Overarching framework for data-based modelling

¹ ICSMB, University of Aberdeen - Aberdeen, UK
² Freiburg Center of Data Analysis and Modeling, University of Freiburg - Freiburg, Germany
³ University Medical Center Freiburg - Freiburg, Germany
⁴ Freiburg Institute for Advanced Studies, University of Freiburg - Freiburg, Germany
⁵ IMS, University of Aberdeen - Aberdeen, UK
⁶ School of Electrical, Computer and Energy Engineering, Arizona State University - Tempe, AZ, USA

Received: 19 October 2013
Accepted: 23 January 2014

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.