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Signatures of criticality arise from random subsampling in simple population models.

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.

SUBMITTER: Nonnenmacher M

PROVIDER: S-EPMC5640238 | biostudies-literature | 2017 Oct

REPOSITORIES: biostudies-literature

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Signatures of criticality arise from random subsampling in simple population models.

Nonnenmacher Marcel M Behrens Christian C Berens Philipp P Bethge Matthias M Macke Jakob H JH

PLoS computational biology 20171003 10

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 ...[more]

PMID: 28972970

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Project description:Identifying relevant signatures for clinical patient outcome is a fundamental task in high-throughput studies. Signatures, composed of features such as mRNAs, miRNAs, SNPs or other molecular variables, are often non-overlapping, even though they have been identified from similar experiments considering samples with the same type of disease. The lack of a consensus is mostly due to the fact that sample sizes are far smaller than the numbers of candidate features to be considered, and therefore signature selection suffers from large variation. We propose a robust signature selection method that enhances the selection stability of penalized regression algorithms for predicting survival risk. Our method is based on an aggregation of multiple, possibly unstable, signatures obtained with the preconditioned lasso algorithm applied to random (internal) subsamples of a given cohort data, where the aggregated signature is shrunken by a simple thresholding strategy. The resulting method, RS-PL, is conceptually simple and easy to apply, relying on parameters automatically tuned by cross validation. Robust signature selection using RS-PL operates within an (external) subsampling framework to estimate the selection probabilities of features in multiple trials of RS-PL. These probabilities are used for identifying reliable features to be included in a signature. Our method was evaluated on microarray data sets from neuroblastoma, lung adenocarcinoma, and breast cancer patients, extracting robust and relevant signatures for predicting survival risk. Signatures obtained by our method achieved high prediction performance and robustness, consistently over the three data sets. Genes with high selection probability in our robust signatures have been reported as cancer-relevant. The ordering of predictor coefficients associated with signatures was well-preserved across multiple trials of RS-PL, demonstrating the capability of our method for identifying a transferable consensus signature. The software is available as an R package rsig at CRAN (http://cran.r-project.org).

Dataset Information

Signatures of criticality arise from random subsampling in simple population models.

Publications

Signatures of criticality arise from random subsampling in simple population models.

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