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MAP Inference for Probabilistic Logic Programming

Published online by Cambridge University Press:  21 September 2020

ELENA BELLODI ,
MARCO ALBERTI ,
FABRIZIO RIGUZZI Open the ORCID record for FABRIZIO RIGUZZI [Opens in a new window]  and
RICCARDO ZESE Open the ORCID record for RICCARDO ZESE [Opens in a new window]
ELENA BELLODI
Affiliation:
Dipartimento di Ingegneria – Università di Ferrara
MARCO ALBERTI
Affiliation:
Dipartimento di Matematica e Informatica – Università di Ferrara Via Saragat 1, 44122, Ferrara, Italy (e-mail: [email protected])
FABRIZIO RIGUZZI
Affiliation:
Dipartimento di Matematica e Informatica – Università di Ferrara Via Saragat 1, 44122, Ferrara, Italy (e-mail: [email protected])
RICCARDO ZESE
Affiliation:
Dipartimento di Ingegneria – Università di Ferrara
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Abstract

In Probabilistic Logic Programming (PLP) the most commonly studied inference task is to compute the marginal probability of a query given a program. In this paper, we consider two other important tasks in the PLP setting: the Maximum-A-Posteriori (MAP) inference task, which determines the most likely values for a subset of the random variables given evidence on other variables, and the Most Probable Explanation (MPE) task, the instance of MAP where the query variables are the complement of the evidence variables. We present a novel algorithm, included in the PITA reasoner, which tackles these tasks by representing each problem as a Binary Decision Diagram and applying a dynamic programming procedure on it. We compare our algorithm with the version of ProbLog that admits annotated disjunctions and can perform MAP and MPE inference. Experiments on several synthetic datasets show that PITA outperforms ProbLog in many cases.

Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 20 , Issue 5: 36th International Conference on Logic Programming Special Issue I , September 2020 , pp. 641 - 655
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Barabasi, A.-L. and Albert, R. 1999. Emergence of scaling in random networks. Science 286, 5439, 509–512.Google Scholar
Darwiche, A. 2004. New advances in compiling CNF into decomposable negation normal form. In 16th European Conference on Artificial Intelligence (ECAI 20014), R. L. de Mántaras and L. Saitta, Eds. IOS Press, 328–332.Google Scholar
Darwiche, A. and Marquis, P. 2002. A knowledge compilation map. J. Artif. Intell. Res. 17, 229–264.Google Scholar
De Raedt, L., Demoen, B., Fierens, D., Gutmann, B., Janssens, G., Kimmig, A., Landwehr, N., Mantadelis, T., Meert, W., Rocha, R., Santos Costa, V., Thon, I., and Vennekens, J. 2008. Towards digesting the alphabet-soup of statistical relational learning. In NIPS 2008 Workshop on Probabilistic Programming.Google Scholar
De Raedt, L., Frasconi, P., Kersting, K., and Muggleton, S., Eds. 2008. Probabilistic Inductive Logic Programming . 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), M. M. Veloso, Ed. Vol. 7. AAAI Press/IJCAI, 2462–2467.Google Scholar
Fierens, D., Van den Broeck, G., Renkens, J., Shterionov, D. S., Gutmann, B., Thon, I., Janssens, G., and De Raedt, L. 2015. Inference and learning in probabilistic logic programs using weighted Boolean formulas. Theor. Pract. Log. Prog. 15, 3, 358–401.Google Scholar
Jiang, C., Babar, J., Ciardo, G., Miner, A. S., and Smith, B. 2017. Variable reordering in binary decision diagrams. In 26th International Workshop on Logic and Synthesis. 1–8.Google Scholar
Poole, D. 1997. The Independent Choice Logic for modelling multiple agents under uncertainty. Artif. Intell. 94, 7–56.Google Scholar
Poole, D. 2000. Abducing through negation as failure: Stable models within the independent choice logic. J. Logic Program. 44, 1-3, 5–35.CrossRefGoogle Scholar
Raedt, L. D., Kimmig, A., and Toivonen, H. 2007. Problog: A probabilistic prolog and its application in link discovery. In IJCAI, M. M. Veloso, Ed. 2462–2467.Google Scholar
Riguzzi, F. 2016. The distribution semantics for normal programs with function symbols. Int. J. Approx. Reason. 77, 1–19.Google Scholar
Riguzzi, F. 2018. Foundations of Probabilistic Logic Programming. River Publishers, Gistrup,Denmark.Google Scholar
Riguzzi, F. and Swift, T. 2010. Tabling and answer subsumption for reasoning on logic programs with annotated disjunctions. In Technical Communications of the 26th International Conference on Logic Programming (ICLP 2010). LIPIcs, vol. 7. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 162–171.Google Scholar
Riguzzi, F. and Swift, T. 2011. The PITA system: Tabling and answer subsumption for reasoning under uncertainty. Theor. Pract. Log. Prog. 11, 4–5, 433–449.Google Scholar
Riguzzi, F. and Swift, T. 2013. Well-definedness and efficient inference for probabilistic logic programming under the distribution semantics. Theor. Pract. Log. Prog. 13, 2, 279–302.CrossRefGoogle Scholar
Sato, T. 1995. A statistical learning method for logic programs with distribution semantics. In Logic Programming, Proceedings of the Twelfth International Conference on Logic Programming, Tokyo, Japan, June 13-16, 1995, L. Sterling, Ed. MIT Press, 715–729.Google Scholar
Shterionov, D. S., Renkens, J., Vlasselaer, J., Kimmig, A., Meert, W., and Janssens, G. 2015. The most probable explanation for probabilistic logic programs with annotated disjunctions. In 24th International Conference on Inductive Logic Programming (ILP 2014), J. Davis and J. Ramon, Eds. Lecture Notes in Computer Science, vol. 9046. Springer, Berlin, Heidelberg, 139–153.Google Scholar
Somenzi, F. 2001. Efficient manipulation of decision diagrams. Int. J. Softw. Tools Technol. Transf. 3, 2, 171–181.CrossRefGoogle Scholar
Valiant, L. G. 1979. The complexity of enumeration and reliability problems. SIAM J. Comput. 8, 3, 410–421.Google Scholar
Van den Broeck, G., Thon, I., van Otterlo, M., and De Raedt, L. 2010. DTProbLog: A decision-theoretic probabilistic Prolog. In Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence, Fox, M. and Poole, D., Eds. AAAI Press, 1217–1222.Google Scholar
Vennekens, J., Verbaeten, S., and Bruynooghe, M. 2004a. Logic programs with annotated disjunctions. In 24th International Conference on Logic Programming (ICLP 2004), Demoen, B. and Lifschitz, V., Eds. Lecture Notes in Computer Science, vol. 3131. Springer, 431–445.Google Scholar
Vennekens, J., Verbaeten, S., and Bruynooghe, M. 2004b. Logic programs with annotated disjunctions. In 24th International Conference on Logic Programming (ICLP 2004), Demoen, B. and Lifschitz, V., Eds. Lecture Notes in Computer Science, vol. 3131. Springer, Berlin, 195–209.Google Scholar