Sparsity in regression analysis of EEG data

Specialeforsvar: Camilla Witt

Title: Sparsity in regression analysis of EEG data

Abstract: This thesis deals with EEG data, which is obtained from recording electrical signal in time on 64 places on the scalp. We model the functional connectivity network between the different locations (channels) on the scalp using a vector autoregressive process and fit the parameters using a regression model.
In this model we have 64 possible response variables and 64 possible predictors for each response, whereas we only have a limited number of observations. Furthermore, we expect that the predictors can be highly correlated and thus multicollinearity can emerge. Throughout this thesis, we explore several strategies on how to handle these issues via shrinkage methods e.g. ridge regression, lasso and elastic net and simultaneously try to recover the underlying network between the channels. We compare the advantages and disadvantages of these methods, such as variance and prediction error, using cross-validation and bootstrap methods. We find that the lasso and the elastic net (_ = 0:75) estimator have lowest prediction errors. Additionally, we see that the estimated networks don't have that many significant connections, especially not the lasso network. Thus, in order to recover the network between the channels, the elastic net estimator is preferred.

Vejleder:  Susanne Ditlevsen
Censor:    Anders Rønn-Nielsen, CBS