Skip to main content Accessibility help
×
Home

Inference in probabilistic logic programs with continuous random variables

Published online by Cambridge University Press:  05 September 2012


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)
Corresponding

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
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.

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.Google 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. 175188.Google Scholar
Forney, G. 1973. The Viterbi algorithm. In Proceedings of the IEEE. 268278.Google Scholar
Friedman, N., Getoor, L., Koller, D. and Pfeffer, A. 1999. Learning probabilistic relational models. In IJCAI. 13001309.Google Scholar
Getoor, L. and Taskar, B. 2007. Introduction to Statistical Relational Learning. The MIT Press.Google Scholar
Goswami, A., Ortiz, L. E. and Das, S. R. 2011. WiGEM: A learning-based approach for indoor localizatio. In SIGCOMM.Google Scholar
Gutmann, B., Jaeger, M. and Raedt, L. D. 2010. Extending ProbLog with continuous distributions. In Proceedings of ILP.Google 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, 663680.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, 146.CrossRefGoogle Scholar
Kersting, K. and Raedt, L. D. 2000. Bayesian logic programs. In ILP Work-in-Progress Reports.Google Scholar
Kersting, K. and Raedt, L. D. 2001. Adaptive Bayesian logic programs. In ILP.Google 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, 3556.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.Google Scholar
Poole, D. 1993. Probabilistic Horn abduction and Bayesian networks. Artificial Intelligence 64, 1, 81129.CrossRefGoogle Scholar
Poole, D. 2008. The independent choice logic and beyond. In Probabilistic ILP. 222243.Google Scholar
Raedt, L. D., Kimmig, A. and Toivonen, H. 2007. ProbLog: A probabilistic prolog and its application in link discovery. In IJCAI. 24622467.Google Scholar
Richardson, M. and Domingos, P. 2006. Markov logic networks. Machine Learning.Google Scholar
Riguzzi, F. and Swift, T. 2010. Tabling and answer subsumption for reasoning on logic programs with annotated disjunctions. In Tech. Comm. of ICLP. 162171.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, 391454.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. 197210.Google 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. 8498.Google Scholar
Vennekens, J., Denecker, M. and Bruynooghe, M. 2009. CP-logic: A language of causal probabilistic events and its relation to logic programming. TPLP.Google Scholar
Vennekens, J., Verbaeten, S. and Bruynooghe, M. 2004. Logic programs with annotated disjunctions. In ICLP. 431445.Google Scholar
Wang, J. and Domingos, P. 2008. Hybrid markov logic networks. In Proceedings of AAAI.Google Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 28 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 5th December 2020. This data will be updated every 24 hours.

Hostname: page-component-b4dcdd7-gq9rl Total loading time: 1.602 Render date: 2020-12-05T23:03:43.324Z Query parameters: { "hasAccess": "0", "openAccess": "0", "isLogged": "0", "lang": "en" } Feature Flags last update: Sat Dec 05 2020 23:01:19 GMT+0000 (Coordinated Universal Time) Feature Flags: { "metrics": true, "metricsAbstractViews": false, "peerReview": true, "crossMark": true, "comments": true, "relatedCommentaries": true, "subject": true, "clr": false, "languageSwitch": true }

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Inference in probabilistic logic programs with continuous random variables
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Inference in probabilistic logic programs with continuous random variables
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Inference in probabilistic logic programs with continuous random variables
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *