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.
Preview
Unable to display preview. Download preview PDF.
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.
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.
Breiman, L., Friedman, J., Olshen, R., and Stone, C. (1984) Classification and Regression Trees, Belmont: Wadsworth.
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.
Bundy, A., Silver, B., and Plummer, D. (1985) An Analytical Comparison of Some Rule-Learning Programs. Artificial Intelligence, 27, 137–181.
Crawford, Stuart (1989) Extensions to the CART Algorithm. The International Journal of Man-Machine Studies, to appear.
Everitt, Brian (1980) Cluster Analysis. Gower Publishing Co. Ltd., Hampshire, England.
Fisher, R. A. The Use of Multiple Measurements in Taxonomic Problems. Annals of Eugenics 7:1, 1936.
Helmbold, D., Sloan, R., and Warmuth, M. Bootstrapping One-sided Learning. Unpublished manuscript, 1988.
Kahneman, D., Slovic, P., and Tversky, A. (1982) Judgement under uncertainty: Heuristics and biases. Cambridge, England: Cambridge University Press.
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.
Kinney, Evlin (1988) Personal communication.
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.
Medin, Douglas and Schaffer, Marguerite (1978) Context theory of classification learning. Psychological Review, 85:3, 207–238.
Michalski, R., Carbonell, J., and Mitchell, T. (eds.) (1983) Machine Learning, Tioga Publishing Co.
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.
Mitchell, Tom Version Spaces: An approach to concept learning. Ph.D. thesis, Stanford University (CS-78-711), 1978.
Mitchell, T., Mahadevan, S., and Steinberg, L. (1985) LEAP: A Learning Apprentice for VLSI Design. Proceedings of IJCAI-85, Los Angeles, California, 573–580.
Mooney, Raymond, and DeJong, Gerald (1985) Learning Schemata for Natural Language Processing. Proceedings of IJCAI-85, Los Angeles, California, 681–687.
Quinlan, J. R. (1986) Induction of Decision Trees. Machine Learning 1:1, 81–106.
Salzberg, Steven (1985) Heuristics for Inductive Learning. Proceedings of IJCAI-85, Los Angeles, California, 603–610.
Salzberg, Steven (1986) Pinpointing Good Hypotheses with Heuristics. In Artificial Intelligence and Statistics, W. Gale (ed.), Addison-Wesley, 133–159.
Salzberg, Steven (1988) Exemplar-based learning: theory and implementation. Technical Report TR-10-88, Center for Research in Computing Technology, Harvard University.
Thornton, Chris (1987) Hypercuboid Formation Behaviour of Two Learning Algorithms. Proceedings of IJCAI-87, Milan, Italy, 301–303.
Valiant, Leslie (1984) A Theory of the Learnable. Communications of the ACM, 27:11, 1134–1142.
Valiant, Leslie (1985) Learning Disjunctions of Conjunctions. Proceedings of IJCAI-85, Los Angeles, California, 560–566.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/3-540-51734-0_61
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51734-4
Online ISBN: 978-3-540-46798-4
eBook Packages: Springer Book Archive