NORDITA, Roslagstullsbacken 23, 10691 Stockholm, Sweden

Dept of Mathematical Statistics, Stockholm University, 10691 Stockholm, Sweden

The Niels Bohr Institute, Copenhagen University, 2100 Copenhagen, Denmark

The simplest model for describing multi-neuron spike statistics is the pairwise Ising model _{i}(^{-1}exp{h's+s'Js} for the spike patterns with the same means and pair correlations as the data, using Boltzmann learning, which is in principle exact. The elements _{ij}, of the matrix J can be considered to be functional couplings. However, Boltzmann learning is prohibitively time-consuming for large networks. Here, we compare the results from five fast approximate methods for finding the couplings with those from Boltzmann learning.

We used data from a simulated network of spiking neurons operating in a balanced state of asynchronous firing with a mean rate of ~10 Hz for excitatory neurons. Employing a bin size of 10 ms, we performed Boltzmann learning to fit Ising models for populations of size ^{2}, treating the Boltzmann couplings as the true ones. We found, as shown in figure

(a) ^{2 }and (b) RMS error for various approximate methods

**(a) R ^{2 }and (b) RMS error for various approximate methods**. Green (dashed dotted), naive mean-field; Purple (dashed double-dotted) low-rate, small