Reconstruction of a neural network from a time series of firing rates

Randomly coupled neural fields demonstrate irregular variation of firing rates, if the coupling is strong enough, as has been shown by Sompolinsky et al. [Phys. Rev. Lett. 61, 259 (1988)]PRLTAO0031-900710.1103/PhysRevLett.61.259. We present a method for reconstruction of the coupling matrix from a time series of irregular firing rates. The approach is based on the particular property of the nonlinearity in the coupling, as the latter is determined by a sigmoidal gain function. We demonstrate that for a large enough data set and a small measurement noise, the method gives an accurate estimation of the coupling matrix and of other parameters of the system, including the gain function.