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Statistical Manifolds, Self-Parallel Curves and Learning Processes

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Seminar on Stochastic Analysis, Random Fields and Applications

Part of the book series: Progress in Probability ((PRPR,volume 45))

Abstract

Introduced is some formalism of information geometry, new domain relating differential geometry to probability theory. Analysis and examinations of structure of some special spaces called statistical manifolds have been done. For the new geometry, covariant properties have been introduced. For that the new formalism the so-called α-geometry provides natural interpretation for the learning process, the learning rules have been discussed. The Boltzmann machine is studied using the previously described analysis of the manifold.

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Author information

Authors and Affiliations

  1. Centre de Physique Théorique, CNRS Luminy, Case 907, 13288, Marseille cedex 09, France

    G. Burdet & Ph. Combe

  2. Colegio dos Jesuitas, Universidade da Madeira, Largo do Colegio, 9000, Funchal, Madeira, Portugal

    H. Nencka

Authors
  1. G. Burdet
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  2. Ph. Combe
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  3. H. Nencka
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Editor information

Editors and Affiliations

  1. Département de Mathématiques, Ecole Polytechnique Fédérale, CH-1015, Lausanne, Switzerland

    Robert C. Dalang

  2. Institut Elie Cartan, Université Henri Poincaré, BP 239, F-54506, Vandoeuvre-les-Nancy Cedex, France

    Marco Dozzi

  3. Département de Mathématiques Institut Galilée, Université Paris 13, F-95430, Villetaneuse, France

    Francesco Russo

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© 1999 Springer Basel AG

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Burdet, G., Combe, P., Nencka, H. (1999). Statistical Manifolds, Self-Parallel Curves and Learning Processes. In: Dalang, R.C., Dozzi, M., Russo, F. (eds) Seminar on Stochastic Analysis, Random Fields and Applications. Progress in Probability, vol 45. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8681-9_7

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  • DOI: https://doi.org/10.1007/978-3-0348-8681-9_7

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9727-3

  • Online ISBN: 978-3-0348-8681-9

  • eBook Packages: Springer Book Archive

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