Stimulus Ensembles

What is the relevant stimulus ensemble?

Information theoretical analysis of spike trains is designed to reveal how well a given set of stimuli can be discriminated from one another on the basis of the neural responses they evoke. It is a highly contextual measure that depends on what the stimuli are, and their relative likelihoods. It is a perfectly objective measure, but one should realize that it doesn't make sense to say a neuron encodes so-and-so many bits per second (as such). The question would be, bits about what? Since we will come up with a different answer for the information transfer rate of a neuron depending on the stimulus ensemble we use, what is the relevant stimulus ensemble?

(The discussion below is written in the context of neural coding of visual information by the retina but can readily be generalized to other examples.)

White Noise Flicker

The random flicker (white noise) visual stimulus asks of the retina that it encode any pattern of light that could possibly fall on it. Since the stimulus is unique and random, the retina has nothing to go on but the light it actually detects. One should realize that although the white noise stimulus is random, it is still well-defined. We will measure the same Information for any white noise stimulus with these statistics, although we may measure a different Information for a different stimulus ensemble.

Natural Scene Ensembles

But what if the visual system didn't evolve to discriminate every possible image, but instead (as is more likely) evolved to allow the animal to discriminate differences among the stimuli actually encountered by that species in its natural environment. Does the visual system exploit the fact that some visual stimuli are much more likely than others? To challenge our hypothesis that the retina is a perfectly generalized detector, we can measure the statistics of such natural scenes, and construct a more restricted stimulus ensemble that reflects the animal's environment. Or we can just use stimuli recorded from the actual natural environment. If we discover that the neuronal system transmits more Information about this ensemble (discriminates these stimuli from one another more effectively) compared to the white noise, then we can conclude that the neural code is optimized for the statistics of the animal's visual world.

Here one should realize that the definition of Information takes into account the fact that knowing the prior probability distribution could allow you to "cheat" or "guess" the visual scene. The transmitted or mutual Information refers to the amount that the spike train reduces your uncertainty about the stimulus, that is, how much better can you guess the stimulus knowing the spike train and the prior probabilities, than just if you only knew the prior probabilities.

Active Sampling

Even within the ensemble of natural stimuli, an organism plays an active role in selecting which stimuli will fall on its retina, because the animal can move its body or head or eyes in order to "look at" things. To find out how this behaviour changes the coding problem for the retina (or how it contributes to the solution of the problem), it is necessary to measure the images falling on the retina of an animal while it is actively exploring natural scenes. We have done some work on where humans look on real-world images .

Behavioral and Survival Relevance

We can take this argument one step further and get into some really difficult territory. Ultimately, the biological function of any sensory system is to allow the animal to select the survival-optimal among alternative possible actions in a given situation. This means the neural code may even be optimized for discriminating important stimulus differences, rather than encoding those differences that are irrelevant to the animal's actions or its survival. To test this idea, one would have to know, not only the structure of the organism's natural visual environment, but which stimulus differences are relevant to the animal's survival, and to what extent can the animal's behavior alter the outcome, given a particular stimulus. Obviously this becomes hard to quantify. Alternatively, we could make a (very dangerous) assumption of optimality and then define "important" stimulus differences as whatever it is the nervous system seems in fact to best discriminate.

Bottom Line

My point is that the strictly random stimulus ensemble is in fact a good starting point for analysis of sensory coding in the nervous system, but the analysis should not stop there. Natural scenes are a subset of this space, the scenes the animal in fact looks at are a subset of natural scenes, and the stimuli the animal "cares about" are a subset of the scenes it looks at.

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