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Effective Dimensions of Partially Observed Polytrees

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2711))

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Abstract

Model complexity is an important factor to consider when selecting among graphical models. When all variables are observed, the complexity of a model can be measured by its standard dimension, i.e. the number of independent parameters. When latent variables are present, however, the standard dimension might no longer be appropriate. Instead, an effective dimension should be used [5]. Zhang & Kočka [13] showed how to compute the effective dimensions of partially observed trees. In this paper we solve the same problem for partially observed polytrees.

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References

  1. Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control AC-19, 716–723 (1974)

    Article  MathSciNet  Google Scholar 

  2. Catchpole, E.A., Morgan, B.J.T.: Deficiency of parameter-redundant models. Biometrika 88(2), 593–598 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cheeseman, P., Stutz, J.: Bayesian classification (AutoClass): Theory and results. In: Fayyad, U., Paitesky-Shapiro, G., Smyth, P., Uthurusamy, R. (eds.) Advances in knowledge discovery and data mining, pp. 153–180 (1995)

    Google Scholar 

  4. Cooper, G., Herskovits, E.: A Bayesian method for the induction of probabilistic networks from data. Machine Learning 9, 309–347 (1992)

    MATH  Google Scholar 

  5. Geiger, D., Heckerman, D., Meek, C.: Asymptotic model selection for directed networks with hidden variables. In: Proc. of the 12th Conference on Uncertainty in Artificial Intelligence, pp. 283–290 (1996)

    Google Scholar 

  6. Kočka, T., Zhang, N.L.: Dimension correction for hierarchical latent class models. In: Proc. of the 18th Conference on Uncertainty in Artificial Intelligence (UAI 2002), pp. 267–274 (2002)

    Google Scholar 

  7. Lauritzen, S.L.: Graphical models. Clarendon Press, Oxford (1996)

    Google Scholar 

  8. Rusakov, D.: Effective dimension calculations for Bayesian networks, code in Matlab (2002), http://www.cs.technion.ac.il/~rusakov/archive/bn_dimension/bn_dimension.m

  9. Rusakov, D., Geiger, D.: Asymptotic model Selection for naive Bayesian networks. In: Proc. of the 18th Conference on Uncertainty in Artificial Intelligence (UAI 2002), pp. 438–445 (2002)

    Google Scholar 

  10. Schwarz, G.: Estimating the dimension of a model. Annals of Statistics 6, 461–464 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  11. Settimi, R., Smith, J.Q.: On the geometry of Bayesian graphical models with hidden variables. In: Proc. of the 14th Conference on Uncertainty in Artificial Intelligence, pp. 472–479 (1998)

    Google Scholar 

  12. Settimi, R., Smith, J.Q.: Geometry, moments and Bayesian networks with hidden variables. In: Proc. of the 7th International Workshop on Artificial Intelligence and Statistics, Fort Lauderdale, Florida, January 3–6. Morgan Kaufmann Publishers, San Francisco (1999)

    Google Scholar 

  13. Zhang, N.L., Kočka, T.: Effective dimensions of hierarchical latent class models, Technical Report HKUST-CS03-03, Department of Computer Science, Hong Kong University of Science and Technology (2003)

    Google Scholar 

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© 2003 Springer-Verlag Berlin Heidelberg

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Kočka, T., Zhang, N.L. (2003). Effective Dimensions of Partially Observed Polytrees. In: Nielsen, T.D., Zhang, N.L. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2003. Lecture Notes in Computer Science(), vol 2711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45062-7_15

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  • DOI: https://doi.org/10.1007/978-3-540-45062-7_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40494-1

  • Online ISBN: 978-3-540-45062-7

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