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Bayes Ağlarda Koşullu Bağımsızlıkların İncelenmesi Üzerine Bir Çalışma

Year 2003, Volume: 2 Issue: 1, 89 - 104, 15.04.2003

Abstract

Bir Bayes ağ, koşullu bağımsızlık özelliklerine sahip yön verilmiş döngüsel olmayan bir grafiktir. Bayes ağ değişkenler ve değişkenler arası yön verilmiş kenarların kümesinden oluşur. Kenarlar değişkenler arası olasılık bağımlılıkları gösterir. Bu bağımlılıklar koşullu olasılıkların kümesinden oluşur. Her bir değişkenin ebeveynleri verildiğinde değişkenin koşullu olasılığı belirlenir. Bir düğümün ebeveynleri olmadığı zaman, bir değişken koşulsuz (marjinal) bir olasılığa sahiptir. Bu çalışmada, Bayes ağlarda, koşullu bağımsızlıklar aşağıdaki farklı üç yoldan araştırılmıştır. Bu yollardan ilki yön verilmiş markov özelliğidir. İkincisi, moral ve üçgen grafik yardımı ile elde edilebilen koşullu bağımsızlıktır. Moral ve üçgen grafikten elde edilebilen takımlar sayesinde birleşme ağacı kurulur. Birleşme ağacından, verilen bayes ağ modeline ilişkin koşullu bağımsızlıklar elde edilir. Üçüncüsü ise, koşullu bağımsızlık kavramının yönsel-ayrılma kriteri ile verilmesidir. Verilen bayes ağ modeli için, üç farklı şekilde koşullu bağımsızlık özellikleri gösterilmiş ve bu yollar arasındaki ilişkiler incelenmiştir.

References

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  • JENSEN, F.V., OLESEN, K.G. and ANDERSEN, S.K. (1990), an Algebra Bayesian Belief Universes for Knowledge-Based Systems, Networks, Vol. 20, 637-659.
  • JENSEN, F.V., (1996), an Introduction to Bayesian Networks, UCL, Press Ltd., London.
  • LAURİTZEN, S.L. (1996), Graphical Models, Oxford University Press, Oxford.
  • LAURİTZEN, S.L. and SPİEGELHALTER, D.J., (1998), Local Computations with Probabilities on Graphical Structures an Their Application to Expert Systems, J.R. Statist. Soc. B., 50(2), 157-224.
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  • LİAROKAPİS, D., (1999), an Introduction to Belief Networks, [ http://www.cs.umb.edu/-dimitris ] Erişim Tarih: 02.11.2000
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  • NEAL, R.M., (2000), on Deducing Conditional Independence From D-Seperation in Causal Graphs with Feedback, Journal of Artificial Intelligence Research, 12, 87-91.
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  • PEARL, J., (1993), From Bayesian Networks to Causal Networks, 49th Session of the International Statistical Institue, Flörence, Italy.
  • PEARL, J., 2000, Causality: Models, Reasoning and Inference, Cambridge University Press, England.
  • RICHARDSON, T., (1997), Introduction and D-Separation, UW Department of Statistics, [http//www.stat.washington.edu/tsr/s538/lec1 ] Erişim Tarihi: 4.11.2000.
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A Study for Examining the Conditional Independence in Bayesian Networks

Year 2003, Volume: 2 Issue: 1, 89 - 104, 15.04.2003

Abstract

A Bayesian network is a directed acyclic graph which has conditional independence properties. Bayesian network consists of variables and the sets of the directed edge between variables. Edges denote probability dependence between variables. This dependence consists of the set of conditional probabiliries. Conditional probability of a variable is determined by giving parents of each variable. When a node has no parent, a variable has an unconditional (marginal) probability. In this study, conditional, independence in Bayesian Networks is examined by following three ways. First of these ways is directed Markovian properties. Second is conditional independence which can be obtained by using moral and triangulated graph. Junction tree is constituted with cliques which can be obtained by using moral and triangulated graph. Conditional independence related with Bayesian network is obtained from junction tree. Third is the definition of the conditional independence by using d-separation criterion. The characteristics of conditional independence are given in three different ways and relations between these ways are examined.

References

  • BUNTINE, W., (1996), a Guide to the Literatüre on Learning Probabilistic Networks From Data, IEEE Transactions on Knowledge and Data Engineering, 8(2), 195-210.
  • COWELL, R.G., (1999), Introduction to Inference in Bayesian Networks, In Learning in Graphical Models, 9-26.
  • EDWARDS, D., (1995), Introduction to Inference Bayesian Networks, Springer-Verlag, New York.
  • FENTON, N., (1997), Basics, of BBNs, [ http://csr.city.ac.uk/people/norman.fenton/bbns/details ] Erişim Tarih: 02.06.2000
  • GEİGER, D., VERMA, T. and PEARL, J., (1990), Identifying Independence in Bayesian Networks, Networks, Vol. 20, 507-534.
  • JENSEN, F.V., OLESEN, K.G. and ANDERSEN, S.K. (1990), an Algebra Bayesian Belief Universes for Knowledge-Based Systems, Networks, Vol. 20, 637-659.
  • JENSEN, F.V., (1996), an Introduction to Bayesian Networks, UCL, Press Ltd., London.
  • LAURİTZEN, S.L. (1996), Graphical Models, Oxford University Press, Oxford.
  • LAURİTZEN, S.L. and SPİEGELHALTER, D.J., (1998), Local Computations with Probabilities on Graphical Structures an Their Application to Expert Systems, J.R. Statist. Soc. B., 50(2), 157-224.
  • LAURİTZEN, S.L. Dawid, A.P., Larsen, B.N., and LEİMER, H.G., (1990), Independence Properties of Directed Markov, Fields, Networks, 20, 491-505.
  • LİAROKAPİS, D., (1999), an Introduction to Belief Networks, [ http://www.cs.umb.edu/-dimitris ] Erişim Tarih: 02.11.2000
  • MADSEN, A.L., and JENSEN, F.V., (1999), LAZY Propagation: a Junction Tree Inference Algorithm Based on Lazy Evaluation, Artificial Intelligence, 113, 203-245.
  • NEAL, R.M., (2000), on Deducing Conditional Independence From D-Seperation in Causal Graphs with Feedback, Journal of Artificial Intelligence Research, 12, 87-91.
  • OLİVER, R.M. and SMITH, J.Q., (1988), Influence Diagrams, Belief Nets and Decision Analysis, John Wiley&Sons, New York.
  • ORAL ERBAŞ, S., ve BAYRAK, H. (1999), Grafiksel Modeller, Gazi Üniversitesi Fen-Edebiyat Fakültesi İstatistik Bölümü, Ankara.
  • PEARL, J., (1993), From Bayesian Networks to Causal Networks, 49th Session of the International Statistical Institue, Flörence, Italy.
  • PEARL, J., 2000, Causality: Models, Reasoning and Inference, Cambridge University Press, England.
  • RICHARDSON, T., (1997), Introduction and D-Separation, UW Department of Statistics, [http//www.stat.washington.edu/tsr/s538/lec1 ] Erişim Tarihi: 4.11.2000.
  • STEPHENSON, T.A., (2000), an Introduction to Bayesian Network Theory and Usage, IDIAP Research Report 00-03.
There are 19 citations in total.

Details

Primary Language Turkish
Subjects Statistical Theory
Journal Section Research Articles
Authors

Hülya Olmuş

Semra Oral Erbaş

Publication Date April 15, 2003
Published in Issue Year 2003 Volume: 2 Issue: 1

Cite

APA Olmuş, H., & Oral Erbaş, S. (2003). Bayes Ağlarda Koşullu Bağımsızlıkların İncelenmesi Üzerine Bir Çalışma. İstatistik Araştırma Dergisi, 2(1), 89-104.