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A simple mechanism for higher-order correlations in integrate-and-fire neurons
BMC Neuroscience volume 13, Article number: P45 (2012)
Recent work  shows that common input gives rise to higher-order correlations in the Dichotomized Gaussian neuron model. Here we study a homogeneous population of integrate-and-fire neurons receiving correlated input. Each neuron receives an independent white noise input and all neurons receive a common Gaussian input. To quantify the contributions of higher-order correlations we use a maximum entropy model. The model with interactions up to second order (i.e. pairwise correlations) is known as the Ising model. The Kullbach-Leibler divergence between the Ising model and the model with interactions of all orders allows us to quantitatively describe the presence of higher-order correlations.
We observe from numerical simulations that for low firing rates, the Kullbach-Leibler divergence grows with increasing correlation i.e. strength of the common input (Figure 1A). For population size N=100, the Ising model predicts a vastly different distribution of spike outputs (Figures 1B,C).
For a leaky IF or exponential IF neuron receiving an input signal identical in all trials, and a background noise independent from trial to trial, it is possible to explicitly calculate the linear response function [2, 3]. We use this linear filter to compute instantaneous firing probabilities for the N cells in our setup. This gives us a theoretical basis for our central finding that strong higher-order correlations arise naturally in integrate and fire cells receiving common inputs.
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This work was funded in part by the Burroughs Wellcome Fund Scientific Interfaces Program.
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Leen, D.A., Shea-Brown, E. A simple mechanism for higher-order correlations in integrate-and-fire neurons. BMC Neurosci 13 (Suppl 1), P45 (2012). https://doi.org/10.1186/1471-2202-13-S1-P45
- Firing Rate
- Ising Model
- Neuron Model
- Pairwise Correlation
- Linear Filter