Biomedical Engineering Reference
In-Depth Information
Figure 13.1
Effect of stimulus-independent patterns on neural coding. Each panel sketches hypo-
thetical distributions of responses to three different stimuli. The response variables
can be considered either to be different bins within the same cell or bins across
different cells. Each ellipse indicates the set of responses elicited by a given stimu-
lus. In each of these examples, signal correlations are positive whereas the sign of
noise correlation differs. In the middle panel, noise correlation is zero, and stimulus-
independent patterns exert no effect on the total information. When noise corre-
lation is positive (left panel), responses to the stimuli are less discriminable and
stimulus-independent spike patterns cause a redundant effect. When noise correla-
tion is negative (right panel), responses are more discriminable and the contribution
of stimulus-independent spike patterns is thus synergistic. In general, if signal and
noise correlations have the same sign, the effect of stimulus-independent patterns is
redundant, if they have opposite signs, it is synergistic. Reproduced with permission
from [25].
13.2.4
Generalised series expansion
Is the breakdown of mutual information into individual spike terms and correlation-
dependent terms a general property of neural encoders or a peculiarity of systems
firing few spikes? Pola et al. [30] have recently investigated this issue, and have
proved that the decomposition is completely general. The break-down of mutual in-
formation into
I
t
,
I
ttb
and
I
ttc
terms generalises in a natural way to the exact case
of Equation (13.1) Moreover, each of the terms in the exact breakdown has a very
similar mathematical expression to their analogues in the second order series expan-
sion. The main difference is that the exact components are expressed in terms of an
interaction coefficient that takes all moments of the spiking response into account,
not just pairwise correlations. Of course, the exact decomposition has the same sam-
pling characteristics as Equation (13.1), so the second order series expansion is often
more convenient to use in practice.
I
tta
,
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