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Spike train analysis and Gibbs distributions

Abstract

Spikes in sensory neurons are conveyed collectively to the cortex using correlated binary patterns (in space and time) which constitute “the neural code”. Since patterns occur irregularly it is appropriate to characterize them using probabilistic descriptions or statistical models. Two major approaches attempt to characterize the spike train statistics: The Maximum Entropy Principle (MaxEnt) and Neuronal Network modeling (N.N). Remarkably, both approaches are related via the concept of Gibbs distributions. MaxEnt models are restricted to time-invariant Gibbs distributions , vi the underlying assumption of stationarity, but this concept extends to non-stationary statistics (not defined via entropy), allowing to handle as well statistics of N.N models and GLM with non-stationary dynamics. We show in this poster that, stationary N.N, GLMmodels and MaxEnt models are equivalent via an explicit mapping. This allows us, in particular, to interpret the so-called "effective interactions" of MaxEnt models in terms of “real connections” models.
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Dates and versions

hal-01378001 , version 1 (08-10-2016)

Identifiers

  • HAL Id : hal-01378001 , version 1

Cite

Rodrigo Cofre, Bruno Cessac. Spike train analysis and Gibbs distributions. Bernstein Conference 2016, Sep 2016, Berlin, Germany. ⟨hal-01378001⟩
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