A note on the interval-valued marginal problem and its maximum entropy solution

Jiřina Vejnarová

Kybernetika (1998)

  • Volume: 34, Issue: 1, page [17]-26
  • ISSN: 0023-5954

Abstract

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This contribution introduces the marginal problem, where marginals are not given precisely, but belong to some convex sets given by systems of intervals. Conditions, under which the maximum entropy solution of this problem can be obtained via classical methods using maximum entropy representatives of these convex sets, are presented. Two counterexamples illustrate the fact, that this property is not generally satisfied. Some ideas of an alternative approach are presented at the end of the paper.

How to cite

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Vejnarová, Jiřina. "A note on the interval-valued marginal problem and its maximum entropy solution." Kybernetika 34.1 (1998): [17]-26. <http://eudml.org/doc/33331>.

@article{Vejnarová1998,
abstract = {This contribution introduces the marginal problem, where marginals are not given precisely, but belong to some convex sets given by systems of intervals. Conditions, under which the maximum entropy solution of this problem can be obtained via classical methods using maximum entropy representatives of these convex sets, are presented. Two counterexamples illustrate the fact, that this property is not generally satisfied. Some ideas of an alternative approach are presented at the end of the paper.},
author = {Vejnarová, Jiřina},
journal = {Kybernetika},
keywords = {interval-valued marginal problem; maximum entropy solution; interval-valued marginal problem; maximum entropy solution},
language = {eng},
number = {1},
pages = {[17]-26},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A note on the interval-valued marginal problem and its maximum entropy solution},
url = {http://eudml.org/doc/33331},
volume = {34},
year = {1998},
}

TY - JOUR
AU - Vejnarová, Jiřina
TI - A note on the interval-valued marginal problem and its maximum entropy solution
JO - Kybernetika
PY - 1998
PB - Institute of Information Theory and Automation AS CR
VL - 34
IS - 1
SP - [17]
EP - 26
AB - This contribution introduces the marginal problem, where marginals are not given precisely, but belong to some convex sets given by systems of intervals. Conditions, under which the maximum entropy solution of this problem can be obtained via classical methods using maximum entropy representatives of these convex sets, are presented. Two counterexamples illustrate the fact, that this property is not generally satisfied. Some ideas of an alternative approach are presented at the end of the paper.
LA - eng
KW - interval-valued marginal problem; maximum entropy solution; interval-valued marginal problem; maximum entropy solution
UR - http://eudml.org/doc/33331
ER -

References

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  1. Cheeseman P., A method of computing generalized Bayesian probability values for expert systems, In: Proc. 6th Internat. Joint Conference on Artificial Intelligence (IJCAI–83), Karlsruhe 1983, pp. 198–202 (1983) 
  2. Deming W. E., Stephan F. F., 10.1214/aoms/1177731829, Ann. Math. Statist. 11 (1940), 427–444 (1940) MR0003527DOI10.1214/aoms/1177731829
  3. Gallager R. R., Information Theory and Reliable Communication, J. Wiley, New York 1968 Zbl0295.94001
  4. Jiroušek R., Perez A., A partial solution of the marginal problem, In: Trans. of the 10th Prague Conference on Inform. Theory, vol. B, Academia, Prague 1987, pp. 11–19 (1987) 
  5. Kellerer H. G., 10.1007/BF00534912, Z. Wahrsch. verw. Gebiete 3 (1964), 247–270 (1964) MR0175158DOI10.1007/BF00534912
  6. Malvestuto F. M., 10.1016/0012-365X(88)90178-1, Discrete Math. 69 (1988), 61–77 (1988) Zbl0637.60021MR0935028DOI10.1016/0012-365X(88)90178-1
  7. Walley P., 10.1016/0004-3702(95)00009-7, Artificial Intelligence 83 (1996), 1–58 (1996) MR1391510DOI10.1016/0004-3702(95)00009-7

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