Parameter and coupling estimation in small groups of Izhikevich neurons

Nowadays, experimental techniques allow scientists to have access to large amounts of data. In order to obtain reliable information from the complex systems which produce these data, appropriate analysis tools are needed}. The Kalman filter is a {frequently used} technique to infer, assuming a model of the system, the parameters of the model from uncertain observations. A well-known implementation of the Kalman filter, the Unscented Kalman filter (UKF), was recently shown to be able to infer the connectivity of a set of coupled chaotic oscillators. {I}n this work, we test whether the UKF can also reconstruct the connectivity of {small groups of} coupled neurons when their links are either electrical or chemical {synapses}. {In particular, w}e consider Izhikevich neurons, and aim to infer which neurons influence each other, considering {simulated spike trains as the experimental observations used by the UKF}. First, we {verify} that the UKF can recover the parameters of a single neuron, even when the parameters vary in time. Second, we analyze small neural ensembles and}} demonstrate that the UKF allows inferring the connectivity between the neurons, even for heterogeneous, directed, and {temporally evolving} networks. {Our results show that time-dependent parameter and coupling estimation is possible in this nonlinearly coupled system