Overarching framework for data-based modelling

Björn Schelter, Malenka Mader, Wolfgang Mader, Linda Sommerlade, Bettina Platt, Ying-Cheng Lai, Celso Grebogi, Marco Thiel

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

One of the main modelling paradigms for complex physical systems are networks. When estimating the network structure from measured signals, typically several assumptions such as stationarity are made in the estimation process. Violating these assumptions renders standard analysis techniques fruitless. We here propose a framework to estimate the network structure from measurements of arbitrary non-linear, non-stationary, stochastic processes. To this end, we propose a rigorous mathematical theory that underlies this framework. Based on this theory, we present a highly efficient algorithm and the corresponding statistics that are immediately sensibly applicable to measured signals. We demonstrate its performance in a simulation study. In experiments of transitions between vigilance stages in rodents, we infer small network structures with complex, time-dependent interactions; this suggests biomarkers for such transitions, the key to understand and diagnose numerous diseases such as dementia. We argue that the suggested framework combines features that other approaches followed so far lack.

Original languageEnglish (US)
Article number30004
JournalEPL
Volume105
Issue number3
DOIs
Publication statusPublished - Feb 2014

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ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Schelter, B., Mader, M., Mader, W., Sommerlade, L., Platt, B., Lai, Y-C., ... Thiel, M. (2014). Overarching framework for data-based modelling. EPL, 105(3), [30004]. https://doi.org/10.1209/0295-5075/105/30004