Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-13T06:42:51.718Z Has data issue: false hasContentIssue false
  • English
  • Français

Lifted Variable Elimination for Probabilistic Logic Programming

Published online by Cambridge University Press:  21 July 2014

ELENA BELLODI ,
EVELINA LAMMA ,
FABRIZIO RIGUZZI ,
VITOR SANTOS COSTA  and
RICCARDO ZESE
ELENA BELLODI
Affiliation:
Dipartimento di Ingegneria - Università di FerraraVia Saragat 1, 44122, Ferrara, Italy
EVELINA LAMMA
Affiliation:
Dipartimento di Ingegneria - Università di FerraraVia Saragat 1, 44122, Ferrara, Italy
FABRIZIO RIGUZZI
Affiliation:
Dipartimento di Matematica e Informatica - Università di FerraraVia Saragat 1, 44122, Ferrara, Italy
VITOR SANTOS COSTA
Affiliation:
CRACS/INESC-TEC and DCC-FCUP - Universidade do Porto, Rua do Campo Alegre, 1021/1055, 4169-007 Porto, Portugal (e-mail: name.surname@unife.it, vsc@dcc.fc.up.pt)
RICCARDO ZESE
Affiliation:
Dipartimento di Ingegneria - Università di FerraraVia Saragat 1, 44122, Ferrara, Italy
Get access Rights & Permissions [Opens in a new window]

Abstract

Lifted inference has been proposed for various probabilistic logical frameworks in order to compute the probability of queries in a time that depends on the size of the domains of the random variables rather than the number of instances. Even if various authors have underlined its importance for probabilistic logic programming (PLP), lifted inference has been applied up to now only to relational languages outside of logic programming. In this paper we adapt Generalized Counting First Order Variable Elimination (GC-FOVE) to the problem of computing the probability of queries to probabilistic logic programs under the distribution semantics. In particular, we extend the Prolog Factor Language (PFL) to include two new types of factors that are needed for representing ProbLog programs. These factors take into account the existing causal independence relationships among random variables and are managed by the extension to variable elimination proposed by Zhang and Poole for dealing with convergent variables and heterogeneous factors. Two new operators are added to GC-FOVE for treating heterogeneous factors. The resulting algorithm, called LP2 for Lifted Probabilistic Logic Programming, has been implemented by modifying the PFL implementation of GC-FOVE and tested on three benchmarks for lifted inference. A comparison with PITA and ProbLog2 shows the potential of the approach.

Keywords

Probabilistic Logic ProgrammingLifted InferenceVariable EliminationDistribution SemanticsProbLogStatistical Relational Artificial Intelligence
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 14 , Special Issue 4-5: 30th International Conference on Logic Programming , July 2014 , pp. 681 - 695
Copyright
Copyright © Cambridge University Press 2014 

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

De Raedt, L., Frasconi, P., Kersting, K., and Muggleton, S., Eds. 2008. Probabilistic Inductive Logic Programming - Theory and Applications. LNCS, vol. 4911. Springer.Google Scholar
De Raedt, L., Kimmig, A., and Toivonen, H. 2007. ProbLog: A Probabilistic Prolog and its application in link discovery. In 20th International Joint Conference on Artificial Intelligence (IJCAI-2007). AAAI Press, 2462–2467.Google Scholar
de Salvo Braz, R., Amir, E., and Roth, D. 2005. Lifted first-order probabilistic inference. In 19th International Joint Conference on Artificial Intelligence, Kaelbling, L. P. and Saffiotti, A., Eds. Professional Book Center, 1319–1325.Google Scholar
Díez, F. J. and Galán, S. F. 2003. Efficient computation for the noisy max. International Journal of Intelligent Systems, 165–177.Google Scholar
Fierens, D., Van den Broeck, G., Renkens, J., Shterionov, D., Gutmann, B., Thon, I., Janssens, G., and De Raedt, L. 2014. Inference and learning in probabilistic logic programs using weighted boolean formulas. Theory and Practice of Logic Programming FirstView Articles.Google Scholar
Getoor, L. and Taskar, B., Eds. 2007. Introduction to Statistical Relational Learning. MIT Press.CrossRefGoogle Scholar
Gomes, T. and Costa, V. S. 2012. Evaluating inference algorithms for the prolog factor language. In 22nd International Conference on Inductive Logic Programming, Riguzzi, F. and Zelezný, F., Eds. LNCS, vol. 7842. Springer, 74–85.Google Scholar
Kisynski, J. and Poole, D. 2009a. Constraint processing in lifted probabilistic inference. In 25th Conference on Uncertainty in Artificial Intelligence, Bilmes, J. and Ng, A. Y., Eds. AUAI Press, 293–302.Google Scholar
Kisynski, J. and Poole, D. 2009b. Lifted aggregation in directed first-order probabilistic models. In 24th International Joint Conference on Artificial Intelligence, C. Boutilier, Ed. 1922–1929.Google Scholar
Meert, W., Struyf, J., and Blockeel, H. 2008. Learning ground CP-Logic theories by leveraging Bayesian network learning techniques. Fundamenta Informaticae 89, 131–160.Google Scholar
Milch, B., Zettlemoyer, L. S., Kersting, K., Haimes, M., and Kaelbling, L. P. 2008. Lifted probabilistic inference with counting formulas. In 23rd AAAI Conference on Artificial Intelligence, Fox, D. and Gomes, C. P., Eds. AAAI Press, 1062–1068.Google Scholar
Poole, D. 1993. Probabilistic horn abduction and Bayesian networks. Artificial Intelligence 64, 1, 81–129.CrossRefGoogle Scholar
Poole, D. 1997. The Independent Choice Logic for modelling multiple agents under uncertainty. Artificial Intelligence 94, 7–56.Google Scholar
Poole, D. 2003. First-order probabilistic inference. In 18th International Joint Conference on Artificial Intelligence, Gottlob, G. and Walsh, T., Eds. Morgan Kaufmann Publishers Inc., 985–991.Google Scholar
Poole, D. 2008. The independent choice logic and beyond. In Probabilistic Inductive Logic Programming, De Raedt, L., Frasconi, P., Kersting, K., and Muggleton, S., Eds. LNCS, vol. 4911. Springer, 222–243.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, International Conference on Logic Programming (ICLP) Special Issue 11, 433–449.Google Scholar
Sato, T. 1995. A statistical learning method for logic programs with distribution semantics. In 12th International Conference on Logic Programming, Sterling, L., Ed. MIT Press, 715–729.Google Scholar
Taghipour, N., Fierens, D., Davis, J., and Blockeel, H. 2013. Lifted variable elimination: Decoupling the operators from the constraint language. Journal of Artificial Intelligence Research 47, 393–439.Google Scholar
Takikawa, M. and D'Ambrosio, B. 1999. Multiplicative factorization of noisy-max. In 15th Conference on Uncertainty in Artificial Intelligence. 622–630.Google Scholar
Van den Broeck, G., Meert, W., and Darwiche, A. 2014. Skolemization for weighted first-order model counting. ArXiv e-prints 1312.5378v2. To appear in the 14th International Conference on Principles of Knowledge Representation and Reasoning.Google Scholar
Van den Broeck, G., Taghipour, N., Meert, W., Davis, J., and Raedt, L. D. 2011. Lifted probabilistic inference by first-order knowledge compilation. In 21st International Joint Conference on Artificial Intelligence, Walsh, T., Ed. IJCAI/AAAI, 2178–2185.Google Scholar
Vennekens, J., Verbaeten, S., and Bruynooghe, M. 2004. Logic Programs With Annotated Disjunctions. In 20th International Conference on Logic Programming, Demoen, B. and Lifschitz, V., Eds. Springer, LNCS 3131, 195–209.Google Scholar
Zhang, N. L. and Poole, D. L. 1996. Exploiting causal independence in bayesian network inference. Journal of Artificial Intelligence Research 5, 301–328.Google Scholar
Supplementary material: PDF

BELLODI et al.

Lifted Variable Elimination for Probabilistic Logic Programming

Download BELLODI et al.(PDF)
PDF 348.2 KB