Learning Ground CP-Logic Theories by Leveraging Bayesian Network Learning Techniques

• Autorzy: Meert W. , Struyf J. , Blockeel H.
• Języki publikacji: EN

Abstrakty

EN

Causal relations are present in many application domains. Causal Probabilistic Logic (CP-logic) is a probabilistic modeling language that is especially designed to express such relations. This paper investigates the learning of CP-logic theories (CP-theories) from training data. Its first contribution is SEM-CP-logic, an algorithm that learns CP-theories by leveraging Bayesian network (BN) learning techniques. SEM-CP-logic is based on a transformation between CP-theories and BNs. That is, the method applies BN learning techniques to learn a CP-theory in the form of an equivalent BN. To this end, certain modifications are required to the BN parameter learning and structure search, the most important one being that the refinement operator used by the search must guarantee that the constructed BNs represent valid CP-theories. The paper’s second contribution is a theoretical and experimental comparison between CP-theory and BN learning. We show that the most simple CP-theories can be represented with BNs consisting of noisy-OR nodes, while more complex theories require close to fully connected networks (unless additional unobserved nodes are introduced in the network). Experiments in a controlled artificial domain show that in the latter cases CP-theory learning with SEM-CP-logic requires fewer training data than BN learning. We also apply SEM-CP-logic in a medical application in the context of HIV research, and show that it can compete with state-of-the-art methods in this domain.

Słowa kluczowe

EN

Statistical Relational Learning; CP-logic

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2008
• Tom: Vol. 89, nr 1
• Strony: 131--160
• Opis fizyczny: bibliogr. 32 poz., tab., wykr.

Twórcy

autor

Meert W.

autor

Struyf J.

autor

Blockeel H.

• Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, 3001 Leuven, Belgium,

Bibliografia

• [1] Beerenwinkel, N., Rahnenfuhrer, J., Daumer, M., Hoffmann, D., Kaiser, R., Selbig, J., Lengauer, T.: Learning multiple evolutionary pathways from cross-sectional data., Journal of Computational Biology, 12(6), 2005, 584-598.
• [2] Blockeel, H., Meert, W.: Towards learning non-recursive LPADs by transforming them into Bayesian networks, Inductive Logic Programming, ILP 2006, Revised Selected Papers, LNCS 4455, Springer, 2007.
• [3] Breese, J., Goldman, R., Wellman, M.: Introduction to the special section on knowledge-based construction of probabilistic and decision models, IEEE Transactions on Systems, Man, and Cybernetics, 24(11), 1994, 1577-1579.
• [4] De Raedt, L., Kimmig, A., Toivonen, H.: ProbLog: A Probabilistic Prolog and its Application in Link Discovery, Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI07), 2007.
• [5] Dempster, N., Laird, A., Rubin, D.: Maximum likelihood from incomplete data via the EM algorithm, J. R. Statist. Soc. B, 39, 1977, 185-197.
• [6] Fierens, D., Blockeel, H., Ramon, J., Bruynooghe, M.: Logical Bayesian networks, Proceedings of the 3rd international workshop on multi-relational data mining, 2004.
• [7] Friedman, N.: Learning belief networks in the presence of missing values and hidden variables, Proceedings of the 14th International Conference on Machine Learning (ICML97), Morgan Kaufmann, 1997.
• [8] Friedman, N., Getoor, L., Koller, D., Pfeffer, A.: Learning Probabilistic Relational Models, Proceedings of the 17th International Joint Conference on Artificial Intelligence (IJCAI01), 2001.
• [9] Gaitanis, K.: Open Bayes for Python, http://www.openbayes.org/, 2007.
• [10] Getoor, L., Taskar, B., Eds.: Statistical Relational Learning, MIT Press, 2007.
• [11] Heckerman, D., Brees, J. S.: Causal independence for probability assessment and inference using Bayesian networks, IEEE Transactions on Systems, Man & Cybernetics, Part A (Systems & Humans), 26(6), 1994, 826-831.
• [12] Heckerman, D., Geiger, D., Chickering, D. M.: Learning Bayesian networks: The combination of knowledge and statistical data, Proceedings of the 11th Conference on Uncertainty in Artificial Intelligence (UAI95), Morgan Kaufmann, 1995.
• [13] Jaeger, M.: Parameter learning for relational Bayesian networks, Proceedings of the 24th International Conference on Machine Learning (ICML07), ACM Press New York, NY, USA, 2007.
• [14] Kersting, K., De Raedt, L.: Basic Principles of Learning Bayesian Logic Programs, Probabilistic Inductive Logic Programming, 2008, 189-221.
• [15] Leray, P., Francois, O.: BNT Structure Learning Package: Documentation and Experiments, Technical report, Laboratoire PSI, 2004.
• [16] Muggleton, S.: Learning Stochastic Logic Programs, Proceedings of the AAAI2000 Workshop on Learning Statistical Models from Relational Data, 2000.
• [17] Muggleton, S., Buntine,W.: Machine invention of first-order predicates by inverting resolution., Proceedings of the 5th International Conference on Machine Learning (ICML88), Morgan Kaufmann, 1988.
• [18] Murphy, K. P.: Bayesian Network Toolbox, http://bnt.sourceforge.net/, 2007.
• [19] Natarajan, S., Tadepalli, P., Altendorf, E., Dietterich, T., Fern, A., Restificar, A.: Learning first-order probabilistic models with combining rules, Proceedings of the 22nd International Conference on Machine Learning (ICML05), 119, ACM Press New York, NY, USA, 2005.
• [20] Neapolitan, R.: Learning Bayesian Networks, Prentice Hall, 2003.
• [21] Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann, 1988.
• [22] Pearl, J.: Causality: Models, Reasoning, and Inference, Cambridge University Press, 2000.
• [23] Poole, D.: The independent choice logic for modelling multiple agents under uncertainty, Artificial Intelligence, 94(1-2), 1997, 7-56.
• [24] Poole, D., Zhang, N.: Exploiting contextual independence in probabilistic inference, Journal of Artificial Intelligence Research, 18, 2003, 263-313.
• [25] Richardson, M., Domingos, P.: Markov logic networks, Machine Learning, 62(1), 2006, 107-136.
• [26] Riguzzi, F.: Learning logic programs with annotated disjunctions, 14th Internation Conference on Inductive Logic Programming (ILP04), LNCS 4455, Springer, 2004.
• [27] Riguzzi, F.: ALLPAD: Approximate learning of logic programs with annotated disjunctions, Machine Learning, 70, 2008, 207-223.
• [28] Sato, T., Kameya, Y.: New Advances in Logic-Based Probabilistic Modeling by PRISM, chapter 6, APRIL, 2007.
• [29] Vennekens, J.: Algebraic and Logical Study of Constructive Processes in Knowledge Representation, Ph.D. Thesis, Department of Computer Science, K.U.Leuven, May 2007.
• [30] Vennekens, J., Denecker, M., Bruynooghe, M.: Representing causal information about a probabilistic process, Logics in Artificial Intelligence, 10th European Conference, Proceedings, LNCS 4160, Springer, 2006.
• [31] Vennekens, J., Verbaeten, S., Bruynooghe, M.: Logic Programs with Annotated Disjunctions, Technical report, KULeuven, 2004.
• [32] Vomlel, J.: Noisy-or classifier, International Journal of Intelligent Systems, 21(3), 2006, 381-398.