To what should you compare the amount of information encoded by a spike train?
Once we have estimated the amount of information a spike train encodes about a stimulus,
(whether by reconstruction or other means), we need to compare the quality
of the reconstruction against some standard. Otherwise, we can just
say a cell transmits X bits per second about some stimulus, but we
have no idea what this means. Is X a lot of information, or very
litte?
Compare it to the stimulus
The simplest measure is what fraction of the stimulus is
reconstructed. The entropy of the stimulus is a strict upper
bound on the information you can reconstruct: it is impossible to
reconstruct more information about a stimulus than was in the
stimulus to begin with. However, this measure can be misleading,
because a neuron could transmit a huge amount of information and still
only capture a tiny fraction of the stimulus entropy, if the
stimulus entropy is very large. Moreover this measure is going to
depend on how the experimenter describes the stimulus. The more
detailed our definition of the stimulus, the smaller fraction of it
the neuron will be said to capture.
Obviously, there are aspects of visual stimuli that are
too small or too fast to be resolved, and
for that matter there are parts of the stimulus that is not falling on the
retina at all, none of which we expect a neuron to encode.
So if there is a lot of such information in the
stimulus as we define it, the neuron will seem to do very poorly if
its reconstruction is measured as a fraction of all the information in
the stimulus. But this doesn't mean that the answer
is to construct only stimuli that have low entropy. After all, the real
world in which our sensory systems must function is full of things
that are too small or too fast to see.
This isn't necessarily a problem, because it is possible to
investigate which aspects of a stimulus are being encoded well
and which aspects poorly, or to quantify the coding of only one
aspect of the stimulus at a time. In this way we can define
experimentally where these boundaries fall, by observing what the cell
can and can't encode. However, it is probably not the case that all
aspects of the stimulus are encoded independently. So it is also a
good idea to construct stimuli for comparison, that omit aspects such
as temporal frequencies or spatial locations that we think are not
being encoded.
All this leaves us with the question of what the transmitted information
rate should be compared to. How will we know if we have decoded all
the information that is encoded in the spike train, if we
concede in advance that we don't expect to reconstruct all the
information that's in the stimulus?
Compare it to the discriminations the animal can make
Ultimately we want to relate the results to what the animal actually
can see. If in a psychophysical test, the animal can make certain
visual discriminations, then the information about that stimulus
difference has to be encoded neurally, at least somewhere in
the animal's brain. And when we are dealing with the very early stages
of visual processing, we have a good idea which neurons those are. So
the animal's perceptual discrimination places a strict lower
bound on the information in the spike trains. (In connection with
coding by retinal ganglion cells in the salamander, there is a bit
known about the visual behavior of
salamanders).
Compare it to the spike train's capacity
An alternative measure is the coding
efficiency: the amount of transmitted information about the
stimulus, as a fraction of the total entropy of the spike train. While
you need to make some assumptions to estimate the spike train entropy,
as well as the assumptions involved in estimating the transmitted information,
the coding efficiency can be estimated in a way that it is a strict lower bound.
Coding efficiency is a very useful measure because, if we can extract as much
information about the stimulus as there is entropy in the spike train,
we know we have all the information we can ever get from the spike
train. In other words, the spike train entropy places another strict
upper bound on the information the neuron can transmit.
copyright 1995 Pam Reinagel
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