×

zbMATH — the first resource for mathematics

Soft quantification in statistical relational learning. (English) Zbl 06843621
Summary: We present a new statistical relational learning (SRL) framework that supports reasoning with soft quantifiers, such as “most” and “a few”. We define the syntax and the semantics of this language, which we call \(\mathrm{PSL}^Q\), and present a most probable explanation inference algorithm for it. To the best of our knowledge, \(\mathrm{PSL}^Q\) is the first SRL framework that combines soft quantifiers with first-order logic rules for modelling uncertain relational data. Our experimental results for two real-world applications, link prediction in social trust networks and user profiling in social networks, demonstrate that the use of soft quantifiers not only allows for a natural and intuitive formulation of domain knowledge, but also improves inference accuracy.
MSC:
68N17 Logic programming
Software:
Fril++; Fuzzydl; HyPER
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alshukaili, D., Fernandes, A. A. A., & Paton, N. W. (2016). Structuring linked data search results using probabilistic soft logic. In International semantic web conference (ISWC).
[2] Bach, S. H., Broecheler, M., Huang, B., & Getoor, L. (2015). Hinge-loss Markov random fields and probabilistic soft logic. arXiv:1505.04406 [cs.LG]. · Zbl 1435.68252
[3] Bach, S. H., Huang, B., London, B., & Getoor, L. (2013). Hinge-loss Markov random fields: Convex inference for structured prediction. In Proceedings of the Uncertainty in Artificial Intelligence (UAI).
[4] Bastian, M., Sebastien, H., & Mathieu, J. (2009). Gephi: An open source software for exploring and manipulating networks. In Proceedings of the international AAAI conference on web and social media (ICWSM) (pp. 361-362). · Zbl 1315.68250
[5] Beltagy, I., & Erk, K. (2015). On the proper treatment of quantifiers in probabilistic logic semantics. In Proceedings of the 11th international conference on computational semantics (IWCS) (p. 140).
[6] Beltagy, I., Erk, K., & Mooney, R. J. (2014). Probabilistic soft logic for semantic textual similarity. In Proceedings of the 52nd annual meeting of the association for computational linguistics (ACL) (pp. 1210-1219). · Zbl 1315.68250
[7] Bobillo, F., & Straccia, U. (2008). fuzzyDL: An expressive fuzzy description logic reasoner. In Proceedings of the IEEE international conference on fuzzy systems (FUZZ-IEEE) (pp. 923-930).
[8] Cao, T. H., Rossiter, J. M., Martin, T. P., & Baldwin, J. F. (2002). On the implementation of Fril++ for object-oriented logic programming with uncertainty and fuzziness. In Technologies for constructing intelligent systems 2 (pp. 393-406). Physica-Verlag HD. · Zbl 1061.68522
[9] Charnes, A; Cooper, WW, Programming with linear fractional functionals, Naval Research Logistics Quarterly, 9, 181-186, (1962) · Zbl 0127.36901
[10] Collins, M. (2002). Discriminative training methods for hidden Markov models: Theory and experiments with perceptron algorithms. In Proceedings of the international conference on empirical methods in natural language processing (ACL) (pp. 1-8). · Zbl 0816.68043
[11] Delgado, M; Ruiz, M-D; Sánchez, D; Vila, M-A, Fuzzy quantification: A state of the art, Fuzzy Sets and Systems, 242, 1-30, (2014) · Zbl 1315.68250
[12] Delgado, M; Sánchez, D; Vila, MA, Fuzzy cardinality based evaluation of quantified sentences, International Journal of Approximate Reasoning, 23, 23-66, (2000) · Zbl 0991.68092
[13] Deng, L., & Wiebe, J. (2015). Joint prediction for entity/event-level sentiment analysis using probabilistic soft logic models. In Conference on empirical methods in natural language processing (EMNLP).
[14] Dijkmans, C; Kerkhof, P; Beukeboom, CJ, A stage to engage: social media use and corporate reputation, Tourism Management, 47, 58-67, (2015)
[15] Ebrahimi, J., Dou, D., & Lowd, D. (2016). Weakly supervised tweet stance classification by relational bootstrapping. In Conference on empirical methods in natural language processing (EMNLP).
[16] Fakhraei, S; Huang, B; Raschid, L; Getoor, L, Network-based drug-target interaction prediction with probabilistic soft logic, IEEE/ACM Transactions on Computational Biology and Bioinformatics, 11, 775-787, (2014)
[17] Farnadi, G., Bach, S., Blondeel, M., Moens, M.-F., Getoor, L., & De Cock, M. (2015). Statistical relational learning with soft quantifiers. In Proceedings of 25th international conference on inductive logic programming (ILP). · Zbl 1347.68330
[18] Farnadi, G., Bach, S. H., Moens, M. F., Getoor, L., & De Cock, M. (2014). Extending PSL with fuzzy quantifiers. In Proceedings of the Fourth International Workshop on Statistical Relational AI at AAAI (StarAI). · Zbl 1347.68330
[19] Farnadi, G., Mahdavifar, Z., Keller, I., Nelson, J., Teredesai, A., Moens, M.-F., & De Cock, M. (2015). scalable adaptive label propagation in Grappa. In Proceedings of IEEE international conference on big data (IEEE-BigData).
[20] Getoor, L., & Taskar, B. (2007). Introduction to statistical relational learning. Cambridge: MIT press. · Zbl 1141.68054
[21] Ha, I; Oh, K-J; Jo, G-S, Personalized advertisement system using social relationship based user modeling, Multimedia Tools and Applications, 74, 8801-8819, (2015)
[22] Heider, F. (1958). The psychology of interpersonal relations. New York: Wiley.
[23] Huang, B., Kimmig, A., Getoor, L., & Golbeck, J. (2013). A flexible framework for probabilistic models of social trust. In Social computing, behavioral-cultural modeling and prediction (pp. 265-273).
[24] Isbell, JR; Marlow, WH, Attrition games, Naval Research Logistics Quarterly, 3, 71-94, (1956)
[25] Jain, D., Barthels, A., & Beetz, M. (2010). Adaptive Markov logic networks: Learning statistical relational models with dynamic parameters. In Proceedings of the European conference on artificial intelligence (ECAI) (pp. 937-942). · Zbl 1211.68321
[26] Kazemi, S. M., Buchman, D., Kersting, K., Natarajan, S., & Poole, D. (2014). Relational logistic regression. In Proceedings of the international conference on principles of knowledge representation and reasoning (KR). · Zbl 0127.36901
[27] Klir, G., & Yuan, B. (1995). Fuzzy sets and fuzzy logic. New Jersey: Prentice Hall.
[28] Kouki, P., Fakhraei, S., Foulds, J., Eirinaki, M., & Getoor, L. (2015). HyPER: A flexible and extensible probabilistic framework for hybrid recommender systems. In ACM conference on recommender systems (RecSys).
[29] Leskovec, J., Huttenlocher, D., & Kleinberg, J. (2010). Signed Networks in Social Media. In Proceedings of the 28th ACM conference on human factors in computing systems (CHI).
[30] Liu, S., Liu, K., He, S., & Zhao, J. (2016). A probabilistic soft logic based approach to exploiting latent and global information in event classification. In AAAI conference on artificial intelligence (AAAI).
[31] Lowd, D., & Domingos, P. (2007). Recursive random fields. In Proceedings of the international joint conference on artificial intelligence (IJCAI) (pp. 950-955).
[32] Milch, B., Zettlemoyer, L. S., Kersting, K., Haimes, M., & Kaelbling, L. P. (2008). Lifted probabilistic inference with counting formulas. In Proceedings of the international conference on artificial intelligence (AAAi) (Vol. 8, pp. 1062-1068).
[33] Muggleton, S; Raedt, L, Inductive logic programming: theory and methods, The Journal of Logic Programming, 19, 629-679, (1994) · Zbl 0816.68043
[34] Poole, D., Buchman, D., Kazemi, S. M., Kersting, K., & Natarajan, S. (2014). Population size extrapolation in relational probabilistic modelling. In Proceedings of the international conference on scalable uncertainty management (SUM) (pp. 292-305). Springer.
[35] Poole, D., Buchman, D., Natarajan, S., & Kersting, K. (2012). Aggregation and population growth: The relational logistic regression and Markov logic cases. In Proceedings of the international workshop on statistical relational AI at UAI (StarAI).
[36] Prade, H., Richard, G., & Serrurier, M. (2003). Learning first order fuzzy logic rules. In Proceedings of the 10th international fuzzy systems world congress (IFSA) (pp. 702-709). Springer. · Zbl 1037.68118
[37] Pujara, J., Miao, H., Getoor, L., & Cohen, W. (2013). Knowledge graph identification. In Proceedings of the international semantic web conference (ISWC).
[38] Richardson, M; Domingos, P, Markov logic networks, Machine Learning, 62, 107-136, (2006)
[39] Sridhar, D; Fakhraei, S; Getoor, L, A probabilistic approach for collective similarity-based drug-drug interaction prediction, Bioinformatics, 32, 3175-3182, (2016)
[40] Van den Broeck, G., Meert, W., & Darwiche, A. (2013). Skolemization for weighted first-order model counting. arXiv preprint arXiv:1312.5378.
[41] Victor, P., Cornelis, C., & De Cock, M. (2011). Trust and recommendations. In Recommender systems handbook (pp. 645-675). Springer.
[42] West, R; Paskov, HS; Leskovec, J; Potts, C, Exploiting social network structure for person-to-person sentiment analysis, Transactions of the Association for Computational Linguistics (TACL), 2, 297-310, (2014)
[43] Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multicriteria decision making. In IEEE transactions on systems, man and cybernetics (IEEE SMC) (pp. 183-190). · Zbl 0637.90057
[44] Zadeh, LA, A computational approach to fuzzy quantifiers in natural languages, Computers and Mathematics with Applications, 9, 149-184, (1983) · Zbl 0517.94028
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.