Karanikolas, Vasileios Georgios2017-03-142017-03-142016-12https://hdl.handle.net/11299/185085University of Minnesota M.S.E.E. thesis. December 2016. Major: Electrical Engineering. Advisor: Georgios Giannakis. 1 computer file (PDF); v, 35 pages.Functional connectivity measures, such as partial correlation (PC) and Granger causality, play a key role in identifying interactions among brain regions from functional magnetic resonance imaging (fMRI) time series. Motivated by the generally nonlinear mechanisms generating the blood-oxygen-level dependent signal, the present thesis introduces kernel- based nonlinear counterparts of partial correlation and partial Granger causality (PGC). The form of kernel-induced nonlinearity that “best” models the data is learned through a data-driven approach that optimally combines multiple kernels. Synthetically generated data based on a dynamic causal model are used to validate the proposed approaches in resting-state (RS) fMRI scenarios, highlighting the gains in edge presence and directionality detection performance when compared with the linear PC and existing PGC methods, respectively. Tests on real RS-fMRI data demonstrate that connectivity patterns revealed by linear and nonlinear models exhibit noticeable differences. In particular, the networks estimated by the proposed kernel-based PC approach capture known features of RS networks, while at the same time being more reflective of the underlying structural connectivity, as compared to linear PC networks.enThesis or Dissertation