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  Signatures of criticality arise from random subsampling in simple population models

Nonnenmacher, M., Behrens, C., Berens, P., Bethge, M., & Macke, J. (2017). Signatures of criticality arise from random subsampling in simple population models. PLoS Computational Biology, 13(10), 1-23. doi:10.1371/journal.pcbi.1005718.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0000-C2A4-B Version Permalink: http://hdl.handle.net/21.11116/0000-0001-877E-A
Genre: Journal Article

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Nonnenmacher, M1, 2, Author              
Behrens, C, Author
Berens, P, Author              
Bethge, M2, 3, Author              
Macke, JH2, 4, Author              
Affiliations:
1Former Research Group Neural Computation and Behaviour, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_2528699              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497794              
3Research Group Computational Vision and Neuroscience, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497805              
4Center of Advanced European Studies and Research (caesar), Max Planck Society, ou_2173675              

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 Abstract: The rise of large-scale recordings of neuronal activity has fueled the hope to gain new insights into the collective activity of neural ensembles. How can one link the statistics of neural population activity to underlying principles and theories? One attempt to interpret such data builds upon analogies to the behaviour of collective systems in statistical physics. Divergence of the specific heat—a measure of population statistics derived from thermodynamics—has been used to suggest that neural populations are optimized to operate at a “critical point”. However, these findings have been challenged by theoretical studies which have shown that common inputs can lead to diverging specific heat. Here, we connect “signatures of criticality”, and in particular the divergence of specific heat, back to statistics of neural population activity commonly studied in neural coding: firing rates and pairwise correlations. We show that the specific heat diverges whenever the average correlation strength does not depend on population size. This is necessarily true when data with correlations is randomly subsampled during the analysis process, irrespective of the detailed structure or origin of correlations. We also show how the characteristic shape of specific heat capacity curves depends on firing rates and correlations, using both analytically tractable models and numerical simulations of a canonical feed-forward population model. To analyze these simulations, we develop efficient methods for characterizing large-scale neural population activity with maximum entropy models. We find that, consistent with experimental findings, increases in firing rates and correlation directly lead to more pronounced signatures. Thus, previous reports of thermodynamical criticality in neural populations based on the analysis of specific heat can be explained by average firing rates and correlations, and are not indicative of an optimized coding strategy. We conclude that a reliable interpretation of statistical tests for theories of neural coding is possible only in reference to relevant ground-truth models.

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 Dates: 2017-10
 Publication Status: Published online
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 Identifiers: DOI: 10.1371/journal.pcbi.1005718
eDoc: e1005718
BibTex Citekey: NonnenmacherBBBM2017
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Title: PLoS Computational Biology
Source Genre: Journal
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Pages: - Volume / Issue: 13 (10) Sequence Number: - Start / End Page: 1 - 23 Identifier: -