Abstract
This paper presents a new reduction algorithm which employs Constraint Satisfaction Techniques for removing redundant literals of a clause efficiently. Inductive Logic Programming (ILP) learning algorithms using a generate and test approach produce hypotheses with redundant literals. Since the reduction is known to be a co-NP-complete problem, most algorithms are incomplete approximations. A complete algorithm proposed by Gottlob and Fermüller is optimal in the number of θ-subsumption calls. However, this method is inefficient since it exploits neither the result of the θ-subsumption nor the intermediary results of similar θ-subsumption calls. Recently, Hirata has shown that this problem is equivalent to finding a minimal solution to a θ-subsumption of a clause with itself, and proposed an incomplete algorithm based on a θ-subsumption algorithm of Scheffer. This algorithm has a large memory consumption and performs many unnecessary tests in most cases. In this work, we overcome this problem by transforming the θ-subsumption problem in a Constraint Satisfaction Problem, then we use an exhaustive search algorithm in order to find a minimal solution. The experiments with artificial and real data sets show that our algorithm outperforms the algorithm of Gottlob and Fermüller by several orders of magnitude, particularly in hard cases.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bessière, C., Régin, J.-C.: MAC and combined heuristics: Two reasons to forsake FC (and CBJ?) on hard problems. In: Freuder, E.C. (ed.) CP 1996. LNCS, vol. 1118, pp. 61–75. Springer, Heidelberg (1996)
De Raedt, L., Bruynooghe, M.: A theory of clausal discovery. In: Proc. Thirteenth International Joint Conference on Artificial Intelligence, pp. 1058–1063. Morgan-Kaufmann, San Francisco (1993)
Dehaspe, L., De Raedt, L.: Mining association rules in multiple relations. In: Džeroski, S., Lavrač, N. (eds.) ILP 1997. LNCS, vol. 1297, pp. 125–132. Springer, Heidelberg (1997)
Ferilli, S., Di Mauro, N., Basile, T.M.A., Esposito, F.: A complete subsumption algorithm. In: Cappelli, A., Turini, F. (eds.) AI*IA 2003. LNCS, vol. 2829, pp. 1–13. Springer, Heidelberg (2003)
Gent, I.P., MacIntyre, E., Prosser, P., Walsh, T.: The constrainedness of search. In: AAAI/IAAI, vol. 1, pp. 246–252 (1996)
Gottlob, G., Fermüller, C.G.: Removing redundancy from a clause. Artificial Intelligence 61(2), 263–289 (1993)
Haralick, R.M., Eliott, G.L.: Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence 14(1), 263–313 (1980)
Hirata, K.: On condensation of a clause. In: Horváth, T., Yamamoto, A. (eds.) ILP 2003. LNCS (LNAI), vol. 2835, pp. 164–179. Springer, Heidelberg (2003)
Kietz, J.-U., Lübbe, M.: An efficient subsumption algorithm for inductive logic programming. In: Cohen, W.W., Hirsh, H. (eds.) Proc. Eleventh International Conference on Machine Learning, pp. 130–138. Morgan-Kaufmann, San Francisco (1994)
King, R.D., Karwath, A., Clare, A., Dephaspe, L.: Genome scale prediction of protein functional class from sequence using data mining. In: Proc. Sixth ACM SIGKDD international conference on Knowledge Discovery and Data mining, pp. 384–389. ACM Press, New York (2000)
Mackworth, K.: Consistency in networks of relations. Artificial Intelligence 8(1), 99–118 (1977)
Maloberti, J., Sebag, M.: Theta-subsumption in a constraint satisfaction perspective. In: Rouveirol, C., Sebag, M. (eds.) ILP 2001. LNCS (LNAI), vol. 2157, pp. 164–178. Springer, Heidelberg (2001)
Maloberti, J., Sebag, M.: Fast theta-subsumption with constraint satisfaction algorithms. Machine Learning Journal 55(2), 137–174 (2004)
Maloberti, J., Suzuki, E.: Improving efficiency of frequent query discovery by eliminating non-relevant candidates. In: Grieser, G., Tanaka, Y., Yamamoto, A. (eds.) DS 2003. LNCS (LNAI), vol. 2843, pp. 220–232. Springer, Heidelberg (2003)
Muggleton, S., Feng, C.: Efficient induction of logic programs. In: Proc. First Conference on Algorithmic Learning Theory, Ohmsma, Tokyo, Japan, pp. 368–381 (1990)
Plotkin, G.D.: A note on inductive generalization. In: Machine Intelligence, vol. 5, pp. 153–163. Edinburgh University Press, Edinburgh (1970)
Reddy, C., Tadepalli, P.: Learning first-order acyclic horn programs from entailment. In: Page, D.L. (ed.) ILP 1998. LNCS, vol. 1446, pp. 23–37. Springer, Heidelberg (1998)
Santos Costa, V., Srinivasan, A., Camacho, R., Blockeel, H., Demoen, B., Janssens, G., Struyf, J., Vandecasteele, H., Van Laer, W.: Query transformations for improving the efficiency of ILP systems. Journal of Machine Learning Research 4, 465–491 (2003)
Scheffer, T., Herbrich, R., Wysotzki, F.: Efficient θ-subsumption based on graph algorithms. In: Proc. Seventh International Workshop on Inductive Logic Programming, pp. 212–228. Springer, Berlin (1997)
Srinivasan, A., King, R.D., Muggleton, S.H., Sternberg, M.: The predictive toxicology evaluation challenge. In: Proc. Fifteenth International Joint Conference on Artificial Intelligence (IJCAI 1997), pp. 1–6. Morgan-Kaufmann, San Francisco (1997)
Srinivasan, S.H., Muggleton, M.J.E.: Sternberg, and R. D. King. Theories for mutagenicity: a study in first order and feature-based induction. Artificial Intelligence 85(1-2), 277–299 (1996)
Tsang, E.: Foundations of Constraint Satisfaction. Academic Press, London (1993)
Ullman, J.D.: Principles of Database and Knowledge-Base Systems, vol. I. Computer Science Press, Rockville (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Maloberti, J., Suzuki, E. (2004). An Efficient Algorithm for Reducing Clauses Based on Constraint Satisfaction Techniques. In: Camacho, R., King, R., Srinivasan, A. (eds) Inductive Logic Programming. ILP 2004. Lecture Notes in Computer Science(), vol 3194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30109-7_19
Download citation
DOI: https://doi.org/10.1007/978-3-540-30109-7_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22941-4
Online ISBN: 978-3-540-30109-7
eBook Packages: Springer Book Archive