  We extend previous mean-field approaches for non-equilibrium neural network
models to estimate correlations in the system. This offers a powerful tool for
approximating the system dynamics as well as a fast method to infer network
parameters from observations. We develop our method in an asymmetric kinetic
Ising model and test its performance on 1) synthetic data generated by an
asymmetric version of the Sherrington Kirkpatric model and 2) recordings of in
vitro neuron spiking activity from the mouse somatosensory cortex. We find that
our mean-field method outperforms previous ones in estimating networks
correlations and successfully reconstructs network dynamics from data near a
phase transition showing large fluctuations.
