Spike Train Statistics from Empirical Facts to Theory: The Case of the Retina - Modeling in Computational Biology and Biomedicine - page 287

8.6.1 Gibbs Distributions and the Neural Code

Although interesting results have come out from the Gibbs analysis of retina spike
trains, the link between spike statistics and their modeling with Gibbs distribution
on one hand, and the way how a visual scene is encoded by G cells spikes emission
on the other hand, remains rather tight. Defining a priori a Gibbs potential from a
set of constraints superimposes upon spike trains a causal structure, purely spatial
or spatio-temporal, associated with “effective interactions”, e.g., the coefficients
β i 1 ,n 1 ,...,i l ,n l ( n ) in the polynomial expansion ( 8.29 ). What do these interactions
teach us about the neural code? How are they related to a visual scene? Given
a Gibbs distribution that fits well retina spike statistics is it possible to infer
information about the visual scene perceived by this retina? Is it possible to build
retina “decoders” from Gibbs statistics? If yes, does a “correlated decoder”, with
correlated G cells perform better than a “rate decoder” where G cells outputs are
independent? Although interesting advances has been done on these questions (see,
e.g., [ 59 ]) we believe that they are far from being solved, and that they constitute a
challenge for the next years.
A related question concerns the concept of receptive field. We have presented in
Sect. 8.2.1.2 the classical notion of RF which is associated with an isolated G cell,
independently of what the neighboring G cells are perceiving. Additionally, e.g.,
Fig. 8.3 , describes well the response of a G cell in terms of firing rates without need
of considering higher order statistics. It is a current approach to model RF as filters,
typically linear, followed by a non-linear correction [ 46 ]. How does the paradigm
of linear-non linear filter connects with the paradigm of Gibbs distribution? Can
we infer the shape of the RF filter from the Gibbs potential? Classical RF filters
are based on firing rates for individual G cells; on the opposite Gibbs statistics
deals with spike events (monomials) for collective behaviors. Are these two visions
coherent? Is there a link e.g., between effective interactions and RF?
To our best knowledge those questions have not been resolved. On the theoretical
side they can be addressed in the context of Gibbs distributions. Given a Gibbs
potential modeling retina response it could be possible to compute the linear
response to a stimulus considered as a weak perturbation of dynamics. This linear
response is characterized by a convolution kernel which could be compared to the
models of receptive field filters used in the literature. This work remains still to be
done though.

8.6.2 Experimental Limits

To our opinion the current experimental set up is faced with the following limits.

￿ Natural stimulus must reproduce ecological environment, where animals lives,

including the way how animals explore it, how they are in action, moving their