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On the Existence of Paths Connecting Probability Distributions

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Geometric Science of Information (GSI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10589))

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Abstract

We introduce a class of paths defined in terms of two deformed exponential functions. Exponential paths correspond to a special case of this class of paths. Then we give necessary and sufficient conditions for any two probability distributions being path connected.

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References

  1. Cena, A., Pistone, G.: Exponential statistical manifold. Ann. Inst. Statist. Math. 59(1), 27–56 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. de Souza, D.C., Vigelis, R.F., Cavalcante, C.C.: Geometry induced by a generalization of Rényi divergence. Entropy 18(11), 407 (2016)

    Article  Google Scholar 

  3. Eguchi, S., Komori, O.: Path connectedness on a space of probability density functions. In: Nielsen, F., Barbaresco, F. (eds.) GSI 2015. LNCS, vol. 9389, pp. 615–624. Springer, Cham (2015). doi:10.1007/978-3-319-25040-3_66

    Chapter  Google Scholar 

  4. Musielak, J.: Orlicz Spaces and Modular Spaces. LNM, vol. 1034. Springer, Heidelberg (1983). doi:10.1007/BFb0072210

    MATH  Google Scholar 

  5. Giovanni Pistone and Maria Piera Rogantin: The exponential statistical manifold: mean parameters, orthogonality and space transformations. Bernoulli 5(4), 721–760 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  6. Santacroce, M., Siri, P., Trivellato, B.: New results on mixture and exponential models by Orlicz spaces. Bernoulli 22(3), 1431–1447 (2016)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Engineering, Campus Sobral, Federal University of Ceará, Sobral, CE, Brazil

    Rui F. Vigelis

  2. Center of Exact and Natural Sciences, Federal Rural University of the Semi-arid Region, Mossoró, RN, Brazil

    Luiza H. F. de Andrade

  3. Department of Teleinformatics Engineering, Wireless Telecommunication Research Group, Federal University of Ceará, Fortaleza, CE, Brazil

    Charles C. Cavalcante

Authors
  1. Rui F. Vigelis
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  2. Luiza H. F. de Andrade
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  3. Charles C. Cavalcante
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Corresponding author

Correspondence to Rui F. Vigelis .

Editor information

Editors and Affiliations

  1. Ecole Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land and Air Systems, Limours, France

    Frédéric Barbaresco

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Vigelis, R.F., de Andrade, L.H.F., Cavalcante, C.C. (2017). On the Existence of Paths Connecting Probability Distributions. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science(), vol 10589. Springer, Cham. https://doi.org/10.1007/978-3-319-68445-1_92

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  • DOI: https://doi.org/10.1007/978-3-319-68445-1_92

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68444-4

  • Online ISBN: 978-3-319-68445-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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