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Information Geometry of the Gaussian Space

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Information Geometry and Its Applications (IGAIA IV 2016)

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Abstract

We discuss the Pistone-Sempi exponential manifold on the finite-dimensional Gaussian space. We consider the role of the entropy, the continuity of translations, Poincaré-type inequalities, the generalized differentiability of probability densities of the Gaussian space.

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Acknowledgements

The author acknowledges support from the de Castro Statistics Initiative, Collegio Carlo Alberto, Moncalieri, Italy. He is a member of INdAM/GNAMPA.

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Authors and Affiliations

  1. de Castro Statistics, Collegio Carlo Alberto, Piazza Vincenzo Arbarello 8, 10122, Turin, Italy

    Giovanni Pistone

Authors
  1. Giovanni Pistone
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Correspondence to Giovanni Pistone .

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Editors and Affiliations

  1. Information Theory of Cognitive Systems, MPI for Mathematics in the Sciences, Leipzig, Germany

    Nihat Ay

  2. Department of Economics and Finance, University of Rome “Tor Vergata”, Rome, Italy

    Paolo Gibilisco

  3. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Prague, Czech Republic

    František Matúš

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Pistone, G. (2018). Information Geometry of the Gaussian Space. In: Ay, N., Gibilisco, P., Matúš, F. (eds) Information Geometry and Its Applications . IGAIA IV 2016. Springer Proceedings in Mathematics & Statistics, vol 252. Springer, Cham. https://doi.org/10.1007/978-3-319-97798-0_5

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