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Testing Algorithms for Extracting Functional Connectivity from Spike Data

Tyrcha, Joanna, (författare)
Stockholms universitet, Matematiska institutionen, Matematisk statistik
Hertz, John (författare)
Stockholms universitet Naturvetenskapliga fakulteten. Matematiska institutionen. (creator_code:org_t)
Ingår i: 1st INCF Congress of Neuroinformatics: Databasing and Modeling the Brain.
  • Konferensbidrag (populärvet., debatt m.m.)
Abstract Ämnesord
  • We can learn something about how large neuronal networks function from models of their spike pattern distributions constructed from data. We do this using the approach introduced by Schneidman et al [1], modeling this distribution by an Ising model: P[S] = Z-1exp(ΣJijSiSj + ΣihiSi). In the work reported here, we explore the accuracy of two algorithms for extracting the model parameters Jij and hi by testing them on data generated by networks in which these parameters are known.Both algorithms use, as input, the firing rates and mutual correlations of the neurons in the network. The first algorithm is straightforward Boltzmann learning. It will yield the parameters correctly if the input statistics are known exactly,but it may be very slow to converge. The second, very fast, algorithm [2] is based on inversion of the Thouless-Anderson-Palmer equations from spin glass theory. It is derived from a small-Jij expansion, but it is in principle correct for all Jij when the network is infinitely large and densely connected.In practice, however, the rates and correlations used as inputs to the algorithms are estimates based on a finite number of measurements. Therefore, there will be errors in the extracted model parameters. Errors will also occur if the data are incomplete, i.e., if the rates and correlations are not measured for all neurons or all pairs. This case is highly relevant to the experimental situation, since in practice it is only possible to record from a small fraction of the neurons in a network.Two particular kinds of error statistics are of special interest: variances of the differences between true and extracted parameters, and variances of the differences between parameters extracted for two independent sets of training data. We study the relation between the two, since the first is what we are interested in but only the second can be computed in the realistic situation, where we do not know the parameters a priori. We also examine the variance of the difference between the true and extracted correlations.Finally, we apply the algorithms to the data of Schneidman et al from salamander retinal ganglion neurons.References--------------------------------------------------------------------------------1. E Schneidman et al, Nature 440 1007-1012 (2006); G Tkacik et al, arXiv:q-bio.NC/0611072 (2006)2. T Tanaka, Phys Rev E 58 2302-2310 (1998); H J Kappen and F B Rodriguez, Neural Comp 10 1137-1156 (1998)


Natural Sciences Biological Sciences Bioinformatics and Systems Biology
Naturvetenskap Biologiska vetenskaper Bioinformatik och systembiologi
Medical and Health Sciences Basic Medicine Neurosciences
Medicin och hälsovetenskap Medicinska grundvetenskaper Neurovetenskaper
Natural Sciences Mathematics Probability Theory and Statistics
Naturvetenskap Matematik Sannolikhetsteori och statistik
NATURAL SCIENCES Biology Other biology Bioinformatics
NATURVETENSKAP Biologi Övrig biologi Bioinformatik
Cell and molecular biology Neurobiology
Cell- och molekylärbiologi Neurobiologi
MATHEMATICS Applied mathematics Mathematical statistics
MATEMATIK Tillämpad matematik Matematisk statistik

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Tyrcha, Joanna
Hertz, John
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Stockholms universitet

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