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Transfer entropy expressions for a class of non-Gaussian distributions
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0001-7194-7996
Stockholm University, Faculty of Science, Department of Mathematics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Transfer entropy is a frequently employed measure of conditional co-dependence in non-parametric analysis of Granger causality. In this paper, we derive analytical expressions for transfer entropy for the multivariate exponential, logistic, Pareto (type I − IV) and Burr distributions. The latter two fall into the class of fat-tailed distributions with power law properties, used frequently in biological, physical and actuarial sciences. We discover that the transfer entropy expressions for all four distributions are identical and depend merely on the multivariate distribution parameter and the number of distribution dimensions. Moreover, we find that in all four cases the transfer entropies are given by the same decreasing function of distribution dimensionality.

National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-101589OAI: oai:DiVA.org:su-101589DiVA: diva2:704414
Funder
EU, FP7, Seventh Framework ProgrammeSwedish Research Council
Available from: 2014-03-12 Created: 2014-03-12 Last updated: 2014-03-13
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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CiteExportLink to record
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Citation style
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