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A Primer on Information Theory with Applications to Neuroscience

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Computational Medicine in Data Mining and Modeling

Abstract

Given the constant rise in quantity and quality of data obtained from neural systems on all scales, information-theoretic analyses became more and more popular over the last decades in the neurosciences. Such analyses can provide deep insights into the functioning of such systems and also be of help in the characterization and analysis of neural dysfunction, a topic that has come into the focus of research in the computational neurosciences recently. This chapter is supposed to give a short introduction to the fundamentals of information theory, not only, but especially, suited for people having a less firm background in mathematics and probability theory. Regarding applications, the focus will be on neuroscientific topics. We start by reviewing fundamentals of probability theory such as the notion of probability, probability distributions, and random variables. We will then discuss the concepts of information and entropy (in the sense of Shannon), mutual information, and transfer entropy (sometimes also referred to as conditional mutual information). As these quantities cannot be computed for measured data in practice, we discuss estimation techniques for information-theoretic quantities. We conclude with a discussion of applications of information theory in the field of neuroscience, including questions of possible medical applications and a short review of software packages that can be used for information-theoretic analyses of neural data.

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Notes

  1. 1.

    Shannon chose the letter H for denoting entropy after Boltzmann’s H-theorem in classical statistical mechanics.

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Acknowledgements

The author would like to thank Nihat Ay, Yuri Campbell, Aleena Garner, Jörg Lehnert, Timm Lochmann, Wiktor Młynarski, and Carolin Stier for their useful comments on the manuscript.

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  1. Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22, 04103, Leipzig, Germany

    Felix Effenberger

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  1. Felix Effenberger
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  1. Mathematical Institute, Serbian Academy of Science and Arts, Belgrade, Serbia

    Goran Rakocevic

  2. Faculty of Engineering, University of Kragujevac, Kragujevac, Serbia

    Tijana Djukic

  3. Faculty of Engineering, University of Kragujevac, Kragujevac, Serbia

    Nenad Filipovic

  4. School of Electrical Engineering, University of Belgrade, Belgrade, Serbia

    Veljko Milutinović

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Effenberger, F. (2013). A Primer on Information Theory with Applications to Neuroscience. In: Rakocevic, G., Djukic, T., Filipovic, N., Milutinović, V. (eds) Computational Medicine in Data Mining and Modeling. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8785-2_5

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