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Stochastic Orders on Two-Dimensional Space: Application to Cross Entropy

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Modeling Decisions for Artificial Intelligence (MDAI 2020)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12256))

Abstract

We present in this paper the extension to 2d probability mass functions (PMFs) of the first and likelihood-ratio stochastic orders for 1d PMFs. We show that first stochastic order ensures Kolmogorov mean order invariance. We also review the concept of comonotonic sequences and show its direct relationship with likelihood-ratio order. We give some application examples related to frequency histograms and cross entropy.

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Acknowledgments

M.S. has been funded by grant TIN2016-75866-C3-3-R from Spanish Government.

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Authors and Affiliations

  1. Graphics and Imaging Laboratory, University of Girona, 17003, Girona, Spain

    Mateu Sbert

  2. Faculty of Economics, University of Kitakyushu, Kitakyushu, 802-8577, Japan

    Yuji Yoshida

Authors
  1. Mateu Sbert
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  2. Yuji Yoshida
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Corresponding author

Correspondence to Mateu Sbert .

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Editors and Affiliations

  1. Department of Computing Science, Umeå University, Umeå, Sweden

    Vicenç Torra

  2. Department of Management Science, Tamagawa University, Tokyo, Japan

    Yasuo Narukawa

  3. Department of Operations, Innovation and Data Sciences, ESADE, Sant Cugat, Spain

    Jordi Nin

  4. Department of Operations, Innovation and Data Sciences, ESADE, Sant Cugat, Spain

    Núria Agell

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Sbert, M., Yoshida, Y. (2020). Stochastic Orders on Two-Dimensional Space: Application to Cross Entropy. In: Torra, V., Narukawa, Y., Nin, J., Agell, N. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2020. Lecture Notes in Computer Science(), vol 12256. Springer, Cham. https://doi.org/10.1007/978-3-030-57524-3_3

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  • DOI: https://doi.org/10.1007/978-3-030-57524-3_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-57523-6

  • Online ISBN: 978-3-030-57524-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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