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Metric Logic Program Explanations for Complex Separator Functions

  • Srijan Kumar
  • Edoardo Serra
  • Francesca SpezzanoEmail author
  • V. S. Subrahmanian
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9858)

Abstract

There are many classifiers that treat entities to be classified as points in a high-dimensional vector space and then compute a separator S between entities in class \(+1\) from those in class \(-1\). However, such classifiers are usually very hard to explain in plain English to domain experts. We propose Metric Logic Programs (MLPs) which are a fragment of constraint logic programs as a new paradigm for explaining S. We present multiple measures of quality of an MLP and define the problem of finding an MLP-Explanation of S and show that it - and various related problems - are NP-hard. We present the MLP_Extract algorithm to extract MLP explanations for S. We show that while our algorithms provide more succinct, simpler, and higher fidelity explanations than association rules that are less expressive, our algorithms do require additional run-time.

Keywords

Support Vector Machine Association Rule Logic Program Past Work Predicate Symbol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Parts of this work were supported by ONR grant N000141612739 and ARO grant W911NF1610342.

References

  1. 1.
  2. 2.
    Agrawal, R., Imieliński, T., Swami, A.: Mining association rules between sets of items in large databases. SIGMOD Rec. 22(2), 207–216 (1993)CrossRefGoogle Scholar
  3. 3.
    Barakat, N.H., Bradley, A.P.: Rule extraction from support vector machines: a review. Neurocomputing 74(1–3), 178–190 (2010)CrossRefGoogle Scholar
  4. 4.
    Beldiceanu, N., Carlsson, M., Flener, P., Pearson, J.: On the reification of global constraints. Constraints 18(1), 1–6 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Breiman, L., Friedman, J., Olshen, R., Stone, C.: Classification and Regression Trees. Wadsworth and Brooks, Monterey (1984)zbMATHGoogle Scholar
  6. 6.
    Cohen, W.W.: Fast effective rule induction. In: ICML, pp. 115–123 (1995)Google Scholar
  7. 7.
    Craven, M.W., Shavlik, J.W.: Extracting tree-structured representations of trained networks. Adv. Neural Inf. Process. Syst. 8, 24–30 (1996)Google Scholar
  8. 8.
    Diederich, J. (ed.): Rule Extraction from Support Vector Machines. Studies in Computational Intelligence, vol. 80. Springer, Heidelberg (2008)zbMATHGoogle Scholar
  9. 9.
    Dyer, M.E., Frieze, A.M.: On the complexity of computing the volume of a polyhedron. SIAM J. Comput. 17(5), 967–974 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Eiter, T., Gottlob, G.: The complexity of logic-based abduction. J. ACM (JACM) 42(1), 3–42 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Jaffar, J., Lassez, J.-L.: Constraint logic programming. In: POPL, pp. 111–119 (1987)Google Scholar
  12. 12.
    Kakas, A.C., Michael, A., Mourlas, C.: ACLP: abductive constraint logic programming. J. Log. Program. 44(1), 129–177 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Lloyd, J.W.: Foundations of Logic Programming. Springer, New York (1987)CrossRefzbMATHGoogle Scholar
  14. 14.
    Martens, D., Baesens, B., Van Gestel, T.: Decompositional rule extraction from support vector machines by active learning. IEEE Trans. Knowl. Data Eng. 21(2), 178–191 (2009)CrossRefGoogle Scholar
  15. 15.
    Quinlan, J.R.: C4.5: Programs for Machine Learning. Morgan Kaufmann Publishers Inc., Los Altos (1993)Google Scholar
  16. 16.
    Reiter, R.: On closed world data bases. In: Ginsberg, M.L. (ed.) Readings in Nonmonotonic Reasoning, pp. 300–310. Kaufmann, Los Altos (1987)Google Scholar
  17. 17.
    Schmitz, G.P., Aldrich, C., Gouws, F.S.: ANN-DT: an algorithm for extraction of decision trees from artificial neural networks. IEEE Trans. Neural Netw. 10(6), 1392–1401 (1999)CrossRefGoogle Scholar
  18. 18.
    Zhu, P., Qinghua, H.: Rule extraction from support vector machines based on consistent region covering reduction. Knowl. Based Syst. 42, 1–8 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Srijan Kumar
    • 1
  • Edoardo Serra
    • 2
  • Francesca Spezzano
    • 2
    Email author
  • V. S. Subrahmanian
    • 1
  1. 1.Computer Science DepartmentUniversity of MarylandCollege ParkUSA
  2. 2.Computer Science DepartmentBoise State UniversityBoiseUSA

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