Uncertainty in Functional Network Representations of Brain Activity of Alcoholic Patients
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ORIGINAL PAPER
Uncertainty in Functional Network Representations of Brain Activity of Alcoholic Patients Massimiliano Zanin1 · Seddik Belkoura2 · Javier Gomez3 · César Alfaro3 · Javier Cano3,4 Received: 23 March 2020 / Accepted: 4 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In spite of the large attention received by brain activity analyses through functional networks, the effects of uncertainty on such representations have mostly been neglected. We here elaborate the hypothesis that such uncertainty is not just a nuisance, but that on the contrary is condition-dependent. We test this hypothesis by analysing a large set of EEG brain recordings corresponding to control subjects and patients suffering from alcoholism, through the reconstruction of the corresponding Maximum Spanning Trees (MSTs), the assessment of their topological differences, and the comparison of two frequentist and Bayesian reconstruction approaches. A machine learning model demonstrates that the Bayesian reconstruction encodes more information than the frequentist one, and that such additional information is related to the uncertainty of the topological structures. We finally show how the Bayesian approach is more effective in the validation of generative models, over and above the frequentist one, by proposing and disproving two models based on additive noise. Keywords Functional networks · Maximum spanning trees · Bayesian statistics · Alcoholism
Introduction During the last decade, neuroscience has witnessed a revolution in the way brain activity is understood and analysed: instead of focusing on the activation patterns of individual brain regions, the attention has shifted towards how these regions are interconnected. This has been possible, among others, thanks to the introduction of graph theory, and more recently of complex networks theory (Strogatz 2001; Newman 2003; Boccaletti et al. 2006). Cognitive functions are no longer localised phenomena, but instead emerge from Handling Editor: Gustavo Deco * Massimiliano Zanin [email protected] 1
Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus UIB, 07122 Palma de Mallorca, Spain
2
Center for Computational Simulation, Universidad Politécnica de Madrid, Madrid, Spain
3
Department of Computer Science and Statistics, Universidad Rey Juan Carlos, Madrid, Spain
4
Department of Statistics, University of Auckland, Auckland, New Zealand
how information is processed at, and transmitted between, multiple areas (Bullmore and Sporns 2009; Bullmore and Bassett 2011). A notably understudied aspect of functional networks is their uncertainty. Different physiological signals (e.g. electrical and magnetic fields) are recorded and used to assess the connectivity between brain regions; yet, these time series have an intrinsically limited duration. Even though very long time series can prima facie be recorded through portable devices, one usually faces the need of obtaining a stationary picture of the c
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