Neural Comput - Quantifying statistical interdependence, part III: N > 2 point processes.

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Resumo

Stochastic event synchrony (SES) is a recently proposed family of similarity measures. First, "events" are extracted from the given signals; next, one tries to align events across the different time series. The better the alignment, the more similar the N time series are considered to be. The similarity measures quantify the reliability of the events (the fraction of "nonaligned" events) and the timing precision. So far, SES has been developed for pairs of one-dimensional (Part I) and multidimensional (Part II) point processes. In this letter (Part III), SES is extended from pairs of signals to N > 2 signals. The alignment and SES parameters are again determined through statistical inference, more specifically, by alternating two steps: (1) estimating the SES parameters from a given alignment and (2), with the resulting estimates, refining the alignment. The SES parameters are computed by maximum a posteriori (MAP) estimation (step 1), in analogy to the pairwise case. The alignment (step?2) is solved by linear integer programming. In order to test the robustness and reliability of the proposed N-variate SES method, it is first applied to synthetic data. We show that N-variate SES results in more reliable estimates than bivariate SES. Next N-variate SES is applied to two problems in neuroscience: to quantify the firing reliability of Morris-Lecar neurons and to detect anomalies in EEG synchrony of patients with mild cognitive impairment. Those problems were also considered in Parts I and II, respectively. In both cases, the N-variate SES approach yields a more detailed analysis.

Resumo Limpo

stochast event synchroni ses recent propos famili similar measur first event extract given signal next one tri align event across differ time seri better align similar n time seri consid similar measur quantifi reliabl event fraction nonalign event time precis far ses develop pair onedimension part multidimension part ii point process letter part iii ses extend pair signal n signal align ses paramet determin statist infer specif altern two step estim ses paramet given align result estim refin align ses paramet comput maximum posteriori map estim step analog pairwis case align step solv linear integ program order test robust reliabl propos nvariat ses method first appli synthet data show nvariat ses result reliabl estim bivari ses next nvariat ses appli two problem neurosci quantifi fire reliabl morrislecar neuron detect anomali eeg synchroni patient mild cognit impair problem also consid part ii respect case nvariat ses approach yield detail analysi

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