A Case Study of Population Coding: Stimulus Localisation in the Barrel Cortex - Computational Neuroscience: A Comprehensive Approach - page 386

lus time. There are two potential solutions to this problem. (1) Since the collection
of vibrissal sensory data under natural conditions is an active process initiated by
a motor command, the sensory system could use the output from the motor system
as an estimate of stimulus time. However, this motor efference signal acting alone
would probably not possess sufficient temporal precision to permit the representation
of information by first spike times. (2) The sensory system could use the relative
timing between spikes in the neuronal population [12, 40]. When whisker D2 is de-
flected, many neurons within its barrel-column fire spikes within a few milliseconds
of each other. Thus a simple way that the rat might decode the deflection of this
whisker would be to detect the occurrence of large-scale simultaneous firing within
the barrel-column. We showed that this barrel activation algorithm can lead to very
good discrimination of whether or not a given whisker was deflected, based purely
on the relative spike times of neurons within the column (Panzeri, Petroni, Diamond
& Petersen, in preparation). The critical feature of the decoding algorithm is that
the simultaneous activity characteristic of whisker deflection can only be detected if
spike times are registered to high temporal precision. Thus, in order to decode the
stimulus in the absence of information about when the stimulus occurred, precise
spike timing is a crucial aspect of the neural code. Spike count codes do not permit
simultaneous firing events to be accurately identified and hence are extremely unin-
formative. The advantage for spike timing codes over spike count codes is even more
marked than in the previous analyses that assumed knowledge of stimulus onset.

13.5.2 Role of cross-correlations in population codes

There have been a number of previous reports that correlated spike patterns across
different neurons play an important part in neural population coding [2, 6, 11, 32,
39, 41]. The strategy in all these studies was to demonstrate the existence of some
stimulus-linked cross-correlation structure that could not be accounted for by the
null hypothesis of independent firing. In the simplest case, the cross-correlogram
was shown to differ significantly from its shift predictor [11]. In other cases, more
sophisticated statistics were deemed necessary (e.g., [13]), but the logic was similar.
The importance of these studies is that they showed that cross-correlated spike
patterns might play a role in neural coding. However, they did not quantify the infor-
mation in spike patterns and compare it to that available in individual spikes. This is
important, since comparison of cross-correlogram to its shift predictor shows neither
how much the cross-correlations contribute to coding, nor whether any contribution
is additive or redundant with the individual spike contribution. The simplest way
that one might seek to quantify the role of spike patterns is to estimate the infor-
mation conveyed by a given neuronal population and to repeat the calculation with
trial-shuffled responses. If shuffling significantly reduces the information, cross-
correlated spike patterns play an important part in the population code. The problem
with this method is that the converse result, where shuffling has no effect, is ambigu-
ous.
The series expansion framework is helpful for clarifying the ambiguity. The effect
of shuffling is to set all correlations equal to the values expected from statistical