Given a set of means and pairwise correlations
between binary spin variables, the maximum entropy Hamiltonian
is that of the Ising model. The inverse Ising problem is to
find the parameters of this Hamiltonian. In the first part of this
talk, we describe exact and approximate methods for finding the
couplings of an Ising model fitted to means and pairwise correlations.
Applying these methods to means and correlations measured from
synthetic data generated by a simulated cortical network, we study
the quality of various approximations as compared to the exact solution.
In the second part, again using synthetic neural data, we compare how
good the best fitted Ising model characterizes the statistics of neural spike
patterns. We show that for small systems and/or low mean spike
probability, the Ising model is a good model for multi-neuron
spiking patterns, but as the population size grows, its quality decays.