Abstract
Logic Programs with Annotated Disjunctions (LPADs) provide a simple and elegant framework for representing probabilistic knowledge in logic programming. In this paper we consider the problem of learning ground LPADs starting from a set of interpretations annotated with their probability. We present the system ALLPAD for solving this problem. ALLPAD modifies the previous system LLPAD in order to tackle real world learning problems more effectively. This is achieved by looking for an approximate solution rather than a perfect one. A number of experiments have been performed on real and artificial data for evaluating ALLPAD, showing the feasibility of the approach.
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Blockeel, H. (2003). Prolog for first-order Bayesian networks: a meta-interpreter approach. In Proceedings of the second workshop on multi-relational data mining.
Blockeel, H. (2004). Probabilistic logical models for Mendel’s experiments: an exercise. In Proceedings of the fourteenth international conference on inductive logic programming, work in progress track.
Cussens, J. (2000). Stochastic logic programs: sampling, inference and applications. In Proceedings of the sixteenth conference on uncertainty in artificial intelligence (pp. 115–122). San Francisco: Kaufmann.
Dehaspe, L., & Raedt, L. D. (1996). DLAB: a declarative language bias formalism. In Z. W. Ras & M. Michalewicz (Eds.), Proceedings of the ninth international symposium on foundations of intelligent systems (pp. 613–622). Berlin: Springer.
Fierens, D., Blockeel, H., Ramon, J., & Bruynooghe, M. (2004). Logical Bayesian networks. In Proceedings of the third workshop on multi-relational data mining (pp. 19–30).
Getoor, L., Friedman, N., Koller, D., & Pfeffer, A. (2001). Learning probabilistic relational models. In S. Dzeroski & N. Lavrac (Eds.), Relational data mining. Berlin: Springer.
Greenberg, S. (1988). Using Unix: collected traces of 168 users (Tech. Rep. No. Research Report 88/333/45). Department of Computer Science, University of Calgary.
Gutmann, B., & Kersting, K. (2006). TildeCRF: conditional random fields for logical sequences. In Proceedings of the seventeenth European conference on machine learning. Berlin: Springer.
Jacobs, N., & Blockeel, H. (2003). User modeling with sequential data. In Proceedings of the tenth international conference on human–computer interaction (pp. 557–561). Mahwah: Lawrence Erlbaum Associates.
Kersting, K., & Gärtner, T. (2004). Fisher kernels for logical sequences. In Proceedings of the fifteenth European conference on machine learning (pp. 205–216). Berlin: Springer.
Kersting, K., & Raedt, L. D. (2000). Bayesian logic programs. In The tenth international conference on inductive logic programming, work in progress track. Available from http://SunSITE.Informatik.RWTH-Aachen.DE/Publications/CEUR-WS/Vol-35/.
Kersting, K., & Raedt, L. D. (2001a). Bayesian logic programs (Tech. rep. No. 151). Freiburg, Germany: Institute for Computer Science, University of Freiburg.
Kersting, K., & Raedt, L.D., (2001b). Towards combining inductive logic programming and Bayesian networks. In C. Rouveirol & M. Sebag (Eds.), Proceedings of the eleventh international conference on inductive logic programming. Berlin: Springer.
Kersting, K., & Raiko, T. (2005). ‘Say EM’ for selecting probabilistic models for logical sequences. In Proceedings of the twenty first conference on uncertainty in artificial intelligence. Arlington: AUAI Press.
Kersting, K., Raedt, L. D., & Raiko, T. (2006). Logical hidden Markov models. Journal of Artificial Intelligence Research, 25, 425–456.
Kersting, K., Raiko, T., Kramer, S., & Raedt, L. D. (2003). Towards discovering structural signatures of protein folds based on logical hidden Markov models. In Proceedings of the pacific symposium on biocomputing (pp. 192–203). Singapore: World Scientific Press.
Muggleton, S. H. (2000). Learning stochastic logic programs. Electronic Transactions in Artificial Intelligence, 4 (041). Available from http://www.ida.liu.se/ext/epa/cis/2000/041/tcover.html.
Poole, D. (1997). The independent choice logic for modelling multiple agents under uncertainty. Artificial Intelligence, 94(1–2), 7–56.
Riguzzi, F. (2004). Learning logic programs with annotated disjunctions. In Proceedings of the fourteenth international conference on inductive logic programming (pp. 270–287). Berlin: Springer.
Riguzzi, F. (2006). ALLPAD: approximate learning of logic programs with annotated disjunctions (Tech. Rep. No. CS-2006-01). University of Ferrara. Available from http://www.ing.unife.it/aree_ricerca/informazione/cs/technical_reports/CS-2006-01.pdf.
Santos Costa, V., Page, D., Qazi, M., & Cussens, J. (2003). CLP( \(\mathcal{BN}\) ): constraint logic programming for probabilistic knowledge. In Proceedings of the nineteenth conference on uncertainty in artificial intelligence. San Francisco: Kaufmann.
Sato, T. (1995). A statistical learning method for logic programs with distribution semantics. In Proceedings of the twelfth international conference on logic programming (pp. 715–729). Cambridge: MIT Press.
Sato, T., & Kameya, Y. (2001). Parameter learning of logic programs for symbolic-statistical modeling. Journal of Artificial Intelligence Research, 15, 391–454.
Stolle, C., Karwath, A., & Raedt, L. D. (2005). Cassic’cl: an integrated ILP system. In Proceedings of the eighth international conference on discovery science. Berlin: Springer.
Turcotte, M., Muggleton, S., & Sternberg, M. J. E. (2001). The effect of relational background knowledge on learning of protein three-dimensional fold signatures. Machine Learning, 43(1/2), 81–95.
Van Gelder, A., Ross, K. A., & Schlipf, J. S. (1991). The well-founded semantics for general logic programs. Journal of the ACM, 38(3), 620–650.
Vennekens, J., & Verbaeten, S. (2003). Logic programs with annotated disjunctions (Tech. Rep. No CW386). K.U. Leuven. Available from http://www.cs.kuleuven.ac.be/~joost/techrep.ps.
Vennekens, J., Verbaeten, S., & Bruynooghe, M., (2004). Logic programs with annotated disjunctions. In Proceedings of the twentieth international conference on logic programming. Berlin: Springer.
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Editors: Stephen Muggleton, Ramon Otero, Simon Colton.
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Riguzzi, F. ALLPAD: approximate learning of logic programs with annotated disjunctions. Mach Learn 70, 207–223 (2008). https://doi.org/10.1007/s10994-007-5032-8
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DOI: https://doi.org/10.1007/s10994-007-5032-8