Machine Learning

, Volume 44, Issue 3, pp 211–243 | Cite as

On Exact Learning of Unordered Tree Patterns

  • Thomas R. Amoth
  • Paul Cull
  • Prasad Tadepalli
Article

Abstract

Tree patterns are natural candidates for representing rules and hypotheses in many tasks such as information extraction and symbolic mathematics. A tree pattern is a tree with labeled nodes where some of the leaves may be labeled with variables, whereas a tree instance has no variables. A tree pattern matches an instance if there is a consistent substitution for the variables that allows a mapping of subtrees to matching subtrees of the instance. A finite union of tree patterns is called a forest. In this paper, we study the learnability of tree patterns from queries when the subtrees are unordered. The learnability is determined by the semantics of matching as defined by the types of mappings from the pattern subtrees to the instance subtrees. We first show that unordered tree patterns and forests are not exactly learnable from equivalence and subset queries when the mapping between subtrees is one-to-one onto, regardless of the computational power of the learner. Tree and forest patterns are learnable from equivalence and membership queries for the one-to-one into mapping. Finally, we connect the problem of learning tree patterns to inductive logic programming by describing a class of tree patterns called Clausal trees that includes non-recursive single-predicate Horn clauses and show that this class is learnable from equivalence and membership queries.

ILP tree patterns exact learning learning from queries 

References

  1. Amoth, T. R., Cull, P., & Tadepalli, P. (1998). Exact learning of tree patterns from queries and counterexamples. In Proceedings of the Eleventh Annual Conference on Computational Learning Theory, (pp. 175–186). New York, NY: ACM.Google Scholar
  2. Amoth, T. R., Cull, P., & Tadepalli. P. (1999). Exact learning of unordered tree patterns from queries. In Proceedings of the Twelth Annual Conference on Computational Learning Theory (pp. 323–332). New York, NY: ACM.Google Scholar
  3. Angluin, D. (1980). Finding patterns common to a set of strings. J. of Comp. and Syst. Sciences, 21, 46–62.Google Scholar
  4. Angluin, D. (1988). Queries and concept learning. Machine Learning, 2:4, 319–342.Google Scholar
  5. Arimura, H., Ishizaka. H., & Shinohara, T. (1995). Learning unions of tree patterns using queries'. In Proceedings of the 6th ALT (Algorithmic Learning Theory) (pp. 66–79). SpringerVerlag. Lecture Notes in Artificial Intelligence 997.Google Scholar
  6. De Raedt, L. (1997). Logical settings for concept learning. Artificial Intelligence, 95:1, 187–201.Google Scholar
  7. Garey, M., & Johnson, D. (1979). Computers and Intractability: A Guide to Theory of NP-completeness. New York, NY: W.H. Freeman.Google Scholar
  8. Goldman, S. A., & Kwek, S. S.(1999). On learning unions of pattern languages and tree patterns. In Proceedings of the 10th ALT (Algorithmic Learning Theory) (pp. 347–363). Springer Verlag. Lecture Notes in Artificial Intelligence 1720.Google Scholar
  9. Gottlob, G. (1987). Subsumption and implication. Information Processing Letters, 24:2, 109–111.Google Scholar
  10. Hellerstein, L., Pillaipakkamnatt, K., Raghavan, V., & Wilkins, D. (1996). How many queries are needed to learn?. Journal of the Association for Computing Machinery, 43:4–6, 840–862.Google Scholar
  11. Ko, K.-I., Marron, A., & Tzeng, W.-G. (1990). Learning string patterns and tree patterns from examples. In B.W. Porter, & R. J. Mooney (Eds.), Proceedings of the Seventh International Conference on Machine Learning (pp. 384–391). San Mateo, CA: Morgan Kaufmann.Google Scholar
  12. Lange, S., & Wiehagen, R. (1991). Polynomial-time inference of arbitrary pattern languages. New Generation Computing, 8, 361–370.Google Scholar
  13. Page, C. D. (1993). Anti-unification in constraint logics: Foundations and applications to learnability in first-order logic, to speed-up learning, and to deduction. Ph.D. Thesis, University of Illinois, Urbana, IL.Google Scholar
  14. Page, C. D., & Frisch, A. M. (1992). Generalization and learnability: A study of constrained atoms. In S. H. Muggleton (Ed.), Inductive Logic Programming. London: Academic Press.Google Scholar
  15. Plotkin, G. (1970). A Note on inductive generalization. In B. Meltzer, & D. Michie (Eds.), Machine intelligence (Vol. 5). New York, NY: Elsevier North-Holland.Google Scholar
  16. Reddy, C., & Tadepalli, P. (1999). Learning horn definitions: Theory and an application to planning. New Generation Computing, 17:1, 77–98.Google Scholar
  17. Schapire, R. E. (1990). Pattern languages are not learnable. In Conference on Computational Learning Theory (pp. 122–129). San Mateo, CA: Morgan Kaufmann.Google Scholar
  18. Valiant, L. (1984). A Theory of the learnable. Communications of the ACM, 27:11, 1134–1142.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Thomas R. Amoth
    • 1
  • Paul Cull
    • 1
  • Prasad Tadepalli
    • 1
  1. 1.Department of Computer ScienceOregon State UniversityCorvallisUSA

Personalised recommendations