Reconstruction of connectivity in sparse neural networks from spike train covariances
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1
Albert-Ludwig University, Faculty of Biology, Germany
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2
Bernstein Center Freiburg, Germany
The inference of causation from correlation is in general highly problematic. Similarly, it is difficult to infer the existence of physical synaptic connections between neurons from correlations in their activity. Covariances in neural spike trains have been the subject of intense research, both experimentally and theoretically. Linear models present a direct way to characterize the influence of recurrent connections on covariances in a resting state of asynchronous activity. The effect of direct connections is then described by a matrix of linear coupling kernels. However, as indirect connections also give rise to covariances, the inverse problem of inferring network structure from covariances can generally not be solved unambiguously.
Here we study to which degree this ambiguity can be resolved if the sparseness of neural networks is taken into account. To reconstruct a sparse network, we determine the minimal network of linear couplings consistent with measured covariances by minimizing the L1 -norm of the coupling matrix under appropriate constraints. Counterintuively, after stochastic optimization of the coupling matrix, the resulting estimate of the underlying network is directed, even if only a symmetric matrix of count covariances is known.
The performance of the method is best if connections are neither exceedingly sparse nor dense, and it is easily applicable for networks of a few hundred nodes. Time dependent coupling kernels can be obtained if the full matrix of covariance functions is known, as is demonstrated from simulated spike train data.
Acknowledgements
This work was supported by the German Research Foundation (CRC 780, subproject C4) and by the German Federal Ministry of Education and Research (BMBF grant 01GQ0420 to BCCN Freiburg).
Keywords:
correlations,
integrate-and-fire neuron,
linear model,
network estimation
Conference:
Bernstein Conference 2012, Munich, Germany, 12 Sep - 14 Sep, 2012.
Presentation Type:
Poster
Topic:
Other
Citation:
Pernice
V and
Rotter
S
(2012). Reconstruction of connectivity in sparse neural networks from spike train covariances
.
Front. Comput. Neurosci.
Conference Abstract:
Bernstein Conference 2012.
doi: 10.3389/conf.fncom.2012.55.00229
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Received:
18 Sep 2012;
Published Online:
12 Sep 2012.
*
Correspondence:
Mr. Volker Pernice, Albert-Ludwig University, Faculty of Biology, Freiburg, Germany, volker.pernice@lps.ens.fr