel patterns of passengers in transportation systems, information cascades in social networks, biological pathways, or time-stamped social interactions. While it is common to apply graph analytics and network analysis to such data, recent works have shown that temporal correlations can invalidate the results of such methods. This raises a fundamental question: When is a network abstraction of time series data justified?

Addressing this open question, we propose a framework that combines Markov chains of multiple, higher orders into a multi-layer network model that captures temporal correlations at multiple length scales simultaneously. We develop a model selection technique to infer the optimal number of layers of such a model and show that our method outperforms baseline Markov order detection techniques.

An application to eight real-world data sets capturing causal paths in time series data on networks shows that the inferred models provide an optimal summarization of the causal topologies of real-world complex systems. Our work highlights fallacies of network-based modelling techniques and provides a principled answer to the open question when they are justified. Generalizing networks to optimal multi-order models, it opens perspectives for the study of complex systems.