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Pruning strategies for the efficient traversal of the search space in PILP environments

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Abstract

Probabilistic inductive logic programming (PILP) is a statistical relational learning technique which extends inductive logic programming by considering probabilistic data. The ability to use probabilities to represent uncertainty comes at the cost of an exponential evaluation time when composing theories to model the given problem. For this reason, PILP systems rely on various pruning strategies in order to reduce the search space. However, to the best of the authors’ knowledge, there has been no systematic analysis of the different pruning strategies, how they impact the search space and how they interact with one another. This work presents a unified representation for PILP pruning strategies which enables end-users to understand how these strategies work both individually and combined and to make an informed decision on which pruning strategies to select so as to best achieve their goals. The performance of pruning strategies is evaluated both time and quality-wise in two state-of-the-art PILP systems with datasets from three different domains. Besides analysing the performance of the pruning strategies, we also illustrate the utility of PILP in one of the application domains, which is a real-world application.

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Notes

  1. Depending on the language bias (mechanism employed to constrain the search space), it might also be the case that the same literal with different arguments can occur multiple times in the rule. However, for the description of the search space, repeated literals in rules can be mimicked by introducing auxiliary predicates (for instance). Therefore, for the sake of simplicity, this case is not considered in what follows.

  2. Remember that a theory is evaluated probabilistically against the set of all examples.

  3. Another option would be to use a probabilistic inference method which determines the prediction values of a theory using an approximation, but this is outside of the scope of this work.

  4. http://www.cs.wisc.edu/~dpage/kddcup2001.

  5. http://rtw.ml.cmu.edu.

References

  1. Bellodi E, Riguzzi F ( 2012) , Learning the structure of probabilistic logic programs. In: Inductive logic programming, Springer, pp 61–75

  2. Bellodi E, Riguzzi F (2015) Structure learning of probabilistic logic programs by searching the clause space. Theory Pract Logic Program 15(02):169–212

    Article  Google Scholar 

  3. Berg WA, Hruban RH, Kumar D, Singh HR, Brem RF, Gatewood OM (1996) Lessons from mammographic histopathologic correlation of large-core needle breast biopsy. Radiographics 16(5):1111–1130

    Article  Google Scholar 

  4. Brancato B, Crocetti E, Bianchi S, Catarzi S, Risso GG, Bulgaresi P, Piscioli F, Scialpi M, Ciatto S, Houssami N (2012) Accuracy of needle biopsy of breast lesions visible on ultrasound: audit of fine needle versus core needle biopsy in 3233 consecutive samplings with ascertained outcomes. Breast 21(4):449–454

    Article  Google Scholar 

  5. Burbank F (1997) Stereotactic breast biopsy: comparison of 14- and 11-gauge mammotome probe performance and complication rates. Am Surg 63(11):988–995

    Google Scholar 

  6. Cook D, Holder L (2006) Mining graph data. Wiley, London

    Book  Google Scholar 

  7. Côrte-Real J, Dries A, Dutra I, Rocha R ( 2018) Improving candidate quality of probabilistic logic models. In: dal Palù A, Tarau P (eds) Technical communications of the 34th international conference on logic programming (ICLP 2018), Oxford, UK

  8. Côrte-Real J, Dutra I, Rocha R (2016) Estimation-based search space traversal in PILP environments. In: Russo A, Cussens J (eds) Proceedings of the 26th international conference on inductive logic programming (ILP 2016), LNAI, Springer, London, UK. Published in 2017

  9. Côrte-Real J, Mantadelis T, Dutra I, Rocha R, Burnside E (2015) SkILL: a stochastic inductive logic learner. In: International conference on machine learning and applications, Miami, Florida, USA

  10. Costa VS, Rocha R, Damas L (2012) The YAP prolog system. J Theory Pract Logic Program 12(1 & 2):5–34

    Article  MathSciNet  Google Scholar 

  11. De Raedt L, Dries A, Thon I, Van den Broeck G, Verbeke M ( 2015) Inducing probabilistic relational rules from probabilistic examples. In: International joint conference on artificial intelligence, AAAI Press, pp 1835–1843

  12. De Raedt L, Kersting K ( 2004) Probabilistic inductive logic programming. In: International conference on algorithmic learning theory. Springer, Berlin, pp 19–36

  13. De Raedt L, Kimmig A (2015) Probabilistic (logic) programming concepts. Mach Learn 100(1):5–47

  14. De Raedt L, Thon I ( 2011) Probabilistic rule learning. In: Inductive logic programming. Springer, pp 47–58

  15. Džeroski S (2010) Relational data mining. Springer, Berlin

    MATH  Google Scholar 

  16. Džeroski S, De Raedt L, Driessens K (2001) Relational reinforcement learning. Mach Learn 43(1–2):7–52

    Article  Google Scholar 

  17. Gonçalves AV, Thuler LC, Kestelman FP, Carmo PA, Lima CF, Cipolotti R (2011) Underestimation of malignancy of core needle biopsy for nonpalpable breast lesions. Rev Bras Ginecol Obstet 33(7):123–131

    Google Scholar 

  18. Halpern J (1990) An analysis of first-order logics of probability. Artif Intell 46(3):311–350

    Article  MathSciNet  Google Scholar 

  19. Kersting K, De Raedt L, Kramer S ( 2000) Interpreting Bayesian logic programs. In: AAAI workshop on learning statistical models from relational data, pp 29–35

  20. Kimmig A, Demoen B, Raedt LD, Costa VS, Rocha R (2011) On the implementation of the probabilistic logic programming language ProbLog. Theory Pract Logic Program 11(2 & 3):235–262

    Article  MathSciNet  Google Scholar 

  21. Kok S, Domingos P ( 2005) Learning the structure of Markov logic networks. In: International conference on machine learning. ACM, pp 441–448

  22. Liberman L (2000) Percutaneous imaging-guided core breast biopsy: state of the art at the millennium. Am J Roentgenol 174(5):1191–1199

    Article  Google Scholar 

  23. Liberman L, Drotman M, Morris EA et al (2000) Imaging-histologic discordance at percutaneous breast biopsy. Cancer 89(12):2538–2546

    Article  Google Scholar 

  24. Muggleton S (1996) Stochastic logic programs. Adv Inductive Logic Program 32:254–264

    MathSciNet  Google Scholar 

  25. Muggleton S, Raedt LD (1994) Inductive logic programming: theory and methods. J Log Program 19(20):629–679

    Article  MathSciNet  Google Scholar 

  26. Muggleton S, Santos J, Almeida C, Tamaddoni-Nezhad A ( 2008) TopLog: ILP using a logic program declarative bias. In: International conference on logic programming, Springer, Berlin, pp 687–692

  27. Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, Prettenhofer P, Weiss R, Dubourg V, Vanderplas J, Passos A, Cournapeau D, Brucher M, Perrot M, Duchesnay E (2011) Scikit-learn: machine learning in python. J Mach Learn Res 12:2825–2830

    MathSciNet  MATH  Google Scholar 

  28. Poole D (1997) The independent choice logic for modelling multiple agents under uncertainty. Artif Intell 94(1):7–56

    Article  MathSciNet  Google Scholar 

  29. Richardson M, Domingos P (2006) Markov logic networks. Mach Learn 62(1–2):107–136

    Article  Google Scholar 

  30. Santos Costa V, Page D, Qazi M, Cussens J ( 2002) CLP(BN): constraint logic programming for probabilistic knowledge. In: Conference on uncertainty in artificial intelligence, pp 517–524

  31. Sato T (1995) A statistical learning method for logic programs with distribution semantics. In: Proceedings of the 12th international conference on logic programming (ICLP 95), Citeseer

  32. Sato T, Kameya Y ( 1997) PRISM: A language for symbolic-statistical modeling. In: International joint conference on artificial intelligence, vol 97, Morgan Kaufmann, pp 1330–1339

  33. Vennekens J, Verbaeten S, Bruynooghe M (2004) Logic programs with annotated disjunctions. In: Logic programming. Springer, pp 431–445

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Acknowledgements

This work was financed by National Funds through the Portuguese funding agency, FCT—Fundação para a Ciência e a Tecnologia, within project UIDB/50014/2020. Joana Côrte-Real was financed by the FCT grant SFRH/BD/52235/2013.

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Authors and Affiliations

  1. Department of Computer Science, Faculty of Sciences, University of Porto, Rua do Campo Alegre, 1021, 4169-007, Porto, Portugal

    Joana Côrte-Real, Inês Dutra & Ricardo Rocha

  2. CRACS & INESC TEC, Porto, Portugal

    Joana Côrte-Real & Ricardo Rocha

  3. CINTESIS, Porto, Portugal

    Inês Dutra

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  1. Joana Côrte-Real
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  2. Inês Dutra
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  3. Ricardo Rocha
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Correspondence to Inês Dutra.

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Côrte-Real, J., Dutra, I. & Rocha, R. Pruning strategies for the efficient traversal of the search space in PILP environments. Knowl Inf Syst 63, 3183–3215 (2021). https://doi.org/10.1007/s10115-021-01620-1

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