Inference in neural networks using conditional mean-field methods

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.