  Simultaneous recordings from multiple neural units allow us to investigate
the activity of very large neural ensembles. To understand how large ensembles
of neurons process sensory information, it is necessary to develop suitable
statistical models to describe the response variability of the recorded spike
trains. Using the information geometry framework, it is possible to estimate
higher-order correlations by assigning one interaction parameter to each degree
of correlation, leading to a $(2^N-1)$-dimensional model for a population with
$N$ neurons. However, this model suffers greatly from a combinatorial
explosion, and the number of parameters to be estimated from the available
sample size constitutes the main intractability reason of this approach. To
quantify the extent of higher than pairwise spike correlations in pools of
multiunit activity, we use an information-geometric approach within the
framework of the extended central limit theorem considering all possible
contributions from high-order spike correlations. The identification of a
deformation parameter allows us to provide a statistical characterisation of
the amount of high-order correlations in the case of a very large neural
ensemble, significantly reducing the number of parameters, avoiding the
sampling problem, and inferring the underlying dynamical properties of the
network within pools of multiunit neural activity.
