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Non-parametric analysis of Granger causality using local measures of divergence
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0001-7194-7996
2013 (English)In: Applied Mathematical Sciences, ISSN 1312-885X, E-ISSN 1314-7552, Vol. 7, no 83, 4107-4236 p.Article in journal (Refereed) Published
Abstract [en]

The employment of Granger causality analysis on temporal data is now a standard routine in many scientific disciplines. Since its in- ception, Granger causality has been modeled using a wide variety of analytical frameworks of which, linear models and derivations thereof have been the dominant choice. Nevertheless, a body of research on Granger causality and its applications has focused on non-linear and non-parametric models. One common choice for such models is based on employment of multivariate density estimators and measures of divergence. However, these models are subject to a number of estimations and tuning components that have a great impact on the final outcome. Here we focus on one such general model and improve a number of its tuning bodies. Crucially, we i) investigate the bandwidth selection issue in kernel density estimation, and ii) discuss and propose a solu- tion to the sensitivity of estimated information theoretic measures of divergence to non-linear correspondence. The resulting framework of analysis is evaluated using varied series of simulations.

Place, publisher, year, edition, pages
HIKARI Ltd, , 2013. Vol. 7, no 83, 4107-4236 p.
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-101588DOI: 10.12988/ams.2013.35275OAI: oai:DiVA.org:su-101588DiVA: diva2:704403
Funder
EU, FP7, Seventh Framework Programme
Available from: 2014-03-12 Created: 2014-03-12 Last updated: 2017-12-05Bibliographically approved
In thesis
1. A Treatise on Measuring Wiener-Granger Causality
Open this publication in new window or tab >>A Treatise on Measuring Wiener-Granger Causality
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Wiener-Granger causality is a well-established concept of causality based on stochasticity and the flow of time, with applications in a broad array of quantitative sciences. The majority of methods used to measure Wiener-Granger causality are based on linear premises and hence insensitive to non-linear signals. Other frameworks based on non-parametric techniques are often computationally expensive and susceptible to overfitting or lack of sensitivity.

In this thesis, Paper I investigates the application of linear Wiener-Granger causality to migrating cancer cell data obtained using a Systems Microscopy experimental platform. Paper II represents a review of non-parametric measures based on information theory and discusses a number of related bottlenecks and potential routes of circumvention. Paper III studies the properties of a frequently used non-parametric information theoretical measure for a class of non-Gaussian distributions. Paper IV introduces a new efficient scheme for non-parametric analysis of Wiener-Granger causality based on kernel canonical correlations, and studies the connection between this new scheme and the information theoretical approach. Lastly, Paper V draws upon the results in the preceding paper to discuss non-parametric analysis of Wiener-Granger causality in partially observed systems.

Altogether, the work presented in this thesis constitutes a comprehensive review on measures of Wiener-Granger causality in general, and in particular, features new insights on efficient non-parametric analysis of Wiener-Granger causality in high-dimensional settings.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University, 2014. 44 p.
Keyword
Wiener-Granger causality, Information theory, Kernel canonical correlation, Systems Microscopy, Cell migration.
National Category
Probability Theory and Statistics Cell Biology
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-101595 (URN)978-91-7447-861-7 (ISBN)
Public defence
2014-04-16, sal 14 hus 5, Kräftriket, Roslagsvägen 101, Stockholm, 10:00 (English)
Opponent
Supervisors
Funder
EU, FP7, Seventh Framework ProgrammeSwedish Research Council
Note

At the time of the doctoral defence, the following papers were unpublished and had a status as follows: Paper 3: Accepted Paper 4: Manuscript; Paper 5: Accepted

Available from: 2014-03-25 Created: 2014-03-12 Last updated: 2014-03-13Bibliographically approved

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