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Biol Cybern. 2018 Apr;112(1-2):13-23. doi: 10.1007/s00422-017-0729-7. Epub 2017 Aug 30.

Coordinate invariance as a fundamental constraint on the form of stimulus-specific information measures.

Author information

1
Institute of Physiology, Czech Academy of Sciences, Videnska 1083, 14220, Prague 4, Czech Republic. kostal@biomed.cas.cz.
2
Institute of Physiology, Czech Academy of Sciences, Videnska 1083, 14220, Prague 4, Czech Republic.

Abstract

The value of Shannon's mutual information is commonly used to describe the total amount of information that the neural code transfers between the ensemble of stimuli and the ensemble of neural responses. In addition, it is often desirable to know which features of the stimulus or response are most informative. The literature offers several different decompositions of the mutual information into its stimulus or response-specific components, such as the specific surprise or the uncertainty reduction, but the number of mutually distinct measures is in fact infinite. We resolve this ambiguity by requiring the specific information measures to be invariant under invertible coordinate transformations of the stimulus and the response ensembles. We prove that the Kullback-Leibler divergence is then the only suitable measure of the specific information. On a more general level, we discuss the necessity and the fundamental aspects of the coordinate invariance as a selection principle. We believe that our results will encourage further research into invariant statistical methods for the analysis of neural coding.

KEYWORDS:

Coordinate invariance; KullbackÔÇôLeibler divergence; Mutual information; Specific information

PMID:
28856427
DOI:
10.1007/s00422-017-0729-7
[Indexed for MEDLINE]

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