Information theoretic analysis of neural populations

Abstract

The information of the stimulus variable S in a population of n observed neurons R0… Rn can be measured using the mutual information I (S: R0… Rn). In order to gain a deeper understanding about the stimulus encoding in the neural population the question arises how to decompose the mutual information. A decomposition may reveal sets of neurons that share the same information about the stimulus, or sets of neurons that encode information synergistically or a single neurons that may encode information about the stimulus that is not present in any of the other observed neurons. There are several properties that seem obviously necessary to hold for a mutual information decomposition. But these properties alone do not provide enough constraints to result in a unique solution and it is not clear how to resolve for this ambiguity. Several approaches have been suggested recently ([Williams2010],[Harder2013],[Griffith2014]) but we find that all of them suffer from certain caveats. Here, we introduce a new approach how to decompose the mutual information of two different neural populations with a stimulus into independent, unique, and synergistic components. We demonstrate its strength compared to previously proposed decompositions and present several examples that corroborate its usefulness. In particular, we believe the decomposition can serve as a useful relaxation to the problem of causality estimation.