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Journal of Computational Neuroscience

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01-10-2011

Fast inference of interactions in assemblies of stochastic integrate-and-fire neurons from spike recordings

Authors: Remi Monasson, Simona Cocco

Published in: Journal of Computational Neuroscience | Issue 2/2011

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Abstract

We present two Bayesian procedures to infer the interactions and external currents in an assembly of stochastic integrate-and-fire neurons from the recording of their spiking activity. The first procedure is based on the exact calculation of the most likely time courses of the neuron membrane potentials conditioned by the recorded spikes, and is exact for a vanishing noise variance and for an instantaneous synaptic integration. The second procedure takes into account the presence of fluctuations around the most likely time courses of the potentials, and can deal with moderate noise levels. The running time of both procedures is proportional to the number S of spikes multiplied by the squared number N of neurons. The algorithms are validated on synthetic data generated by networks with known couplings and currents. We also reanalyze previously published recordings of the activity of the salamander retina (including from 32 to 40 neurons, and from 65,000 to 170,000 spikes). We study the dependence of the inferred interactions on the membrane leaking time; the differences and similarities with the classical cross-correlation analysis are discussed.

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We consider here that the a priori measure over the couplings and currents is flat.

Due to the limited temporal resolution of the measurement two inputs of amplitudes J and J′ can apparently arrive at the same time; if so, we consider, based on models (1) and (2), that a single input of amplitude J + J′ enters the neuron.

This choice is arbitrary; other values, ranging from \(\frac 14\) to 1 have been tried, do not qualitatively affect the results presented later in this article.

Note that the inferred parameters might be less sensitive than the time course of the potential to the noise level σ. The reason is that the corrections to the log-likelihood L ^*, to the lowest order in the noise variance σ ², do not depend on the current and interactions (Appendix D).

Note that the ratio of the time to calculate H ⁽ⁱ⁾ over the time required for the inversion of the Hessian matrix is equal to \(N_{co}\; N^2/N^3 \sim S/N^2\), and is generally much larger than one. The reason is that the number of parameters to be inferred, N, has to be smaller than the number of constraints over the optimal potential, N _co. For the real data analyzed in Section 3.2, we have S/N ² ≃ 64 and 108 for, respectively, Dark and Natural Movie data sets.

When g = 0, changing the value of the current I amounts to changing the time-scale of the evolution of the potential in Eq. (1). Hence, the errors ϵ _s depend on the parameters I, C, σ, V _th through the value of r only (as long as I > 0).

The case of three or a higher number of values for the noise can be handled exactly in the same way.

This situation can not happen in the g = 0 case, where the noise and the noise coefficient coincide.

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Title: Fast inference of interactions in assemblies of stochastic integrate-and-fire neurons from spike recordings
Authors: Remi Monasson
Simona Cocco
Publication date: 01-10-2011
Publisher: Springer US
Published in: Journal of Computational Neuroscience / Issue 2/2011
Print ISSN: 0929-5313
Electronic ISSN: 1573-6873
DOI: https://doi.org/10.1007/s10827-010-0306-8

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