Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-18T01:05:09.359Z Has data issue: false hasContentIssue false
  • English
  • Français

Inference in probabilistic logic programs with continuous random variables

Published online by Cambridge University Press:  05 September 2012

MUHAMMAD ASIFUL ISLAM ,
C. R. RAMAKRISHNAN  and
I. V. RAMAKRISHNAN
MUHAMMAD ASIFUL ISLAM
Affiliation:
Department of Computer Science, Stony Brook University, Stony Brook, NY 11794 (e-mail: maislam@cs.sunysb.edu, cram@cs.sunysb.edu, ram@cs.sunysb.edu)
C. R. RAMAKRISHNAN
Affiliation:
Department of Computer Science, Stony Brook University, Stony Brook, NY 11794 (e-mail: maislam@cs.sunysb.edu, cram@cs.sunysb.edu, ram@cs.sunysb.edu)
I. V. RAMAKRISHNAN
Affiliation:
Department of Computer Science, Stony Brook University, Stony Brook, NY 11794 (e-mail: maislam@cs.sunysb.edu, cram@cs.sunysb.edu, ram@cs.sunysb.edu)
Get access Rights & Permissions [Opens in a new window]

Abstract

Probabilistic Logic Programming (PLP), exemplified by Sato and Kameya's PRISM, Poole's ICL, Raedt et al.'s ProbLog and Vennekens et al.'s LPAD, is aimed at combining statistical and logical knowledge representation and inference. However, the inference techniques used in these works rely on enumerating sets of explanations for a query answer. Consequently, these languages permit very limited use of random variables with continuous distributions. In this paper, we present a symbolic inference procedure that uses constraints and represents sets of explanations without enumeration. This permits us to reason over PLPs with Gaussian or Gamma-distributed random variables (in addition to discrete-valued random variables) and linear equality constraints over reals. We develop the inference procedure in the context of PRISM; however the procedure's core ideas can be easily applied to other PLP languages as well. An interesting aspect of our inference procedure is that PRISM's query evaluation process becomes a special case in the absence of any continuous random variables in the program. The symbolic inference procedure enables us to reason over complex probabilistic models such as Kalman filters and a large subclass of Hybrid Bayesian networks that were hitherto not possible in PLP frameworks.

Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 12 , Issue 4-5: 28th International Conference on Logic Programming , July 2012 , pp. 505 - 523
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bancilhon, F., Maier, D., Sagiv, Y. and Ullman, J. 1986. Magic sets and other strange ways to implement logic programs. In Proceedings of PODS.CrossRefGoogle Scholar
Bishop, C. 2006. Pattern Recognition and Machine Learning. Springer.Google Scholar
Chu, D., Popa, L., Tavakoli, A., Hellerstein, J. M., Levis, P., Shenker, S. and Stoica, I. 2007. The design and implementation of a declarative sensor network system. In SenSys. 175–188.CrossRefGoogle Scholar
Forney, G. 1973. The Viterbi algorithm. In Proceedings of the IEEE. 268–278.CrossRefGoogle Scholar
Friedman, N., Getoor, L., Koller, D. and Pfeffer, A. 1999. Learning probabilistic relational models. In IJCAI. 1300–1309.Google Scholar
Getoor, L. and Taskar, B. 2007. Introduction to Statistical Relational Learning. The MIT Press.CrossRefGoogle Scholar
Goswami, A., Ortiz, L. E. and Das, S. R. 2011. WiGEM: A learning-based approach for indoor localizatio. In SIGCOMM.CrossRefGoogle Scholar
Gutmann, B., Jaeger, M. and Raedt, L. D. 2010. Extending ProbLog with continuous distributions. In Proceedings of ILP.CrossRefGoogle Scholar
Gutmann, B., Thon, I., Kimmig, A., Bruynooghe, M. and Raedt, L. D. 2011. The magic of logical inference in probabilistic programming. TPLP 11, 4–5, 663–680.Google Scholar
Islam, M., Ramakrishnan, C. R. and Ramakrishnan, I. V. 2011. Inference in Probabilistic Logic Programs with Continuous Random Variables. ArXiv e-prints. http://arxiv.org/abs/1112.2681.Google Scholar
Islam, M., Ramakrishnan, C. R. and Ramakrishnan, I. V. 2012. Parameter Learning in PRISM Programs with Continuous Random Variables. ArXiv e-prints. http://arxiv.org/abs/1203.4287.Google Scholar
Islam, M. A. 2012. Inference and Learning in Probabilistic Logic Programs with Continuous Random Variables, PhD Thesis. http://www.cs.sunysb.edu/~cram/asiful2012.pdf.Google Scholar
Jaffar, J., Maher, M. J., Marriott, K. and Stuckey, P. J. 1998. The semantics of constraint logic programs. Journal of Logic Programming 37, 1–3, 1–46.CrossRefGoogle Scholar
Kersting, K. and Raedt, L. D. 2000. Bayesian logic programs. In ILP Work-in-Progress Reports.CrossRefGoogle Scholar
Kersting, K. and Raedt, L. D. 2001. Adaptive Bayesian logic programs. In ILP.CrossRefGoogle Scholar
Lari, K. and Young, S. J. 1990. The estimation of stochastic context-free grammars using the inside-outside algorithm. Computer Speech and Language 4, 35–56.CrossRefGoogle Scholar
Muggleton, S. 1996. Stochastic logic programs. In Advances in inductive Logic Programming.Google Scholar
Murphy, K. 1998. Inference and Learning in Hybrid Bayesian Networks, Technical Report UCB/CSD-98-990.Google Scholar
Narman, P., Buschle, M., Konig, J. and Johnson, P. 2010. Hybrid probabilistic relational models for system quality analysis. In Proceedings of EDOC.CrossRefGoogle Scholar
Poole, D. 1993. Probabilistic Horn abduction and Bayesian networks. Artificial Intelligence 64, 1, 81–129.CrossRefGoogle Scholar
Poole, D. 2008. The independent choice logic and beyond. In Probabilistic ILP. 222–243.CrossRefGoogle Scholar
Raedt, L. D., Kimmig, A. and Toivonen, H. 2007. ProbLog: A probabilistic prolog and its application in link discovery. In IJCAI. 2462–2467.Google Scholar
Richardson, M. and Domingos, P. 2006. Markov logic networks. Machine Learning.CrossRefGoogle Scholar
Riguzzi, F. and Swift, T. 2010. Tabling and answer subsumption for reasoning on logic programs with annotated disjunctions. In Tech. Comm. of ICLP. 162–171.Google Scholar
Russell, S. and Norvig, P. 2003. Arficial Intelligence: A Modern Approach. Prentice Hall.Google Scholar
Sato, T. and Kameya, Y. 1997. PRISM: A symbolic-statistical modeling language. In IJCAI.Google Scholar
Sato, T. and Kameya, Y. 1999. Parameter learning of logic programs for symbolic-statistical modeling. Journal of Artificial Intelligence Research, 391–454.Google Scholar
Singh, A., Ramakrishnan, C. R., Ramakrishnan, I. V., Warren, D. and Wong, J. 2008. A methodology for in-network evaluation of integrated logical-statistical models. In SenSys. 197–210.CrossRefGoogle Scholar
Swift, T., Warren, D. S. et al. . 2012. The XSB Logic Programming System, Version 3.3. Technical rep., Computer Science, SUNY, Stony Brook. http://xsb.sourceforge.net.Google Scholar
Tamaki, H. and Sato, T. 1986. OLD resolution with tabulation. In ICLP. 84–98.CrossRefGoogle Scholar
Vennekens, J., Denecker, M. and Bruynooghe, M. 2009. CP-logic: A language of causal probabilistic events and its relation to logic programming. TPLP.CrossRefGoogle Scholar
Vennekens, J., Verbaeten, S. and Bruynooghe, M. 2004. Logic programs with annotated disjunctions. In ICLP. 431–445.CrossRefGoogle Scholar
Wang, J. and Domingos, P. 2008. Hybrid markov logic networks. In Proceedings of AAAI.Google Scholar