Special Issue "Information Geometry"
A special issue of Entropy (ISSN 1099-4300).
Deadline for manuscript submissions: closed (31 March 2014)
Prof. Dr. Geert Verdoolaege
1 Research Unit Nuclear Fusion, Department of Applied Physics, Ghent University, Sint-Pietersnieuwstraat 41, B-9000 Ghent, Belgium 2 Laboratory for Plasma Physics, Royal Military Academy (ERM/KMS), Renaissancelaan 30 Avenue de la Renaissance, B-1000 Brussels, Belgium
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Interests: probability theory; Bayesian inference; machine learning; information geometry; differential geometry; nuclear fusion; plasma physics; plasma turbulence; continuum mechanics; statistical mechanics
The mathematical field of Information Geometry originated from the observation by C.R. Rao in 1945 that the Fisher information can be used to define a Riemannian metric in spaces of probability distributions. This led to a geometrical description of probability theory and statistics, allowing the study of the invariant properties of statistical manifolds. It was through the works of S.-I. Amari and others, that it was later realized that the differential-geometric structure of a statistical manifold can be derived from divergence functions, yielding a Riemannian metric and a pair of dually coupled affine connections.
Since then, Information Geometry has become a truly interdisciplinary field with applications in various domains. It enables a deeper understanding of the methods of statistical inference and machine learning, while providing a powerful framework for deriving new algorithms as well. As such, Information Geometry has many applications in optimization (e.g. on matrix manifolds), signal and image processing, computer vision, neural networks and other subfields of the information sciences. Furthermore, the methods of Information Geometry have been applied to a wide variety of topics in physics, mathematical finance, biology and the neurosciences. In physics, there are many links through the fields of (nonextensive) statistical mechanics and quantum mechanics, since these are also based on probability theory. In addition, there are recent indications that the formalism of Information Geometry may be suitable for explaining or deriving other physical laws as well.
For this special issue we welcome submissions related to the foundations and applications of Information Geometry. We envisage contributions that aim at clarifying the connection of Information Geometry with both the information sciences and the physical sciences, so as to demonstrate the profound impact of the field in these disciplines. In addition, we hope to receive original papers illustrating the wide variety of applications of the methods of Information Geometry.
Dr. Geert Verdoolaege
Manuscript Submission Information
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- information geometry
- probability theory
- machine learning
- signal processing
- image processing
- statistical mechanics
- quantum mechanics