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Nested hyper-rectangles for exemplar-based learning

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Analogical and Inductive Inference (AII 1989)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 397))

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Abstract

Exemplar-based learning is a theory in which learning is accomplished by storing points in Euclidean n-space, E n. This paper presents a new theory in which these points are generalized to become hyper-rectangles. These hyper-rectangles, in turn, may be nested to arbitrary depth inside one another. This representation scheme is sharply different from the usual inductive learning paradigms, which learn by replacing boolean formulae by more general formulae, or by creating decision trees. The theory is described and then compared to other inductive learning theories. An implementation, Each, has been tested empirically on three different domains: predicting the recurrence of breast cancer, classifying iris flowers, and predicting survival times for heart attack patients. In each case, the results are compared to published results using the same data sets and different machine learning algorithms. Each performs as well as or better than other algorithms on all of the data sets.

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References

  • Aha, D. and Kibler, D. (1989) Noise-Tolerant Instance-Based Learning Algorithms. Proceedings of the International Joint Conference on Artificial Intelligence, Morgan Kaufmann Publishers.

    Google Scholar 

  • Blumer, A., Ehrenfeucht, A., Haussler, D., and Warmuth, M. (1987) Learnability and the Vapnik-Chervonenkis Dimension. Technical Report UCSC-CRL-87-20, University of California, Santa Cruz, CA.

    Google Scholar 

  • Breiman, L., Friedman, J., Olshen, R., and Stone, C. (1984) Classification and Regression Trees, Belmont: Wadsworth.

    Google Scholar 

  • Buchanan, Bruce, and Mitchell, Tom (1978) Model-directed learning of production rules. In Waterman, D. and Hayes-Roth, F. (eds.), Pattern-Directed Inference Systems. New York: Academic Press.

    Google Scholar 

  • Bundy, A., Silver, B., and Plummer, D. (1985) An Analytical Comparison of Some Rule-Learning Programs. Artificial Intelligence, 27, 137–181.

    Google Scholar 

  • Crawford, Stuart (1989) Extensions to the CART Algorithm. The International Journal of Man-Machine Studies, to appear.

    Google Scholar 

  • Everitt, Brian (1980) Cluster Analysis. Gower Publishing Co. Ltd., Hampshire, England.

    Google Scholar 

  • Fisher, R. A. The Use of Multiple Measurements in Taxonomic Problems. Annals of Eugenics 7:1, 1936.

    Google Scholar 

  • Helmbold, D., Sloan, R., and Warmuth, M. Bootstrapping One-sided Learning. Unpublished manuscript, 1988.

    Google Scholar 

  • Kahneman, D., Slovic, P., and Tversky, A. (1982) Judgement under uncertainty: Heuristics and biases. Cambridge, England: Cambridge University Press.

    Google Scholar 

  • Kan, G., Visser, C., Koolen, J., and Dunning, A. (1986) Short and long term predictive value of wall motion score in acute myocardial infarction. British Heart Journal, 56, 422–427.

    Google Scholar 

  • Kinney, Evlin (1988) Personal communication.

    Google Scholar 

  • Larson, J. (1977) INDUCE-1: An Interactive Inductive Inference Program in VL21 Logic System. Report UIUCDCS-R-77-876, Computer Science Dept., U. of Illinois.

    Google Scholar 

  • Medin, Douglas and Schaffer, Marguerite (1978) Context theory of classification learning. Psychological Review, 85:3, 207–238.

    Google Scholar 

  • Michalski, R., Carbonell, J., and Mitchell, T. (eds.) (1983) Machine Learning, Tioga Publishing Co.

    Google Scholar 

  • Michalski, R., Mozetic, I., Hong, J., and Lavrac, N. (1986) The Multi-Purpose Incremental Learning System AQ15 and Its Testing Application to Three Medical Domains. Proceedings of AAAI-86, Philadelphia, Pennsylvania, 1041–1045.

    Google Scholar 

  • Mitchell, Tom Version Spaces: An approach to concept learning. Ph.D. thesis, Stanford University (CS-78-711), 1978.

    Google Scholar 

  • Mitchell, T., Mahadevan, S., and Steinberg, L. (1985) LEAP: A Learning Apprentice for VLSI Design. Proceedings of IJCAI-85, Los Angeles, California, 573–580.

    Google Scholar 

  • Mooney, Raymond, and DeJong, Gerald (1985) Learning Schemata for Natural Language Processing. Proceedings of IJCAI-85, Los Angeles, California, 681–687.

    Google Scholar 

  • Quinlan, J. R. (1986) Induction of Decision Trees. Machine Learning 1:1, 81–106.

    Google Scholar 

  • Salzberg, Steven (1985) Heuristics for Inductive Learning. Proceedings of IJCAI-85, Los Angeles, California, 603–610.

    Google Scholar 

  • Salzberg, Steven (1986) Pinpointing Good Hypotheses with Heuristics. In Artificial Intelligence and Statistics, W. Gale (ed.), Addison-Wesley, 133–159.

    Google Scholar 

  • Salzberg, Steven (1988) Exemplar-based learning: theory and implementation. Technical Report TR-10-88, Center for Research in Computing Technology, Harvard University.

    Google Scholar 

  • Thornton, Chris (1987) Hypercuboid Formation Behaviour of Two Learning Algorithms. Proceedings of IJCAI-87, Milan, Italy, 301–303.

    Google Scholar 

  • Valiant, Leslie (1984) A Theory of the Learnable. Communications of the ACM, 27:11, 1134–1142.

    Google Scholar 

  • Valiant, Leslie (1985) Learning Disjunctions of Conjunctions. Proceedings of IJCAI-85, Los Angeles, California, 560–566.

    Google Scholar 

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Klaus P. Jantke

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© 1989 Springer-Verlag Berlin Heidelberg

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Salzberg, S. (1989). Nested hyper-rectangles for exemplar-based learning. In: Jantke, K.P. (eds) Analogical and Inductive Inference. AII 1989. Lecture Notes in Computer Science, vol 397. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51734-0_61

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  • DOI: https://doi.org/10.1007/3-540-51734-0_61

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51734-4

  • Online ISBN: 978-3-540-46798-4

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