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Higher-order correlations in common input shapes the output spiking activity of a neural population

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  • Montangie, Lisandro
  • Montani, Fernando

Abstract

Recent neurophysiological experiments suggest that populations of neurons use a computational scheme in which spike timing is regulated by common non-Gaussian inputs across neurons. The presence of beyond-pairwise correlations in the neuronal inputs and the spiking outputs following a non-Gaussian statistics elicits the need of developing a new theoretical framework taking into account the complexity of synchronous activity patterns. To this end, we quantify the amount of higher-order correlations in the common neuronal inputs and outputs of a population of neurons. We provide a novel formalism, of easy numerical implementation, that can capture the subtle changes of the inputs heterogeneities. Within our approach, correlations across neurons arise from q-Gaussian inputs into threshold neurons and higher-order correlations in the spiking outputs activity are quantified by the parameter q. We present an exhaustive analysis of how input statistics are transformed in this threshold process into output statistics, and we show under which conditions higher-order correlations can lead to either bigger or smaller number of synchronized spikes in the neural population outputs.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:471:y:2017:i:c:p:845-861
    DOI: 10.1016/j.physa.2016.12.002
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    References listed on IDEAS

    as
    1. 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.
    2. Hideaki Shimazaki & Shun-ichi Amari & Emery N Brown & Sonja Grün, 2012. "State-Space Analysis of Time-Varying Higher-Order Spike Correlation for Multiple Neural Spike Train Data," PLOS Computational Biology, Public Library of Science, vol. 8(3), pages 1-27, March.
    3. 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.
    4. 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.
    5. D. R. Cox, 2002. "On some models for multivariate binary variables parallel in complexity with the multivariate Gaussian distribution," Biometrika, Biometrika Trust, vol. 89(2), pages 462-469, June.
    6. 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.
    7. 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.
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    Cited by:

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    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.

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