The Fisher information as a neural guiding principle for independent component analysis

  • The Fisher information constitutes a natural measure for the sensitivity of a probability distribution with respect to a set of parameters. An implementation of the stationarity principle for synaptic learning in terms of the Fisher information results in a Hebbian self-limiting learning rule for synaptic plasticity. In the present work, we study the dependence of the solutions to this rule in terms of the moments of the input probability distribution and find a preference for non-Gaussian directions, making it a suitable candidate for independent component analysis (ICA). We confirm in a numerical experiment that a neuron trained under these rules is able to find the independent components in the non-linear bars problem. The specific form of the plasticity rule depends on the transfer function used, becoming a simple cubic polynomial of the membrane potential for the case of the rescaled error function. The cubic learning rule is also an excellent approximation for other transfer functions, as the standard sigmoidal, and can be used to show analytically that the proposed plasticity rules are selective for directions in the space of presynaptic neural activities characterized by a negative excess kurtosis.

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Author:Rodrigo Echeveste, Samuel EckmannORCiDGND, Claudius GrosORCiDGND
Parent Title (English):Entropy
Place of publication:Basel
Document Type:Article
Date of Publication (online):2015/06/09
Date of first Publication:2015/06/09
Publishing Institution:Universit├Ątsbibliothek Johann Christian Senckenberg
Release Date:2016/05/30
Tag:Fisher information; Hebbian learning; excess kurtosis; guiding principle; independent component analysis; objective functions; synaptic plasticity
Page Number:19
First Page:3838
Last Page:3856
c 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (
Institutes:Physik / Physik
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoCreative Commons - Namensnennung 4.0