Abstract
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.
Highlights
Analysis of causality, as a natural extension of correlative analysis, has been of great interest in many scientific disciplines
Granger causality is a particular definition of causality where using temporal resolution, a variable is said to Granger-cause another if the earlier values of the former can enhance the prediction of the present value of the latter in the presence of the latter’s earlier values
The framework outlined here in this study based on kernel density estimation (KDE) via adaptive bandwidths, information-theoretic measures of divergence, and bootstrap tests of significance, constitutes a fully non-parametric platform for analysis of Granger causality
Summary
As a natural extension of correlative analysis, has been of great interest in many scientific disciplines. Granger causality is a particular definition of causality where using temporal resolution, a variable is said to Granger-cause another if the earlier values of the former can enhance the prediction of the present value of the latter in the presence of the latter’s earlier values. This particular definition of causality presumes a temporal signal asymmetry where the cause precedes the effect and where the information embedded in the causal variable about the occurrence of the effect conditioned on all other embedded information is unique [15, 22]. Expressed using the mathematical language of probability theory, under H0, given k lags and variables A, B and C, {B} does not Granger-cause {A} at observation index t, if
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