Overarching framework for data-based modelling

Björn Schelter, Malenka Mader, Wolfgang Mader, Linda Sommerlade, Bettina Platt, Yingcheng Lai, Celso Grebogi, Marco Thiel

Research output: Contribution to journalArticle

12 Citations (Scopus)

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
Article number30004
JournalEurophysics Letters
Volume105
Issue number3
DOIs
Publication statusPublished - 20 Feb 2014

Fingerprint

rodents
biomarkers
stochastic processes
estimating
statistics
estimates
simulation
interactions

Cite this

Overarching framework for data-based modelling. / Schelter, Björn; Mader, Malenka; Mader, Wolfgang; Sommerlade, Linda; Platt, Bettina; Lai, Yingcheng; Grebogi, Celso; Thiel, Marco.

In: Europhysics Letters, Vol. 105, No. 3, 30004, 20.02.2014.

Research output: Contribution to journalArticle

Schelter, Björn ; Mader, Malenka ; Mader, Wolfgang ; Sommerlade, Linda ; Platt, Bettina ; Lai, Yingcheng ; Grebogi, Celso ; Thiel, Marco. / Overarching framework for data-based modelling. In: Europhysics Letters. 2014 ; Vol. 105, No. 3.
@article{414d9bfbccac47209f9aa333c1ce91cc,
title = "Overarching framework for data-based modelling",
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.",
author = "Bj{\"o}rn Schelter and Malenka Mader and Wolfgang Mader and Linda Sommerlade and Bettina Platt and Yingcheng Lai and Celso Grebogi and Marco Thiel",
year = "2014",
month = "2",
day = "20",
doi = "10.1209/0295-5075/105/30004",
language = "English",
volume = "105",
journal = "Europhysics Letters",
issn = "0295-5075",
publisher = "EPL ASSOCIATION, EUROPEAN PHYSICAL SOCIETY",
number = "3",

}

TY - JOUR

T1 - Overarching framework for data-based modelling

AU - Schelter, Björn

AU - Mader, Malenka

AU - Mader, Wolfgang

AU - Sommerlade, Linda

AU - Platt, Bettina

AU - Lai, Yingcheng

AU - Grebogi, Celso

AU - Thiel, Marco

PY - 2014/2/20

Y1 - 2014/2/20

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84897695990&partnerID=8YFLogxK

U2 - 10.1209/0295-5075/105/30004

DO - 10.1209/0295-5075/105/30004

M3 - Article

AN - SCOPUS:84897695990

VL - 105

JO - Europhysics Letters

JF - Europhysics Letters

SN - 0295-5075

IS - 3

M1 - 30004

ER -