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Estimating the Entropy Rate of Spike Trains via Lempel-Ziv Complexity

jm.amigo{at}umh.es, Centro de Investigación Operativa, Universidad Miguel Hernández, 03202 Elche, Spain

Janusz Szczepaski

jszczepa{at}ippt.gov.pl, Institute of Fundamental Technological Research, Swietokrzyska 21, 00-049 Warsaw, Poland, and Centre of Trust and Certification "Centrast" Co., Poland

Elek Wajnryb

ewajnryb{at}ippt.gov.pl, Institute of Fundamental Technological Research, Swietokrzyska 21, 00-049 Warsaw, Poland

Maria V. Sanchez-Vives

mavi.sanchez{at}umh.es, Instituto de Neurociencias, Universidad Miguel Hernández-CSIC, 03550 San Juan de Alicante, Spain

Normalized Lempel-Ziv complexity, which measures the generation rate of new patterns along a digital sequence, is closely related to such important source properties as entropy and compression ratio, but, in contrast to these, it is a property of individual sequences. In this article, we propose to exploit this concept to estimate (or, at least, to bound from below) the entropy of neural discharges (spike trains). The main advantages of this method include fast convergence of the estimator (as supported by numerical simulation) and the fact that there is no need to know the probability law of the process generating the signal. Furthermore, we present numerical and experimental comparisons of the new method against the standard method based on word frequencies, providing evidence that this new approach is an alternative entropy estimator for binned spike trains.

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