Tropical probability theory and an application to the entropic cone

Rostislav Matveev; Jacobus W. Portegies

Kybernetika (2020)

  • Volume: 56, Issue: 6, page 1133-1153
  • ISSN: 0023-5954

Abstract

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In a series of articles, we have been developing a theory of tropical diagrams of probability spaces, expecting it to be useful for information optimization problems in information theory and artificial intelligence. In this article, we give a summary of our work so far and apply the theory to derive a dimension-reduction statement about the shape of the entropic cone.

How to cite

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Matveev, Rostislav, and Portegies, Jacobus W.. "Tropical probability theory and an application to the entropic cone." Kybernetika 56.6 (2020): 1133-1153. <http://eudml.org/doc/297051>.

@article{Matveev2020,
abstract = {In a series of articles, we have been developing a theory of tropical diagrams of probability spaces, expecting it to be useful for information optimization problems in information theory and artificial intelligence. In this article, we give a summary of our work so far and apply the theory to derive a dimension-reduction statement about the shape of the entropic cone.},
author = {Matveev, Rostislav, Portegies, Jacobus W.},
journal = {Kybernetika},
keywords = {tropical probability; entropic cone; non-Shannon inequality},
language = {eng},
number = {6},
pages = {1133-1153},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Tropical probability theory and an application to the entropic cone},
url = {http://eudml.org/doc/297051},
volume = {56},
year = {2020},
}

TY - JOUR
AU - Matveev, Rostislav
AU - Portegies, Jacobus W.
TI - Tropical probability theory and an application to the entropic cone
JO - Kybernetika
PY - 2020
PB - Institute of Information Theory and Automation AS CR
VL - 56
IS - 6
SP - 1133
EP - 1153
AB - In a series of articles, we have been developing a theory of tropical diagrams of probability spaces, expecting it to be useful for information optimization problems in information theory and artificial intelligence. In this article, we give a summary of our work so far and apply the theory to derive a dimension-reduction statement about the shape of the entropic cone.
LA - eng
KW - tropical probability; entropic cone; non-Shannon inequality
UR - http://eudml.org/doc/297051
ER -

References

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