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Estimating the interaction graph of stochastic neuronal dynamics by observing only pairs of neurons

Author

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  • De Santis, E.
  • Galves, A.
  • Nappo, G.
  • Piccioni, M.

Abstract

We address the questions of identifying pairs of interacting neurons from the observation of their spiking activity. The neuronal network is modeled by a system of interacting point processes with memory of variable length. The influence of a neuron on another can be either excitatory or inhibitory. To identify the existence and the nature of an interaction we propose an algorithm based only on the observation of joint activity of the two neurons in successive time slots. This reduces the amount of computation and storage required to run the algorithm, thereby making the algorithm suitable for the analysis of real neuronal data sets. We obtain computable upper bounds for the probabilities of false positive and false negative detection. As a corollary we prove the consistency of the identification algorithm.

Suggested Citation

  • De Santis, E. & Galves, A. & Nappo, G. & Piccioni, M., 2022. "Estimating the interaction graph of stochastic neuronal dynamics by observing only pairs of neurons," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 224-247.
    • Handle: RePEc:eee:spapps:v:149:y:2022:i:c:p:224-247
    DOI: 10.1016/j.spa.2022.03.016
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    References listed on IDEAS

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    1. Tata Subba Rao & Granville Tunnicliffe Wilson & Michael Eichler & Rainer Dahlhaus & Johannes Dueck, 2017. "Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 225-242, March.
    2. André, Morgan & Planche, Léo, 2021. "The effect of graph connectivity on metastability in a stochastic system of spiking neurons," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 292-310.
    3. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
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