Abstract
Over the last decade Inductive Logic Programming systems have been dominated by use of top-down refinement search techniques. In this paper we re-examine the use of bottom-up approaches to the construction of logic programs. In particular, we explore variants of Plotkin’s Relative Least General Generalisation (RLGG) which are based on subsumption relative to a bottom clause. With Plotkin’s RLGG, clause length grows exponentially in the number of examples. By contrast, in the Golem system, the length of ij-determinate RLGG clauses were shown to be polynomially bounded for given values of i and j. However, the determinacy restrictions made Golem inapplicable in many key application areas, including the learning of chemical properties from atom and bond descriptions. In this paper we show that with Asymmetric Relative Minimal Generalisations (or ARMGs) relative to a bottom clause, clause length is bounded by the length of the initial bottom clause. ARMGs, therefore do not need the determinacy restrictions used in Golem. An algorithm is described for constructing ARMGs and this has been implemented in an ILP system called ProGolem which combines bottom-clause construction in Progol with a Golem control strategy which uses ARMG in place of determinate RLGG. ProGolem has been evaluated on several well-known ILP datasets. It is shown that ProGolem has a similar or better predictive accuracy and learning time compared to Golem on two determinate real-world applications where Golem was originally tested. Moreover, ProGolem was also tested on several non-determinate real-world applications where Golem is inapplicable. In these applications, ProGolem and Aleph have comparable times and accuracies. The experimental results also suggest that ProGolem significantly outperforms Aleph in cases where clauses in the target theory are long and complex.
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References
Arias, M., Khardon, R.: Bottom-up ILP using large refinement steps. In: Camacho, R., King, R., Srinivasan, A. (eds.) ILP 2004. LNCS (LNAI), vol. 3194, pp. 26–43. Springer, Heidelberg (2004)
Badea, L., Stanciu, M.: Refinement operators can be (weakly) perfect. In: Džeroski, S., Flach, P.A. (eds.) ILP 1999. LNCS (LNAI), vol. 1634, pp. 21–32. Springer, Heidelberg (1999)
Basilio, R., Zaverucha, G., Barbosa, V.C.: Learning logic programs with neural networks. In: Rouveirol, C., Sebag, M. (eds.) ILP 2001. LNCS (LNAI), vol. 2157, pp. 15–26. Springer, Heidelberg (2001)
Botta, M., Giordana, A., Saitta, L., Sebag, M.: Relational learning as search in a critical region. J. Mach. Learn. Res. 4, 431–463 (2003)
Cheng, J., Hatzis, C., Hayashi, H., Krogel, M., Morishita, S., Page, D., Sese, J.: Kdd cup 2001 report. SIGKDD Explorations 3(2), 47–64 (2002)
King, R.D., Muggleton, S.H., Lewis, R., Sternberg, M.: Drug design by machine learning. Proceedings of the National Academy of Sciences 89(23), 11322–11326 (1992)
King, R.D., Srinivasan, A., Sternberg, M.J.E.: Relating chemical activity to structure: an examination of ILP successes. New Generation Computing 13, 411–433 (1995)
Kuwabara, M., Ogawa, T., Hirata, K., Harao, M.: On generalization and subsumption for ordered clauses. In: Washio, T., Sakurai, A., Nakajima, K., Takeda, H., Tojo, S., Yokoo, M. (eds.) JSAI Workshop 2006. LNCS (LNAI), vol. 4012, pp. 212–223. Springer, Heidelberg (2006)
Kuzelka, O., Zelezný, F.: Fast estimation of first-order clause coverage through randomization and maximum likelihood. In: Proceedings of the 25th International Conference (ICML 2008), pp. 504–511 (2008)
Lee, S.D., De Raedt, L.: Constraint Based Mining of First Order Sequences in SeqLog. In: Database Support for Data Mining Applications, pp. 155–176 (2003)
Maloberti, J., Sebag, M.: Fast theta-subsumption with constraint satisfaction algorithms. Machine Learning 55(2), 137–174 (2004)
Muggleton, S.: Progol datasets (1996), http://www.doc.ic.ac.uk/~shm/software/progol4.2/
Muggleton, S., Feng, C.: Efficient induction of logic programs. In: Muggleton, S. (ed.) Inductive Logic Programming, pp. 281–298. Academic Press, London (1992)
Muggleton, S.H.: Duce, an oracle based approach to constructive induction. In: IJCAI 1987, pp. 287–292. Kaufmann, San Francisco (1987)
Muggleton, S.H.: Inverse entailment and Progol. New Generation Computing 13, 245–286 (1995)
Muggleton, S.H., Buntine, W.: Machine invention of first-order predicates by inverting resolution. In: Proceedings of the 5th International Conference on Machine Learning, pp. 339–352. Kaufmann, San Francisco (1988)
Muggleton, S.H., King, R., Sternberg, M.: Protein secondary structure prediction using logic-based machine learning. Protein Engineering 5(7), 647–657 (1992)
Muggleton, S.H., Tamaddoni-Nezhad, A.: QG/GA: A stochastic search for Progol. Machine Learning 70(2-3), 123–133 (2007), doi:10.1007/s10994-007-5029-3
Nienhuys-Cheng, S.-H., de Wolf, R.: Foundations of Inductive Logic Programming. LNCS (LNAI), vol. 1228, pp. 168–169. Springer, Heidelberg (1997)
Nilsson, N.J.: Principles of Artificial Intelligence. Tioga, Palo Alto (1980)
Plotkin, G.D.: Automatic Methods of Inductive Inference. PhD thesis, Edinburgh University (August 1971)
Quinlan, J.R.: Learning logical definitions from relations. Machine Learning 5, 239–266 (1990)
De Raedt, L., Bruynooghe, M.: A theory of clausal discovery. In: Proceedings of the 13th International Joint Conference on Artificial Intelligence. Morgan Kaufmann, San Francisco (1993)
Richard, A.M., Williams, C.R.: Distributed structure-searchable toxicity (DSSTox) public database network: A proposal. Mutation Research 499, 27–52 (2000)
Shapiro, E.Y.: Algorithmic program debugging. MIT Press, Cambridge (1983)
Srinivasan, A., King, R.D., Muggleton, S.H., Sternberg, M.: Carcinogenesis predictions using ILP. In: Džeroski, S., Lavrač, N. (eds.) ILP 1997. LNCS, vol. 1297, pp. 273–287. Springer, Heidelberg (1997)
Srinivasan, A.: The Aleph Manual. University of Oxford (2007)
Tamaddoni-Nezhad, A., Muggleton, S.H.: The lattice structure and refinement operators for the hypothesis space bounded by a bottom clause. Machine Learning 76(1), 37–72 (2009)
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Muggleton, S., Santos, J., Tamaddoni-Nezhad, A. (2010). ProGolem: A System Based on Relative Minimal Generalisation. In: De Raedt, L. (eds) Inductive Logic Programming. ILP 2009. Lecture Notes in Computer Science(), vol 5989. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13840-9_13
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DOI: https://doi.org/10.1007/978-3-642-13840-9_13
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