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Infinite probability computation by cyclic explanation graphs

Published online by Cambridge University Press:  04 November 2013

TAISUKE SATO  and
PHILIPP MEYER
TAISUKE SATO
Affiliation:
Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro, Tokyo, Japan (e-mail: sato@mi.cs.titech.ac.jp)
PHILIPP MEYER
Affiliation:
Technical University Munich, Munich, Germany (e-mail: meyerphi@in.tum.de)
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Abstract

Tabling in logic programming has been used to eliminate redundant computation and also to stop infinite loop. In this paper we investigate another possibility of tabling, i.e. to compute an infinite sum of probabilities for probabilistic logic programs. Using PRISM, a logic-based probabilistic modeling language with a tabling mechanism, we generalize prefix probability computation for probabilistic context-free grammars (PCFGs) to probabilistic logic programs. Given a top-goal, we search for all proofs with tabling and obtain an explanation graph which compresses them and may be cyclic. We then convert the explanation graph to a set of linear probability equations and solve them by matrix operation. The solution gives us the probability of the top-goal, which, in nature, is an infinite sum of probabilities. Our general approach to prefix probability computation through tabling not only allows to deal with non-probabilistic context-free grammars such as probabilistic left-corner grammars but has applications such as plan recognition and probabilistic model checking and makes it possible to compute probability for probabilistic models describing cyclic relations.

Keywords

tablingprobability computationprefixprobability equation
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 14 , Issue 6 , November 2014 , pp. 909 - 937
Copyright
Copyright © Cambridge University Press 2013 

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References

Amft, O., Kusserow, M. and Troster, G. 2007. Probabilistic parsing of dietary activity events. In Proceedings of the International Workshop on Wearable and Implantable Body Sensor Networks, Aachen, Germany, 2007, Springer IFMBE Proceedings, vol. 13, 242–247.Google Scholar
Baker, J. K. 1979. Trainable grammars for speech recognition. In Proceedings of Spring Conference of the Acoustical Society of America, 547–550.Google Scholar
Bobick, A. and Ivanov, Y. 1998. Action recognition using probabilistic parsing. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'98), 196–202.Google Scholar
De Raedt, L., Kimmig, A. and Toivonen, H. 2007. ProbLog: A probabilistic Prolog and its application in link discovery. In Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI'07), 2468–2473.Google Scholar
Etessami, K. and Yannakakis, M. 2009. Recursive Markov chains, stochastic grammars, and monotone systems of nonlinear equations. Journal of ACM 56, 1.Google Scholar
Geib, C. and Goldman, R. 2011. Reorgnizing plans with loops represented in a lexicalized grammar. In Proceedings of the Twenty-Fifth AAAI Conference on Artificial Intelligence (AAAI'11), 958–963.Google Scholar
Gorlin, A., Ramakrishnan, C. and Smolka, S. 2012. Model checking with probabilistic tabled logic programming. Theory and Practice of Logic Programming (TPLP) 12, 4–5, 681–700.Google Scholar
Hinton, A., Kwiatkowska, M., Norman, G. and Parker, D. 2006. PRISM: A tool for automatic verification of probabilistic systems. In Proceedings of the 12th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS'06), LNCS, vol. 3920. Springer, New York, 441–444.Google Scholar
Jelinek, F. and Lafferty, J. 1991. Computation of the probability of initial substring generation by stochastic context-free grammars. Computational Linguistics 17, 3, 315–323.Google Scholar
Kameya, Y. and Sato, T. 2000. Efficient EM learning for parameterized logic programs. In Proceedings of the 1st Conference on Computational Logic (CL'00), Lecture Notes in Artificial Intelligence, vol. 1861. Springer, New York, 269–294.Google Scholar
Kwiatkowska, M., Norman, G. and Parker, D. 2011. PRISM 4.0: Verification of probabilistic real-time systems. In Proceeding of the 23rd International Conference on Computer Aided Verification (CAV'11), Gopalakrishnan, G. and Qadeer, S., Eds., LNCS, vol. 6806. Springer, New York, 585–591.Google Scholar
Lymberopoulos, D., Teixeira, T. and Savvides, A. 2007. Detecting patterns for assisted living using sensor networks: A case study. In Proceedings of the 2007 International Conference on Sensor Technologies and Applications (SENSORCOMM '07), 590–596.Google Scholar
Manning, C. 1997. Probabilistic parsing using left corner language models. In Proceedings of the 5th International Conference on Parsing Technologies (IWPT-97). MIT Press, Cambridge, MA, 147–158.Google Scholar
Manning, C. D. and Schütze, H. 1999. Foundations of Statistical Natural Language Processing. MIT Press, Cambridge, MA, USA.Google Scholar
Mantadelis, T. and Janssens, G. 2010. Dedicated tabling for a probabilistic setting. In Proceedings of the 26th International Conference on Logic Programming (ICLP'10) (Technical Communications), 124–133.Google Scholar
Meyer, C., Ed. 2000. Matrix Analysis and Applied Linear Algebra. Society for Industrial and Applied Mathematics, Philadelphia, PA.Google Scholar
Nederhof, M., Anoop Sarkar, A. and Satta, G. 1998. Prefix probabilities from stochastic tree adjoining grammars. In Proceedings of the 36th Annual Meeting of the Association for Computational Linguistics (ACL'98), 953–959.Google Scholar
Nederhof, M. and Satta, G. 2011a. Computation of infix probabilities for probabilistic context-free grammars. In Proceedings of the 2011 Conference on Empirical Methods in Natural Language Processing (EMNLP'11), 1213–1221.Google Scholar
Nederhof, M. and Satta, G. 2011b. Prefix probability for probabilistic synchronous context-free grammars. In Proceedings of the 48th Annual Meeting of the Association for Computational Linguistics (ACL'11), 460–469.Google Scholar
Pomponio, L., Le Goc, M., Eric, P. and Alain, A. 2011. Combining timed data and expert's knowledge to model human behavior. In Proceedings of the Health Ambient Information Systems Workshop (HamIS'11), http://ceur-ws.org/Vol-729/, vol. 729.Google Scholar
Riguzzi, F. and Swift, T. 2011. The PITA system: Tabling and answer subsumption for reasoning under uncertainty. Theory and Practice of Logic Programming (TPLP) 11, 4–5, 433–449.Google Scholar
Roark, B. and Johnson, M. 1999. Efficient probabilistic top-down and left-corner parsing. In Proceedings of the 37th Annual Meeting of the Association for Computational Linguistics, 421–428.Google Scholar
Rocha, R., Silva, F. and Costa, V. 2005. On applying or-parallelism and tabling to logic programs. Theory and Practice of Logic Programming (TPLP) 5, 1–2, 161–205.CrossRefGoogle Scholar
Sato, T. 2008. A glimpse of symbolic-statistical modeling by PRISM. Journal of Intelligent Information Systems 31, 2, 161–176.Google Scholar
Sato, T. and Kameya, Y. 1997. PRISM: A language for symbolic-statistical modeling. In Proceedings of the 15th International Joint Conference on Artificial Intelligence (IJCAI'97), 1330–1335.Google Scholar
Sato, T. and Kameya, Y. 2001. Parameter learning of logic programs for symbolic-statistical modeling. Journal of Artificial Intelligence Research 15, 391–454.CrossRefGoogle Scholar
Sato, T. and Kameya, Y. 2008. New advances in logic-based probabilistic modeling by PRISM. In Probabilistic Inductive Logic Programming, Raedt, L. De, Frasconi, P., Kersting, K. and Muggleton, S., Eds., LNAI, vol. 4911. Springer, New York, 118–155.Google Scholar
Sato, T. and Meyer, P. 2012. Tabling for infinite probability computation. In Technical Communications of the 28th International Conference on Logic Programming (ICLP'12), Budapest, Hungary, Leibniz International Proceedings in Informatics, vol. 17. Kluwer, Boston, MA, 348–358.Google Scholar
Stolcke, A. 1995. An efficient probabilistic context-free parsing algorithm that computes prefix probabilities. Computational Linguistics 21, 2, 165–201.Google Scholar
Swift, T. and Warren, D. 2012. XSB: Extending prolog with tabled logic programming. Theory and Practice of Logic Programming (TPLP) 12, 1–2, 157–187.Google Scholar
Tamaki, H. and Sato, T. 1986. OLD resolution with tabulation. In Proceedings of the 3rd International Conference on Logic Programming (ICLP'86), Lecture Notes in Computer Science, vol. 225. Springer, New York, 84–98.Google Scholar
Uratani, N., Takezawa, T., Matsuo, H. and Morita, C. 1994. ATR integrated speech and language database. Tech. Rep., TR-IT-0056, ATR Interpreting Telecommunications Research Laboratories, Kyoto, Japan.Google Scholar
Van Uytsel, D., Van Compernolle, D. and Wambacq, P. 2001. Maximum-likelihood training of the PLCG-based language model. In Proceedings of the IEEE Automatic Speech Recognition and Understanding Workshop 2001 (ASRU'01).Google Scholar
Warren, D. S. 1992. Memoing for logic programs. Communications of the ACM 35, 3, 93–111.Google Scholar
Wetherell, C. S. 1980. Probabilistic languages: A review and some open questions. Computing Surveys 12, 4, 361–379.Google Scholar
Zhou, N.-F., Kameya, Y. and Sato, T. 2010. Mode-directed tabling for dynamic programming, machine learning, and constraint solving. In Proceedings of the 22nd International Conference on Tools with Artificial Intelligence (ICTAI-2010).Google Scholar
Zhou, N.-F. and Sato, T. 2003. Toward a high-performance system for symbolic and statistical modeling. In Proceedings of IJCAI-03 Workshop on Learning Statistical Models from Relational Data (SRL'03), http://scholarworks.umass.edu/cgi/viewcontent.cgi?article=1163&context=cs_faculty_pubs, 133–140.Google Scholar
Zhou, N.-F., Sato, T. and Shen, Y.-D. 2008. Linear tabling strategies and optimization. Theory and Practice of Logic Programming (TPLP) 8, 1, 81–109.CrossRefGoogle Scholar