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A Treatise on Measuring Wiener-Granger Causality
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0001-7194-7996
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 [en]
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: urn:nbn:se:su:diva-101595ISBN: 978-91-7447-861-7 (print)OAI: oai:DiVA.org:su-101595DiVA: diva2:704532
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
List of papers
1. Plasticity in the Macromolecular-Scale Causal Networks of Cell Migration
Open this publication in new window or tab >>Plasticity in the Macromolecular-Scale Causal Networks of Cell Migration
Show others...
2014 (English)In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 9, no 2, e90593- p.Article in journal (Refereed) Published
Abstract [en]

Heterogeneous and dynamic single cell migration behaviours arise from a complex multi-scale signalling network comprising both molecular components and macromolecular modules, among which cell-matrix adhesions and F-actin directly mediate migration. To date, the global wiring architecture characterizing this network remains poorly defined. It is also unclear whether such a wiring pattern may be stable and generalizable to different conditions, or plastic and context dependent. Here, synchronous imaging-based quantification of migration systemorganization, represented by 87 morphological and dynamic macromolecular module features, and migration system behaviour, i.e., migration speed, facilitated Granger causality analysis. We thereby leveraged natural cellular heterogeneity to begin mapping the directionally specific causal wiring between organizational and behavioural features of the cell migration system. This represents an important advance on commonly used correlative analyses that do not resolve causal directionality. We identified organizational features such as adhesion stability and adhesion F-actin content that, as anticipated, causally influenced cell migration speed. Strikingly, we also found that cell speed can exert causal influence over organizationalfeatures, including cell shape and adhesion complex location, thus revealing causality in directions contradictory to previous expectations. Importantly, by comparing unperturbed and signalling-modulated cells, we provide proof-of-principle that causal interaction patterns are in fact plastic and context dependent, rather than stable and generalizable.

National Category
Medical and Health Sciences Mathematics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-101587 (URN)10.1371/journal.pone.0090593 (DOI)000332396200233 ()
Funder
EU, FP7, Seventh Framework Programme, HEALTH-F4-2010-258068Swedish Research Council
Available from: 2014-03-12 Created: 2014-03-12 Last updated: 2017-12-05Bibliographically approved
2. Non-parametric analysis of Granger causality using local measures of divergence
Open this publication in new window or tab >>Non-parametric analysis of Granger causality using local measures of divergence
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
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-101588 (URN)10.12988/ams.2013.35275 (DOI)
Funder
EU, FP7, Seventh Framework Programme
Available from: 2014-03-12 Created: 2014-03-12 Last updated: 2017-12-05Bibliographically approved
3. Transfer entropy expressions for a class of non-Gaussian distributions
Open this publication in new window or tab >>Transfer entropy expressions for a class of non-Gaussian distributions
(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:nbn:se:su:diva-101589 (URN)
Funder
EU, FP7, Seventh Framework ProgrammeSwedish Research Council
Available from: 2014-03-12 Created: 2014-03-12 Last updated: 2014-03-13
4. Robust Non-linear Wiener-Granger Causality For Large High-dimensional Data
Open this publication in new window or tab >>Robust Non-linear Wiener-Granger Causality For Large High-dimensional Data
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Wiener-Granger causality is a widely used framework of causal analysis for temporally resolved events. We introduce a new measure of Wiener-Granger causality based on kernelization of partial canonical correlation analysis with specific advantages in the context of large high-dimensional data. The introduced measure is able to detect non-linear and non-monotonous signals, is designed to be immune to noise, and offers tunability in terms of computational complexity in its estimations. Furthermore, we show that, under specified conditions, the intro- duced measure can be regarded as an estimate of conditional mutual information (tranfer entropy). The functionality of this measure is assessed using comparative simulations where it outperforms other existing methods. The paper is concluded with an application to climatological data.

National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-101590 (URN)
Funder
EU, FP7, Seventh Framework ProgrammeSwedish Research Council
Available from: 2014-03-12 Created: 2014-03-12 Last updated: 2014-03-13
5. Non-parametric Wiener-Granger Causality in Partially Observed Systems
Open this publication in new window or tab >>Non-parametric Wiener-Granger Causality in Partially Observed Systems
2014 (English)In: IEEE 2014 Conference on Norbert Wiener in the 21st Century: Driving Technology's Future, 2014Conference paper, Oral presentation only (Refereed)
Abstract [en]

Wiener’s definition of causality, now known as Wiener-Granger causality, has become a frequently used quantification of temporally resolved causality in numerous fields of science. In many empirical studies, the system of interest cannot be observed in its entirety and the observations may include non-informative data. To this end, partial Wiener-Granger causality has been developed to circumvent this issue. In this paper, we extend partial Wiener-Granger causality to the non-parametric case and discuss two approaches to obtain estimates of this non-parametric, entropy-based measure.

National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-101592 (URN)
Conference
IEEE 2014 Conference on Norbert Wiener in the 21st Century 24-26 June 2014, Boston MA
Note

The paper is accepted to the conference  mentioned dabove

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

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