Volume 12 Supplement 1
Neural network reconstruction using kinetic Ising models with memory
© Witoelar and Roudi; licensee BioMed Central Ltd. 2011
Published: 18 July 2011
Ising models with simple Markov chain kinetics have been recently introduced as a tool for inferring asymmetric interactions in neuronal networks . In such an approach, one discretizes time and uses the spike pattern at time step t to predict the pattern at time step t+1 and infer the effective interaction between neurons J(i,j) which influences these dynamics. It is however a priori hard to justify that the effect of spikes in only one time bin from the temporal discretization determines the future state of the system. What happens if we use shorter/longer time bins than the characteristic time steps of the network? How do the inferred couplings change if we allow for interactions with memory of multiple past time steps? To answer these questions, we extend the kinetic Ising approach to higher-order Markov chains by introducing time-delayed interactions using (1) a set of couplings derived from scaling the original J(i,j) and (2) an auxiliary set of couplings K(i,j). A model of this sort is closely related to the Generalized Linear Model and its simplicity allows for detailed analysis of the model parameters.
The authors would like to thank John Hertz for providing the key simulations for the cortical column .
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