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The Fisher Information as a Neural Guiding Principle for Independent Component Analysis

Institute for Theoretical Physics, Goethe University Frankfurt, Frankfurt, 60438, Germany
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Entropy 2015, 17(6), 3838-3856; https://doi.org/10.3390/e17063838
Received: 27 February 2015 / Revised: 28 May 2015 / Accepted: 5 June 2015 / Published: 9 June 2015
(This article belongs to the Special Issue Information Theoretic Incentives for Cognitive Systems)
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. View Full-Text
Keywords: Fisher information; guiding principle; excess kurtosis; objective functions; synaptic plasticity; Hebbian learning; independent component analysis Fisher information; guiding principle; excess kurtosis; objective functions; synaptic plasticity; Hebbian learning; independent component analysis
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Echeveste, R.; Eckmann, S.; Gros, C. The Fisher Information as a Neural Guiding Principle for Independent Component Analysis. Entropy 2015, 17, 3838-3856.

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