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Browsing by Author "Karanikolas, Vasileios Georgios"

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    Learning nonlinear functions and graph topologies
    (2021-08) Karanikolas, Vasileios Georgios
    Network science has successfully permeated a wide gamut of disciplines. A key first step to applying network science concepts to a complex system of interest, is obtaining a graph representation thereof, that accurately captures the dependencies among its constituent nodes. This is a challenging task, especially when accounting for generally nonlinear or time-varying nodal interactions. A key domain where these may arise, that is also of particular interest to this thesis, is that of identifying the topology of networks of the brain from functional magnetic resonance imaging (fMRI) time-series. To handle complex dependencies, the present thesis introduces novel nonlinear counterparts of linear association measures such as partial correlation and Granger causality, along with a nonlinear graph change detection scheme to unveil temporal variations. Choosing the type of nonlinearity to model is instrumental, as it dictates the form of nodal dependencies under consideration. To address this challenge in a data-driven fashion, the present thesis introduces the use of multi-kernel learning approaches to the realm of graph topology identification. The merits of the proposed framework are illustrated on real and synthetic resting-state fMRI data. Key to the novel approaches for capturing complex dependencies are methods for learning nonlinear functions. In this context, the second part of this thesis deals with Gaussian process (GP) based online learning. Two highly desirable, yet conflicting properties are identified, namely adaptability to a wide range of operational environments and scalability. The successful joint pursuit of these is elusive in the GP literature. To this end, a novel framework leveraging random feature kernel approximants and ensemble learning techniques is introduced. Algorithms for supervised learning are developed and associated performance analyses are provided. Finally, a novel unsupervised learning scheme extending the ubiquitous GP latent variable model is developed, capitalizing on the same key concepts. Tests on benchmark datasets highlight the benefits of the proposed approaches over state-of-the-art methods.
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    Multi-kernel based nonlinear functional connectivity models
    (2016-12) Karanikolas, Vasileios Georgios
    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.