Skip to main content

An Axiomatization of Loglinear Models with an Application to the Model-Search Problem

  • Chapter
Learning from Data

Part of the book series: Lecture Notes in Statistics ((LNS,volume 112))

Abstract

A good strategy to save computational time in a model-search problem consists in endowing the search procedure with a mechanism of logical inference, which sometimes allows a loglinear model to be accepted or rejected on logical grounds, without resorting to the numeric test. In principle, the best inferential mechanism should based on a complete axiomatization of loglinear models. We present a (probably incomplete) axiomatization, which can be translated into a graphical inference procedure working with directed acyclic graphs, and show how it can be applied to find an efficient solution to the model-search problem.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bishop, Y.M., Fienberg, S. and Holland, P., Discrete Multivariate Analysis. M.I.T. Press, 1975.

    MATH  Google Scholar 

  2. Edwards, D., and Havranek, T., A fast procedure for model search in multidimensional contingency tables, Biometrika 72 (1985), 339–351.

    Article  MathSciNet  MATH  Google Scholar 

  3. Edwards, D., and Havranek, T., A fast model selection procedure for large families of models, J. of the American Statistical Association 82 (1987), 205–213.

    Article  MathSciNet  MATH  Google Scholar 

  4. Geiger, D., Paz, A. and Pearl, J., Axioms and algorithms for inferences involving probabilistic independence, Information and Computation 91 (1991), 128–141.

    Article  MathSciNet  MATH  Google Scholar 

  5. Geiger, D. and Pearl, J., Logical and algorithmic properties of conditional independence and graphical models, The Annals of Statistics 21 (1993), 2001–2021.

    Article  MathSciNet  MATH  Google Scholar 

  6. Havranek, T., On application of statistical model search techniques in constructing a probabilistic knowledge base, Trans. 11th Prague Conf. on “Information Theory, Statistical Decision Functions and Random Processes” (1990).

    Google Scholar 

  7. Havranek, T., On model methods, Proc. 8th Symposium on “Computational Statistics” (1990).

    Google Scholar 

  8. Havranek, T., On model methods, Proc. Con. on “Symbolic-Numeric Data Analysis and Learning” (1991).

    Google Scholar 

  9. Hill, J.R., Comment, Statistical Science 8 (1993), 258–261.

    Article  Google Scholar 

  10. Malvestuto, F.M., A unique formal system for binary decompositions of database relations, probability distributions, and graphs, Information Sciences 59 (1992), 21–52.

    Article  MathSciNet  Google Scholar 

  11. Malvestuto, F.M., Testing implication of hierarchical log-linear models for probability distributions, to appear in Statistics and Computing.

    Google Scholar 

  12. Malvestuto, F.M., Formal treatment of loglinear models for probability distributions, Proc. 3rd Workshop on “Uncertainty Processing in Expert Systems” (1994).

    Google Scholar 

  13. Malvestuto, F.M., Statistical versus relational join dependencies, Proc. 7th Int. Conf on “Scientific & Statistical Database Management” (1994).

    Google Scholar 

  14. Malvestuto, F.M., Formal theories of probabilistic dependency models, Proc. World Conf. on “Fundamentals of Artificial Intelligence” (1995).

    Google Scholar 

  15. Pearl, J., Probabilistic Reasoning in Intelligent Systems. Morgan Kaufman Pub., 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Malvestuto, F.M. (1996). An Axiomatization of Loglinear Models with an Application to the Model-Search Problem. In: Fisher, D., Lenz, HJ. (eds) Learning from Data. Lecture Notes in Statistics, vol 112. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2404-4_17

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-2404-4_17

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94736-5

  • Online ISBN: 978-1-4612-2404-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics