Information theory and neural coding

Abstract

Information theory quantifies how much information a neural response carries about the stimulus. This can be compared to the information transferred in particular models of the stimulus-response function and to maximum possible information transfer. Such comparisons are crucial because they validate assumptions present in any neurophysiological analysis. Here we review information-theory basics before demonstrating its use in neural coding. We show how to use information theory to validate simple stimulus-response models of neural coding of dynamic stimuli. Because these models require specification of spike timing precision, they can reveal which time scales contain information in neural coding. This approach shows that dynamic stimuli can be encoded efficiently by single neurons and that each spike contributes to information transmission. We argue, however, that the data obtained so far do not suggest a temporal code, in which the placement of spikes relative to each other yields additional information.

On the number of states of the neuronal sources

“…distribution function of quantities characterizing stimuli) or about the individual stimuli that caused the spike train under consideration (Borst and Theunissen, 1999)? This is something that, in general, can only be answered out of experience, although the very definition of the coding might help to figure out the relevant aspects involved.…”

“…Basically all the information that travels without decay along neuronal axons and is transmitted between neurons, does it in the form of individual spikes or trains of spikes. It is still a challenging problem to find out what kind of encoding and decoding mechanisms are used by the neurons and which are the properties of these biological encoders (Borst and Theunissen, 1999). Important for the mathematical modeler is the fact that the relation between stimulus and neuron response is not one-to-one: the same input s can generate different outputs r k because of noise in the neuron.…”

To Burst or Not to Burst?

“…There are several ways of determining estimates for the mutual information rate (Borst and Theunissen, 1999). We first describe the indirect method, that aims at estimating the mutual information indirectly through the stimulus reconstruction technique.…”

“…Alternatively, one can use the indirect method to obtain a lower bound on information transfer since this measure relies on linear decoding (Gabbiani, 1996;Rieke et al, 1996). One can thus use the direct method to gauge the goodness of the lower bound estimate obtained with the indirect method (Borst and Theunissen, 1999). A difference between the lower bound and the direct method indicates that some features of the stimulus might be decoded in a non-linear manner.…”

“…We also use information theory (Borst and Theunissen, 1999) to quantify the amount of information transmitted by each neuron. This information can be computed in two ways: the direct method of computing the mutual information makes no assumptions on the nature of the neural code while the indirect method assumes a linear decoder (Rieke et al, 1996;Borst and Theunissen, 1999) and thus computes a lower bound to the rate of information transmission (Theunissen et al, 1996). We compare results obtained using both methods to estimate the amount of information that can be decoded through both linear and non-linear means.…”