Abstract
In this paper, we propose an example representation system that combines a greater expressive richness than that of the Boolean framework and an analogous treatment complexity. The model we have chosen is algebraic, and has been used up to now to cope with program semantics [4]. The examples are represented by labelled, recursive typed trees. A signature enables us to define the set of all allowed (partial or complete) representations. This model properly contains Boolean representations. We show that in the PAC framework defined by Valiant [10], the extensions to this model of two Boolean formula classes: k-DNF and k-DL, remain polynomially learnable.
Chapter PDF
Similar content being viewed by others
References
Blumer, A., Ehrenfeucht, A., Haussler, D. and Warmuth, M.K. (1986). Classifying learnable geometric concepts with the Vapnik-Chervonenkis dimension. Proceedings of the Eighteenth Annual ACM Symposium on Theory of Computing. 273–282.
Courcelle, B. (1986). Equivalences and transformations of regular systems — applications to recursive program schemes and grammars, Theoretical Computer Science 42(1), 1–122.
Cohen, W.W. (1993). Pac-Learning a Restricted Class of Recursive Logic Programs. Proceedings of the Tenth National Conference on Artificial Intelligence. 86–92.
Goguen, J.A., Thatcher, J.W., Wagner, E.G. and Wright, J.B. (1977). Initial algebra semantics and continuous algebras, Journal A.C.M. 24 (1), 68–95.
Gold, M. (1978). Complexity of automaton identification from given data, Information and control 37, 302–320.
Haussler, D. (1989). Learning conjunctive concepts in structural domains, Machine Learning 4,7–40.
Jappy, P., Daniel-Vatonne, M.C., Gascuel, O. and de la Higuera., C. (1993). Learning from Recursive, Tree Structured Examples. Rapport de Recherche LIRMM. No 93040.
Muggleton, S.H. (1992). Inductive Logic Programming. Academic Press.
Rivest, R.L. (1987). Learning decision list, Machine Learning 2(3), 229–246.
Valiant, L.G. (1984). A theory of the learnable. ACM Com. 27, 1134–1142.
Winston, P.H. (1975). Learning Structural descriptions from Examples, in The psychology of computer vision, Winston, P. H. (Ed.), Mc Graw Hill, New York, 157–209.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jappy, P., Daniel-Vatonne, M.C., Gascuel, O., de la Higuera, C. (1994). Learning from recursive, tree structured examples. In: Bergadano, F., De Raedt, L. (eds) Machine Learning: ECML-94. ECML 1994. Lecture Notes in Computer Science, vol 784. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57868-4_75
Download citation
DOI: https://doi.org/10.1007/3-540-57868-4_75
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57868-0
Online ISBN: 978-3-540-48365-6
eBook Packages: Springer Book Archive