title: Chow-Liu trees are sufficient predictive models for reproducing key features of functional networks of periictal EEG time-series.
abstract: Seizure freedom in patients suffering from pharmacoresistant epilepsies is still not achieved in 20-30% of all cases. Hence, current therapies need to be improved, based on a more complete understanding of ictogenesis. In this respect, the analysis of functional networks derived from intracranial electroencephalographic (iEEG) data has recently become a standard tool. Functional networks however are purely descriptive models and thus are conceptually unable to predict fundamental features of iEEG time-series, e.g., in the context of therapeutical brain stimulation. In this paper we present some first steps towards overcoming the limitations of functional network analysis, by showing that its results are implied by a simple predictive model of time-sliced iEEG time-series. More specifically, we learn distinct graphical models (so called Chow-Liu (CL) trees) as models for the spatial dependencies between iEEG signals. Bayesian inference is then applied to the CL trees, allowing for an analytic derivation/prediction of functional networks, based on thresholding of the absolute value Pearson correlation coefficient (CC) matrix. Using various measures, the thus obtained networks are then compared to those which were derived in the classical way from the empirical CC-matrix. In the high threshold limit we find (a) an excellent agreement between the two networks and (b) key features of periictal networks as they have previously been reported in the literature. Apart from functional networks, both matrices are also compared element-wise, showing that the CL approach leads to a sparse representation, by setting small correlations to values close to zero while preserving the larger ones. Overall, this paper shows the validity of CL-trees as simple, spatially predictive models for periictal iEEG data. Moreover, we suggest straightforward generalizations of the CL-approach for modeling also the temporal features of iEEG signals.
authors.affiliation: Department of Neurology, Inselspital, Bern University Hospital, University of Bern, Freiburgstrasse, CH-3010 Bern, Switzerland. Electronic address: Andreas.Steimer@insel.ch.
authors.forename: Andreas
authors.initials: A
authors.lastname: Steimer
authors.affiliation: Department of Neurology, Inselspital, Bern University Hospital, University of Bern, Freiburgstrasse, CH-3010 Bern, Switzerland.
authors.forename: Frédéric
authors.initials: F
authors.lastname: Zubler
authors.affiliation: Department of Neurology, Inselspital, Bern University Hospital, University of Bern, Freiburgstrasse, CH-3010 Bern, Switzerland.
authors.forename: Kaspar
authors.initials: K
authors.lastname: Schindler
mesh_terms: D000293:Adolescent; D000328:Adult; D000465:Algorithms; D001499:Bayes Theorem; D001921:Brain / Q000503:physiopathology*; D002648:Child; D004569:Electroencephalography; D004827:Epilepsy / Q000503:physiopathology*; D005260:Female; D006801:Humans; D008297:Male; D008875:Middle Aged; D008959:Models, Neurological; D009415:Nerve Net / Q000503:physiopathology*; D012815:Signal Processing, Computer-Assisted; D055815:Young Adult
keywords: Bayesian inference; Chow–Liu algorithm; Chow–Liu tree; Epilepsy; Functional networks; Graphical models; Minimum spanning tree; Periictal EEG; Predictive modeling