Masterclass with Dimitris Kugiumtzis

30 March 2017, 9.30-12.30pm
Institute of Advanced Studies, UWA
Postgraduate Students, Early Career Researchers, Academics, Professional Researchers


Dimension Reduction in Estimating Complex Networks from Multivariate Time Series

A masterclass with Dimitris Kugiumtzis, Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Greece and 2017 Institute of Advanced Studies Visiting Fellow.

In the study of complex dynamical systems, such as brain dynamics and financial market dynamics, from multivariate time series, a main objective is the estimation of the connectivity structure of the observed variables (or subsystems), where connectivity is also referred to as inter-dependence, coupling, information flow or Granger causality. Having selected a connectivity measure to estimate the driving-response connections among the observed variables, the complex network is then formed, also called connectivity or causality network, where the nodes are the observed variables and the connections are the estimated inter-dependences. For a network with binary connections the inter-dependneces are discretized to zero (not significant) and one (significant) by applying a criterion for the significance, e.g. arbitrary threshold or statistical testing.

There is a main and practical issue in the connectivity analysis: esimation of direct inter-dependence in the presence of many observed variables, where direct inter-dependence between two variables excludes the inter-dependence mediated by the presence of the other observed variables. To address this issue, inevitably one has to involve a dimension reduction scheme in the estimation of direct connectivity. In our research group, we have developed appropriate methodology for this scope. Specifically, we have developed a measure that applies dimension reduction in a time-dependent context to the standard (linear) vector autoregressive model used to quantify the conditional Granger causality, called restricted conditional Granger causality index (RCGCI). The same scheme has been further used for the Granger causality defined in the frequency domain. We have used a similar dimension reduction approach and developed an information measure for direct connectivity, called partial mutual information from mixed embedding (PMIME).

In this masterclass, Professor Kugiumtzis will present the framework of connectivity analysis of multivariate time series and focus on direct connections and many observed variables. He will then describe the connectivity measures RCGCI and PMIME that apply dimension reduction in a linear and nonlinear setting, respectively. He will illustrate on simulated data the advantages of dimension reduction and the performance of the RCGCI and PMIME compared to other connectivity measures. Further, he will concentrate on the PMIME and demonstrate its ability to identify the underlying complex network (connectivity structure of the underlying complex system) solely on the basis of the observed multivariate times series. He will then move to real-world applications and use the PMIME to estimate changes of the connectivity structure in time series records of epileptic electroendephalograms and world financial markets.

Dimitris Kugiumtzis (BSc in Mathematics at the Aristotle University of Thessaloniki, MSc and PhD in Informatics at the University of Oslo) is a Professor in the Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki (AUTh), Greece. He was previously a Lecturer at the University of Glasgow (2000-2001) and guest scientist (Postdoc) at the Max Planck Institute for Physics of Complex Systems (1998-1999). His main research area is time series analysis in conjunction with dynamical systems, chaos and complexity, as well as computational statistics and data mining. Applications extend from neuroscience to climate and finance. He has participated in several national and European research projects, acted as EU evaluator and regular reviewer for a number of journals.

Professor Kugiumtzis is a 2017 Institute of Advanced Studies Visiting Fellow.