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Statistical modelling of higher-order correlations in pools of neural activity

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  • Montani, Fernando
  • Phoka, Elena
  • Portesi, Mariela
  • Schultz, Simon R.

Abstract

Simultaneous recordings from multiple neural units allow us to investigate the activity of very large neural ensembles. To understand how large ensembles of neurons process sensory information, it is necessary to develop suitable statistical models to describe the response variability of the recorded spike trains. Using the information geometry framework, it is possible to estimate higher-order correlations by assigning one interaction parameter to each degree of correlation, leading to a (2N−1)-dimensional model for a population with N neurons. However, this model suffers greatly from a combinatorial explosion, and the number of parameters to be estimated from the available sample size constitutes the main intractability reason of this approach. To quantify the extent of higher than pairwise spike correlations in pools of multiunit activity, we use an information-geometric approach within the framework of the extended central limit theorem considering all possible contributions from higher-order spike correlations. The identification of a deformation parameter allows us to provide a statistical characterisation of the amount of higher-order correlations in the case of a very large neural ensemble, significantly reducing the number of parameters, avoiding the sampling problem, and inferring the underlying dynamical properties of the network within pools of multiunit neural activity.

Suggested Citation

  • Montani, Fernando & Phoka, Elena & Portesi, Mariela & Schultz, Simon R., 2013. "Statistical modelling of higher-order correlations in pools of neural activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 3066-3086.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:14:p:3066-3086
    DOI: 10.1016/j.physa.2013.03.012
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    References listed on IDEAS

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    1. Elad Schneidman & Michael J. Berry & Ronen Segev & William Bialek, 2006. "Weak pairwise correlations imply strongly correlated network states in a neural population," Nature, Nature, vol. 440(7087), pages 1007-1012, April.
    2. Yasser Roudi & Sheila Nirenberg & Peter E Latham, 2009. "Pairwise Maximum Entropy Models for Studying Large Biological Systems: When They Can Work and When They Can't," PLOS Computational Biology, Public Library of Science, vol. 5(5), pages 1-18, May.
    3. Martı́nez, S & Pennini, F & Plastino, A & Portesi, M, 2004. "q-thermostatistics and the analytical treatment of the ideal Fermi gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 230-248.
    4. Ifije E. Ohiorhenuan & Ferenc Mechler & Keith P. Purpura & Anita M. Schmid & Qin Hu & Jonathan D. Victor, 2010. "Sparse coding and high-order correlations in fine-scale cortical networks," Nature, Nature, vol. 466(7306), pages 617-621, July.
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    Cited by:

    1. Montani, Fernando & Deleglise, Emilia B. & Rosso, Osvaldo A., 2014. "Efficiency characterization of a large neuronal network: A causal information approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 58-70.
    2. Baravalle, Roman & Rosso, Osvaldo A. & Montani, Fernando, 2017. "A path integral approach to the Hodgkin–Huxley model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 986-999.
    3. Jan Humplik & Gašper Tkačik, 2017. "Probabilistic models for neural populations that naturally capture global coupling and criticality," PLOS Computational Biology, Public Library of Science, vol. 13(9), pages 1-26, September.
    4. Montangie, Lisandro & Montani, Fernando, 2017. "Higher-order correlations in common input shapes the output spiking activity of a neural population," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 845-861.
    5. Montangie, Lisandro & Montani, Fernando, 2015. "Quantifying higher-order correlations in a neuronal pool," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 388-400.

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