IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v471y2017icp845-861.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437116309736
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2016.12.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yin, Likang & Deng, Yong, 2018. "Measuring transferring similarity via local information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 498(C), pages 102-115.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. 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.
    3. 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.
    4. Christian Donner & Klaus Obermayer & Hideaki Shimazaki, 2017. "Approximate Inference for Time-Varying Interactions and Macroscopic Dynamics of Neural Populations," PLOS Computational Biology, Public Library of Science, vol. 13(1), pages 1-27, January.
    5. 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.
    6. 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.
    7. Einat Granot-Atedgi & Gašper Tkačik & Ronen Segev & Elad Schneidman, 2013. "Stimulus-dependent Maximum Entropy Models of Neural Population Codes," PLOS Computational Biology, Public Library of Science, vol. 9(3), pages 1-14, March.
    8. Arno Onken & Valentin Dragoi & Klaus Obermayer, 2012. "A Maximum Entropy Test for Evaluating Higher-Order Correlations in Spike Counts," PLOS Computational Biology, Public Library of Science, vol. 8(6), pages 1-12, June.
    9. Cofré, Rodrigo & Cessac, Bruno, 2013. "Dynamics and spike trains statistics in conductance-based integrate-and-fire neural networks with chemical and electric synapses," Chaos, Solitons & Fractals, Elsevier, vol. 50(C), pages 13-31.
    10. Stojan Jovanović & Stefan Rotter, 2016. "Interplay between Graph Topology and Correlations of Third Order in Spiking Neuronal Networks," PLOS Computational Biology, Public Library of Science, vol. 12(6), pages 1-28, June.
    11. 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.
    12. Battey, H.S. & Cox, D.R., 2022. "Some aspects of non-standard multivariate analysis," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    13. Volker Pernice & Benjamin Staude & Stefano Cardanobile & Stefan Rotter, 2011. "How Structure Determines Correlations in Neuronal Networks," PLOS Computational Biology, Public Library of Science, vol. 7(5), pages 1-14, May.
    14. Miśkiewicz, Janusz, 2016. "Improving quality of sample entropy estimation for continuous distribution probability functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 473-485.
    15. Urs Köster & Jascha Sohl-Dickstein & Charles M Gray & Bruno A Olshausen, 2014. "Modeling Higher-Order Correlations within Cortical Microcolumns," PLOS Computational Biology, Public Library of Science, vol. 10(7), pages 1-12, July.
    16. Porta Mana, PierGianLuca & Rostami, Vahid & Torre, Emiliano & Roudi, Yasser, 2018. "Maximum-entropy and representative samples of neuronal activity: a dilemma," OSF Preprints uz29n, Center for Open Science.
    17. Dimitri Yatsenko & Krešimir Josić & Alexander S Ecker & Emmanouil Froudarakis & R James Cotton & Andreas S Tolias, 2015. "Improved Estimation and Interpretation of Correlations in Neural Circuits," PLOS Computational Biology, Public Library of Science, vol. 11(3), pages 1-28, March.
    18. Baravalle, Roman & Rosso, Osvaldo A. & Montani, Fernando, 2018. "Discriminating imagined and non-imagined tasks in the motor cortex area: Entropy-complexity plane with a wavelet decomposition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 27-39.
    19. Forcina, A. & Dardanoni, V., 2008. "Regression models for multivariate ordered responses via the Plackett distribution," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2472-2478, November.
    20. Andrea K Barreiro & Shree Hari Gautam & Woodrow L Shew & Cheng Ly, 2017. "A theoretical framework for analyzing coupled neuronal networks: Application to the olfactory system," PLOS Computational Biology, Public Library of Science, vol. 13(10), pages 1-37, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:471:y:2017:i:c:p:845-861. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.