Abstract
We discuss the statistical bundle of the manifold of two-variate stricly positive probability functions with given marginals. The fiber associated to each coupling turns out to be the vector space of interacions in the ANOVA decomposition with respect to the given weight. In this setting, we derive the form of the gradient flow equation for the Kantorovich optimal transport problem.
The author is supported by de Castro Statistics, Collegio Carlo Alberto. He is a member of INdAM-GNAMPA.
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Acknowledgments
The author thanks three anonymous referees whose comments suggested a complete revision of the first version. The author thanks L. Malagò and L. Montrucchio for valuable suggestions. We first presented the gradient flow argument of Sect. 3 to the “Computational information geometry for image and signal processing” Conference, Sep 21–25 2015 ICMS, Edinburgh.
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Pistone, G. (2021). Statistical Bundle of the Transport Model. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science(), vol 12829. Springer, Cham. https://doi.org/10.1007/978-3-030-80209-7_81
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DOI: https://doi.org/10.1007/978-3-030-80209-7_81
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