Skip to main content

Mining Tolerance Regions with Model Trees

  • Conference paper
Foundations of Intelligent Systems (ISMIS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4203))

Included in the following conference series:

Abstract

Many problems encountered in practice involve the prediction of a continuous attribute associated with an example. This problem, known as regression, requires that samples of past experience with known continuous answers are examined and generalized in a regression model to be used in predicting future examples. Regression algorithms deeply investigated in statistics, machine learning and data mining usually lack measures to give an indication of how “good” the predictions are. Tolerance regions, i.e., a range of possible predictive values, can provide a measure of reliability for every bare prediction. In this paper, we focus on tree-based prediction models, i.e., model trees, and resort to the inductive inference to output tolerance regions in addition to bare prediction. In particular, we consider model trees mined by SMOTI (Stepwise Model Tree Induction) that is a system for data-driven stepwise construction of model trees with regression and splitting nodes and we extend the definition of trees to build tolerance regions to be associated with each leaf. Experiments evaluate validity and quality of output tolerance regions.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
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. Breiman, L., Friedman, J., Olshen, R., Stone, J.: Classification and regression tree. Wadsworth & Brooks (1984)

    Google Scholar 

  2. Chaudhuri, P., Huang, M.C., Loh, W.Y., Yao, R.: Piecewise-polynomial regression trees. Statistica Sinica 4, 143–167 (1994)

    MATH  Google Scholar 

  3. Cowan, G.: Statistical Data Analysis. Oxford University Press, USA (1998)

    Google Scholar 

  4. Dobra, A., Gehrke, J.E.: SECRET: A scalable linear regression tree algorithm. In: Proceedings of the Eighth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Edmonton, Alberta, Canada (2002)

    Google Scholar 

  5. Draper, N.R., Smith, H.: Applied regression analysis. John Wiley, Chichester (1982)

    Google Scholar 

  6. Fraser, D.A.S.: Non-parametric Methods in Statistics. Wiley, New York (1957)

    Google Scholar 

  7. Gammerman, A., Vovk, V., Vapnik, V.: Learning by transduction. In: 14th Conference on Uncertainty in Artificial Intelligence, pp. 148–155 (1998)

    Google Scholar 

  8. Hahn, G.J., Meeker, W.Q.: Statistical Intervals: A Guide for Practitioners. Series in Probability and Statistics. John Wiley & Sons, Chichester (1991)

    MATH  Google Scholar 

  9. Nouretdinov, V.V.I., Gammerman, A.: Transductive confidence machine is universal. In: Gavaldá, R., Jantke, K.P., Takimoto, E. (eds.) ALT 2003. LNCS (LNAI), vol. 2842, p. 283. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  10. Karalic, A.: Linear regression in regression tree leaves. In: Proceedings of Int. School for Synthesis of Expert Knowledge, ISSEK 1992, pp. 151–163 (1992)

    Google Scholar 

  11. Loh, W.Y.: Regression trees with unbiased variable selection and interaction detection. Statistica Sinica 12, 361–386 (2002)

    MATH  MathSciNet  Google Scholar 

  12. Malerba, D., Esposito, F., Ceci, M., Appice, A.: Top down induction of model trees with regression and splitting nodes. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(5), 612–625 (2004)

    Article  Google Scholar 

  13. Melluish, T., Saunders, C., Nouretdinov, I., Vovk, V.: Comparing the bayes and typicalness frameworks. In: Flach, P.A., De Raedt, L. (eds.) ECML 2001. LNCS (LNAI), vol. 2167, Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  14. Papadopoulos, H., Proedrou, K., Vovk, V., Gammerman, A.: Inductive confidence machines for regression. In: Elomaa, T., Mannila, H., Toivonen, H. (eds.) ECML 2002. LNCS (LNAI), vol. 2430, pp. 345–356. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  15. Proedrou, K., Nouretdinov, I., Vovk, V., Gammerman, A.: Transductive confidence machines for pattern recognition (2001)

    Google Scholar 

  16. Quinlan, J.R.: Learning with continuous classes. In: Adams, Sterling (eds.) Proceedings of the 5th Australian Joint Conference on Artificial Intelligence, pp. 343–348. World Scientific, Singapore (1992)

    Google Scholar 

  17. Torgo, L.: Functional models for regression tree leaves. In: Fisher, D. (ed.) Proceedings of the Fourteenth International Conference on Machine Learning, ICML 1997, Nashville, Tennessee, pp. 385–393 (1997)

    Google Scholar 

  18. Torgo, L.: Inductive Learning of Tree-based Regression Models. PhD thesis, Department of Computer Science, University of Porto, Porto, Portugal (1999)

    Google Scholar 

  19. Wang, Y., Witten, I.H.: Inducing model trees for continuous classes. In: van Someren, M., Widmer, G. (eds.) ECML 1997. LNCS, vol. 1224, pp. 128–137. Springer, Heidelberg (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Appice, A., Ceci, M. (2006). Mining Tolerance Regions with Model Trees. In: Esposito, F., Raś, Z.W., Malerba, D., Semeraro, G. (eds) Foundations of Intelligent Systems. ISMIS 2006. Lecture Notes in Computer Science(), vol 4203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11875604_63

Download citation

  • DOI: https://doi.org/10.1007/11875604_63

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45764-0

  • Online ISBN: 978-3-540-45766-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics