Journal ArticleDOI
The relation between information theory and the differential geometry approach to statistics
TLDR
It is shown that the Riemannian metric on the probability simplex ∑xi = 1 defined by (ds) 2 = ∑(dx i ) 2 x i has an invariance property under certain probabilistically natural mappings.About:
This article is published in Information Sciences.The article was published on 1985-06-01. It has received 65 citations till now. The article focuses on the topics: Information geometry & Fisher information metric.read more
Citations
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Journal ArticleDOI
Natural gradient works efficiently in learning
TL;DR: In this paper, the authors used information geometry to calculate the natural gradients in the parameter space of perceptrons, the space of matrices (for blind source separation), and the spaces of linear dynamical systems for blind source deconvolution, and proved that Fisher efficient online learning has asymptotically the same performance as the optimal batch estimation of parameters.
Journal ArticleDOI
Riemannian geometry in thermodynamic fluctuation theory
TL;DR: The covariant thermodynamic fluctuation theory as mentioned in this paper is an extension of the basic structure of the classical one of a subsystem in contact with an infinite uniform reservoir, where a hierarchy of concentric subsystems, each of which samples only the thermodynamic state of the subsystem immediately larger than it, is used.
Journal ArticleDOI
Information geometry on hierarchy of probability distributions
TL;DR: The orthogonal decomposition of an exponential family or mixture family of probability distributions has a natural hierarchical structure is given and is important for extracting intrinsic interactions in firing patterns of an ensemble of neurons and for estimating its functional connections.
References
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Book
Information Theory and Reliable Communication
TL;DR: This chapter discusses Coding for Discrete Sources, Techniques for Coding and Decoding, and Source Coding with a Fidelity Criterion.