Spike Train Statistics from Empirical Facts to Theory: The Case of the Retina - Modeling in Computational Biology and Biomedicine - page 280

able to reproduce spike trains of populations of neurons in the retina submitted
to natural images. The network of these effective interactions is organized in a
hierarchical and modular manner so that large network models can be constructed
from smaller sub-networks in a modular fashion. Thus, by a suitable scaling
of parameters, one could be able to extrapolate the Gibbs potential of a small
population of neurons to large populations. Moreover, in some sense, this effective
network “underlies the code”, from the terminology of the authors. This means
that the spike generation, as a response to a stimulus (an image), results from a
dynamical process which can be summarized by the Gibbs potential of the model.
This work raises however several questions. First, the potential considered by
the authors is memory-less. No time dependent process takes place in the potential.
In some sense, the time-causality expected in a neural network is hidden by the
effective potential. Another critical aspect is the interpretation of the effective
interaction. It is stated in [ 18 ] that “although the pairwise interactions in the
model do not necessarily reflect a physical interaction between cells, they give a
unique functional interaction map between the neurons in the network and represent
statistical dependence between pairs of units.” But, if they do not represent physical
interactions (synapses), what do these functional interactions correspond to? To our
knowledge this question has not been yet resolved.

8.4.4 Spike Train Analysis in a Neural Network Model

The maximal entropy principle relies on the assumption of stationarity as well
as an a priori and somewhat ad hoc choice of observables. This choice severely
constrains the form of the statistical model and the information that can be extracted
about the underlying neuronal network producing the spike. In particular, the
choice of observables determines the transition probabilities and implicitly fixes
a causal structure to analyze spike events. Especially, memory-less models focuses
on synchronous events, hiding somewhat temporal causality.
Obviously, it is extremely difficult to obtain a clear cut characterization of spike
trains statistics from experimental data, taking into account the experimental set
up, spike acquisition, spike sorting, but also the relatively small size of spike trains
(typically, in retina experiments T< 10

5 − 6 ). So, a natural question is: “Can one
have a reasonable idea of what spike statistics could be in neural network model ”?
The answer is “yes”.
In neural networks spikes result from the collective and non linear dynamics of
neurons coupled by synapses (electrical or chemical) and submitted to “external”
stimuli. As a consequence statistics of spike train is closely related to this network
structure (neurons and synapses characteristics) and to the stimulus. The idea
is to show here the relationships between the neural network structure and the
form of transition probabilities in an explicit example, a conductance-based neural