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Zusammenfassung:
The relative merits of different population coding schemes have mostly been studied in the framework of stimulus reconstruction using Fisher Information, minimum mean square error or mutual information. Here, we analyze neural population codes using the minimal discrimination error (MDE) and the Jensen-Shannon information in a two alternatives forced choice (2AFC) task. In a certain sense, this approach is more informative than the previous ones as it defines an error that is specific to any pair of possible stimuli - in particular, it includes Fisher Information as a special case. We demonstrate several advantages of the minimal discrimination error: (1) it is very intuitive and easier to compare to experimental data, (2) it is easier to compute than mutual information or minimum mean square error, (3) it allows studying assumption about prior distributions, and (4) it provides a more reliable assessment of coding accuracy than Fisher information.
First, we introduce the Jensen-Shannon information and explain how it can be used to bound the MDE. In particular, we derive a new lower bound on the minimal discrimination error that is tighter than previous ones. Also, we explain how Fisher information can be derived from the Jensen-Shannon information and conversely to what extent Fisher information can be used to predict the minimal discrimination error for arbitrary pairs of stimuli depending on the properties of the tuning functions.
Second, we use the minimal discrimination error to study population codes of angular variables. In particular, we assess the impact of different noise correlations structures on coding accuracy in long versus short decoding time windows. That is, for long time window we use the common Gaussian noise approximation while we analyze the Ising model with identical noise correlation structure to address the case of short time windows. As an important result, we find that the beneficial effect of stimulus dependent correlations in the absence of 'limited-range' correlations holds only true for long-term population codes while they provide no advantage in case of short decoding time windows.
In this way, we provide for a new rigorous framework for assessing the functional consequences of correlation structures for the representational accuracy of neural population codes in short time scales.
