Skip to main content Accessibility help

Inference in probabilistic logic programs with continuous random variables



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.



Hide All
Bancilhon, F., Maier, D., Sagiv, Y. and Ullman, J. 1986. Magic sets and other strange ways to implement logic programs. In Proceedings of PODS.
Bishop, C. 2006. Pattern Recognition and Machine Learning. Springer.
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. 175188.
Forney, G. 1973. The Viterbi algorithm. In Proceedings of the IEEE. 268278.
Friedman, N., Getoor, L., Koller, D. and Pfeffer, A. 1999. Learning probabilistic relational models. In IJCAI. 13001309.
Getoor, L. and Taskar, B. 2007. Introduction to Statistical Relational Learning. The MIT Press.
Goswami, A., Ortiz, L. E. and Das, S. R. 2011. WiGEM: A learning-based approach for indoor localizatio. In SIGCOMM.
Gutmann, B., Jaeger, M. and Raedt, L. D. 2010. Extending ProbLog with continuous distributions. In Proceedings of ILP.
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, 663680.
Islam, M., Ramakrishnan, C. R. and Ramakrishnan, I. V. 2011. Inference in Probabilistic Logic Programs with Continuous Random Variables. ArXiv e-prints.
Islam, M., Ramakrishnan, C. R. and Ramakrishnan, I. V. 2012. Parameter Learning in PRISM Programs with Continuous Random Variables. ArXiv e-prints.
Islam, M. A. 2012. Inference and Learning in Probabilistic Logic Programs with Continuous Random Variables, PhD Thesis.
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, 146.
Kersting, K. and Raedt, L. D. 2000. Bayesian logic programs. In ILP Work-in-Progress Reports.
Kersting, K. and Raedt, L. D. 2001. Adaptive Bayesian logic programs. In ILP.
Lari, K. and Young, S. J. 1990. The estimation of stochastic context-free grammars using the inside-outside algorithm. Computer Speech and Language 4, 3556.
Muggleton, S. 1996. Stochastic logic programs. In Advances in inductive Logic Programming.
Murphy, K. 1998. Inference and Learning in Hybrid Bayesian Networks, Technical Report UCB/CSD-98-990.
Narman, P., Buschle, M., Konig, J. and Johnson, P. 2010. Hybrid probabilistic relational models for system quality analysis. In Proceedings of EDOC.
Poole, D. 1993. Probabilistic Horn abduction and Bayesian networks. Artificial Intelligence 64, 1, 81129.
Poole, D. 2008. The independent choice logic and beyond. In Probabilistic ILP. 222243.
Raedt, L. D., Kimmig, A. and Toivonen, H. 2007. ProbLog: A probabilistic prolog and its application in link discovery. In IJCAI. 24622467.
Richardson, M. and Domingos, P. 2006. Markov logic networks. Machine Learning.
Riguzzi, F. and Swift, T. 2010. Tabling and answer subsumption for reasoning on logic programs with annotated disjunctions. In Tech. Comm. of ICLP. 162171.
Russell, S. and Norvig, P. 2003. Arficial Intelligence: A Modern Approach. Prentice Hall.
Sato, T. and Kameya, Y. 1997. PRISM: A symbolic-statistical modeling language. In IJCAI.
Sato, T. and Kameya, Y. 1999. Parameter learning of logic programs for symbolic-statistical modeling. Journal of Artificial Intelligence Research, 391454.
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. 197210.
Swift, T., Warren, D. S. et al. . 2012. The XSB Logic Programming System, Version 3.3. Technical rep., Computer Science, SUNY, Stony Brook.
Tamaki, H. and Sato, T. 1986. OLD resolution with tabulation. In ICLP. 8498.
Vennekens, J., Denecker, M. and Bruynooghe, M. 2009. CP-logic: A language of causal probabilistic events and its relation to logic programming. TPLP.
Vennekens, J., Verbaeten, S. and Bruynooghe, M. 2004. Logic programs with annotated disjunctions. In ICLP. 431445.
Wang, J. and Domingos, P. 2008. Hybrid markov logic networks. In Proceedings of AAAI.


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed