Statistical approaches to connectivity estimation for multivariate times series with application to EEG data

摘要

In the analysis of EEG data, there has been much interest in functional connectivity network modelling. However, the high-dimensional nature of this type of data renders conventional network analysis methods intractable.udOne popular approach consists of treating EEG signals as multidimensional time series, and then analysing them in the spectral domain. For this, we need good estimators for the inverse spectral density function (SDF) matrix. However, issues of ill-definedness or singularities oftenudarise.udThere exist many regularisation methods designed to address these problems. Amongst them, shrinkage has received particular interest in recent work. A large amount of research has gone into the development of shrinkage methods for real-valued covariance matrices, but they canudalso be applied to the estimation of inverse SDF matrices. This PhD project aims to:ud• Further shrinkage estimation in the frequency domain. We show how the equivalent of the Ledoit-Wolf shrinkage estimator for spectral matrices can be improved upon using a Rao-Blackwell estimator. We also further a non-linear method based on Random MatrixudTheory (RMT);ud• Improve the estimation of inverse spectral matrices and associated variables called the partial coherences, which measure direct conditional dependence between any two variables in a multidimensional system. We discuss the impact of shrinkage and another regularisation method on the quality of the partial coherence estimates, and show how these methodologies can be improved for this purpose;ud• In frequency domain analysis, results are derived for each frequency, over a set of discretised frequencies. However, we are interested in deriving an overall result for the entire band. We investigate the performance of p-value combiners for frequency-domain data.udAll of these results are applied to EEG data collected from 34 schizophrenic subjects and 24 healthy control individuals, and compared with conventional methods in terms of matrix loss and graph distance.