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From Stochastic Nonlinear Integrate-and-Fire to Generalized Linear Models
Skander Mensi · Richard Naud · Wulfram Gerstner

Mon Dec 12 10:00 AM -- 02:59 PM (PST) @

Variability in single neuron models is typically implemented either by a stochastic Leaky-Integrate-and-Fire model or by a model of the Generalized Linear Model (GLM) family. We use analytical and numerical methods to relate state-of-the-art models from both schools of thought. First we find the analytical expressions relating the subthreshold voltage from the Adaptive Exponential Integrate-and-Fire model (AdEx) to the Spike-Response Model with escape noise (SRM as an example of a GLM). Then we calculate numerically the link-function that provides the firing probability given a deterministic membrane potential. We find a mathematical expression for this link-function and test the ability of the GLM to predict the firing probability of a neuron receiving complex stimulation. Comparing the prediction performance of various link-functions, we find that a GLM with an exponential link-function provides an excellent approximation to the Adaptive Exponential Integrate-and-Fire with colored-noise input. These results help to understand the relationship between the different approaches to stochastic neuron models.

Author Information

Skander Mensi (Brain-Mind Institute)
Richard Naud (Ecole Polytechnique Federale de Lausanne)
Wulfram Gerstner (EPFL)

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