On structural approximating multivariate discrete probability distributions

Jiří Grim

Kybernetika (1984)

  • Volume: 20, Issue: 1, page 1-17
  • ISSN: 0023-5954

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Grim, Jiří. "On structural approximating multivariate discrete probability distributions." Kybernetika 20.1 (1984): 1-17. <http://eudml.org/doc/28830>.

@article{Grim1984,
author = {Grim, Jiří},
journal = {Kybernetika},
keywords = {optimisation; approximation of discrete distributions; finite mixtures; product approximations; maximum-likelihood principle; convergent iterative procedure; structural approximations},
language = {eng},
number = {1},
pages = {1-17},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On structural approximating multivariate discrete probability distributions},
url = {http://eudml.org/doc/28830},
volume = {20},
year = {1984},
}

TY - JOUR
AU - Grim, Jiří
TI - On structural approximating multivariate discrete probability distributions
JO - Kybernetika
PY - 1984
PB - Institute of Information Theory and Automation AS CR
VL - 20
IS - 1
SP - 1
EP - 17
LA - eng
KW - optimisation; approximation of discrete distributions; finite mixtures; product approximations; maximum-likelihood principle; convergent iterative procedure; structural approximations
UR - http://eudml.org/doc/28830
ER -

References

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  1. D. T. Brown, A note on approximations to discrete probability distributions, Inform. and Control 2 (1959), 4, 386-392. (1959) Zbl0117.14804MR0110598
  2. C. K. Chow, Tree dependence in normal distributions, International Symposium on Information Theory, Nordwijk, The Netherlands 1970. (1970) 
  3. C. K. Chow, C. N. Liu, Approximating discrete probability distributions with dependence trees, IEEE Trans. Inform. Theory IT-14 (1968), 3, 462-467. (1968) Zbl0165.22305
  4. C. K. Chow, T. J. Wagner, Consistency of an estimate of tree-dependent probability distribution, IEEE Trans. Inform. Theory IT-19 (1973), 5, 369-371. (1973) 
  5. W. E. Deming, F. F. Stephan, On a least squares adjustement of a sampled frequency table when the expected marginal totals are known, Ann. Math. Statist. 77 (1940), 427-444. (1940) MR0003527
  6. W. A. Gibson, Three multivariate models: factor analysis, latent structure analysis and latent profile analysis, Psychometrika 24 (1959), 229 - 252. (1959) MR0109097
  7. J. Grim, On estimation of multivariate probability density functions for situation recognition in large scale systems, In: Proceedings of Third Formator Symposium (J. Benes, L. Bakule, eds.), Academia, Prague 1979. (1979) Zbl0485.93006
  8. J. Grim, On numerical evaluation of maximum-likelihood estimates for finite mixtures of distributions, Kybernetika 18 (1982), 3, 173-190. (1982) Zbl0489.62028MR0680154
  9. J. Grim, Application of finite mixtures to multivariate statistical pattern recognition, In: Proceedings of DIANA Conference held in Liblice near Prague, September 27 - October 1, 1982. (1982) 
  10. C. T. Ireland, S. Kullback, Contingency tables with given marginals, Biometrika 55 (1968), 179-188. (1968) Zbl0155.26701MR0229329
  11. A. Д. Юдин, Об информативных структурах многомерных случайных величин, (On information structures of multidimensional random variables.) Известия AH CCCP - Teхническая кибернетика (1977), 6, 135-144. (1977) Zbl1170.01341
  12. H. H. Ku, S. Kullback, Approximating discrete probability distributions, IEEE Trans. Inform. Theory IT-15 (1969), 444-447. (1969) MR0243669
  13. S. Kullback, Probability densities with given marginals, Ann. Math. Statist. 39 (1968), 4, 1236-1243. (1968) Zbl0165.20303MR0229330
  14. P. F. Lazarsfeld, N. W. Henry, Latent structure analysis, Houghton Mifflin, Boston 1968. (1968) Zbl0182.52201
  15. P. M. Lewis, Approximating probability distributions to reduce storage requirements, Inform. and Control 2 (1959), 214-225. (1959) Zbl0095.32602MR0110597
  16. A. Perez, ϵ -admissible simplification of the dependence structure of a set random variables, Kybernetika 13 (1977), 6, 439-449. (1977) MR0472224
  17. R. C. Prim, Shortest connection networks and some generalizations, Bell System Tech. J. 36 (1957), 1389-1401. (1957) 
  18. F. F. Stephan, An iterative method of adjusting sample frequency tables when expected marginal totals are known, Ann. Math. Statist. 13 (1942), 166- 178. (1942) Zbl0060.31505MR0006674

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