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  The effect of common input on higher-order correlations and entropy in neural populations

Macke, J., Opper, M., & Bethge, M. (2011). The effect of common input on higher-order correlations and entropy in neural populations. Poster presented at Computational and Systems Neuroscience Meeting (COSYNE 2011), Salt Lake City, UT, USA.

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Macke, JH1, 2, Author           
Opper, M, Author
Bethge, M1, 2, Author           
Affiliations:
1Research Group Computational Vision and Neuroscience, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497805              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: Finding models for capturing the statistical structure of multi-neuron firing patterns is a major challenge in sensory neuroscience. Recently, Maximum Entropy (MaxEnt) models have become popular tools for studying neural population recordings [4, 3]. These studies have found that small populations in retinal, but not in local cortical circuits, are well described by models based on pairwise correlations. It has also been found that entropy in small populations grows sublinearly [4], that sparsity in the population code is related to correlations [3], and it has been conjectured that neural populations might be at a ícritical pointí. While there have been many empirical studies using MaxEnt models, there has arguably been a lack of analytical studies that might explain the diversity of their findings. In particular, theoretical models would be of great importance for investigating their implications for large populations. Here, we study these questions in a simple, tractable population model of neurons receiving Gaussian inputs [1, 2]. Although the Gaussian input has maximal entropy, the spiking-nonlinearities yield non-trivial higher-order correlations (íhocsí). We find that the magnitude of hocs is strongly modulated by pairwise correlations, in a manner which is consistent with neural recordings. In addition, we show that the entropy in this model grows sublinearly for small, but linearly for large populations. We characterize how the magnitude of hocs grows with population size. Finally, we find that the hocs in this model lead to a diverging specific heat, and therefore, that any such model appears to be at a critical point. We conclude that common input might provide a mechanistic explanation for a wide range of recent empirical observations. [1] SI Amari, H Nakahara, S Wu, Y Sakai. Neural Comput, 2003. [2] JH Macke, M Opper, M Bethge. ArXiv, 2010. [3] IE Ohiorhenuan, et. al Nature, 2010. [4] E Schneidman, MJ Berry, R Segev, W Bialek. Nature, 2006.

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 Dates: 2011-02
 Publication Status: Issued
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 Identifiers: URI: http://www.cosyne.org/c/index.php?title=Cosyne_11_posters3
BibTex Citekey: MackeOB2011_2
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Title: Computational and Systems Neuroscience Meeting (COSYNE 2011)
Place of Event: Salt Lake City, UT, USA
Start-/End Date: 2011-02-24 - 2011-02-27

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Title: Computational and Systems Neuroscience Meeting (COSYNE 2011)
Source Genre: Proceedings
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Pages: - Volume / Issue: - Sequence Number: III-68 Start / End Page: - Identifier: -