John Hertz (Nordita)
Ising models form a natural framework for modeling the distribution of multi-neuron spike patterns: Of all models that correctly describe the firing rates and pairwise firing correlations, the Ising model is the one of maximum entropy. The problem at hand here is an inverse one to that we usually encounter. Normally, one has a model with given couplings (Jij) and the task is to compute averages and correlation functions of the variables of the model. Here we are given the averages and correlations and the task is to find the couplings. In the simplest approach to this problem, one considers only the measured firing rates and equal-time pairwise firing correlations and tries to find the Ising model that has these statistics. In our work we have explored and compared a number of methods for doing this, using data from a realistic model network of spiking neurons. Several of these methods work remarkably well. This success is tempered, however, by our second set of findings. Using an information-theoretic measure of the overall quality of fit, we find that, while the Ising model is a good description of the distribution of spike patterns for small populations of neurons (~ 10), it does worse and worse for larger and larger populations (for reasons that are not yet understood). Finally, I will describe some recent work, which extends the Ising approach to describe non-equal-time firing correlations.