Abstract
We have been developing a general symbolic-statistical modeling language [6,19,20] based on the logic programming framework that semantically unifies (and extends) major symbolic-statistical frameworks such as hidden Markov models (HMMs) [18], probabilistic context-free grammars (PCFGs) [23] and Bayesian networks [16]. The language, PRISM, is intended to model complex symbolic phenomena governed by rules and probabilities based on the distributional semantics [19]. Programs contain statistical parameters and they are automatically learned from randomly sampled data by a specially derived EM algorithm, the graphical EM algorithm. It works on support graphs representing the shared structure of explanations for an observed goal. In this paper, we propose the use of tabulation technique to build support graphs, and show that as a result, the graphical EM algorithm attains the same time complexity as specilized EM algorithms for HMMs (the Baum-Welch algorithm [18]) and PCFGs (the Inside-Outside algorithm [1]).
This is a preview of subscription content, log in via an institution to check access.
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
Baker, J. K., Trainable grammars for speech recognition, Proc. of Spring Conf. of the Acoustical Society of America, pp. 547–550, 1979.
Breese, J. S., Construction of belief and decision networks, Computational Intelligence, Vol. 8, No. 4, pp. 624–647, 1992.
Cussens, J., Loglinear models for first-order probabilistic reasoning, Proc. of UAI’99, pp. 126–133, 1999.
Dekhtyar, A. and Subrahmanian, V. S., Hybrid probabilistic programs, Proc. of ICLP’97, pp. 391–405, 1997.
Doets, K., From Logic to Logic Programming, The MIT Press, 1994.
Kameya, Y., Ueda, N. and Sato, T., A graphical method for parameter learning of symbolic-statistical models, Proc. of DS’99, LNAI 1721, pp. 264–276, 1999.
Kita, K., Morimoto, T., Ohkura, K., Sagayama, S. and Yano, Y., Spoken sentence recognition based on HMM-LR with hybrid language modeling, IEICE Trans. on Information & Systems, Vol. E77-D, No. 2, 1994.
Koller, D. and Pfeffer, A., Learning probabilities for noisy first-order rules, Proc. of IJCAI’97, pp. 1316–1321, 1997.
Koller, D., McAllester, D. and Pfeffer, A., Effective Bayesian Inference for Stochastic Programs, Proc. of AAAI’97, pp. 740–747, 1997.
Lakshmanan, L. V. S. and Sadri, F., Probabilistic deductive databases, Proc. of ILPS’94, pp. 254–268, 1994.
Manning, C. D. and Schütze, H., Foundations of Statistical Natural Language Processing, The MIT Press, 1999.
Muggleton, S., Stochastic logic programs, In Advances in Inductive Logic Programming (Raedt, L.Deed.), OSP Press, pp. 254–264, 1996.
Ng, R. and Subrahmanian, V. S., Probabilistic logic programming, Information and Computation, Vol. 101, pp. 150–201, 1992.
Ngo, L. and Haddawy, P., Answering queries from context-sensitive probabilistic knowledge bases, Theoretical Computer Science, Vol. 171, pp. 147–177, 1997.
Nilsson, N. J., Probabilistic logic, Artificial Intelligence, Vol. 28, pp. 71–87, 1986.
Pearl, J., Probabilistic Reasoning in Intelligent Systems, Morgan Kaufmann, 1988.
Poole, D., Probabilistic Horn abduction and Bayesian networks, Artificial Intelligence, Vol. 64, pp. 81–129, 1993.
Rabiner, L. and Juang, B., Foundations of Speech Recognition, Prentice-Hall, 1993.
Sato, T., A statistical learning method for logic programs with distribution semantics, Proc. of ICLP’95, pp. 715–729, 1995.
Sato, T. and Kameya, Y., PRISM: a language for symbolic-statistical modeling, Proc. of IJCAI’97, pp. 1330–1335, 1997.
Tamaki, H. and Sato, T., OLD resolution with tabulation, Proc. of ICLP’86, LNCS 225, pp. 84–98, 1986.
Tanner, M., Tools for Statistical Inference (2nd ed.), Springer-Verlag, 1986.
Wetherell, C.S., Probabilistic languages: a review and some open questions, Computing Surveys, Vol. 12, No. 4, pp. 361–379, 1980.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kameya, Y., Sato, T. (2000). Efficient EM Learning with Tabulation for Parameterized Logic Programs. In: Lloyd, J., et al. Computational Logic — CL 2000. CL 2000. Lecture Notes in Computer Science(), vol 1861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44957-4_18
Download citation
DOI: https://doi.org/10.1007/3-540-44957-4_18
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67797-0
Online ISBN: 978-3-540-44957-7
eBook Packages: Springer Book Archive