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Three–Way Classification: Ambiguity and Abstention in Machine Learning

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Rough Sets (IJCRS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11499))

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Abstract

Ambiguity, that is the lack of information to produce a specific classification, is an important issue in decision–making and supervised classification. In case of ambiguity, human–decision makers can resort to abstaining from making precise classifications (especially when error-related costs are high), but this behaviour has been scarcely addressed, and applied, in machine learning algorithms. This contribution grounds on previous works in the areas of three–way decisions, cautious classification and orthopairs, and proposes a set of techniques we developed to address this form of ambiguity, by providing both a general–purpose technique to create three–way algorithms from probabilistic ones, and also more specific techniques which could be applied to popular machine learning frameworks. We also evaluate the proposed idea, by performing a set of experiments where we compare classical classification algorithms with the corresponding three–way generalizations, in order to study the trade–off between classification accuracy and abstention: the results are promising.

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References

  1. Bartlett, P.L., Wegkamp, M.H.: Classification with a reject option using a hinge loss. J. Mach. Learn. Res. 9, 1823–1840 (2008)

    MathSciNet  MATH  Google Scholar 

  2. Bello, R., Falcon, R.: Rough sets in machine learning: a review. In: Wang, G., Skowron, A., Yao, Y., Ślęzak, D., Polkowski, L. (eds.) Thriving Rough Sets, pp. 87–118. Springer International Publishing, Cham (2017)

    Chapter  Google Scholar 

  3. Breiman, L.: Random forests. Mach. Learn. 45(1), 5–32 (2001)

    Article  Google Scholar 

  4. Cabitza, F., Ciucci, D., Rasoini, R.: A giant with feet of clay: on the validity of the data that feed machine learning in medicine. In: Cabitza, F., Batini, C., Magni, M. (eds.) Organizing for the Digital World. LNISO, vol. 28, pp. 121–136. Springer, Cham (2019). https://doi.org/10.1007/978-3-319-90503-7_10

    Chapter  Google Scholar 

  5. Campagner, A., Cabitza, F., Ciucci, D.: Exploring medical data classification with three-way decision tree. In: Proceedings of the 12th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2019) - Volume 5: HEALTHINF. pp. 147–158. SCITEPRESS (2019)

    Google Scholar 

  6. Campagner, A., Ciucci, D.: Three-way and semi-supervised decision tree learning based on orthopartitions. In: Medina, J., Ojeda-Aciego, M., Verdegay, J.L., Pelta, D.A., Cabrera, I.P., Bouchon-Meunier, B., Yager, R.R. (eds.) IPMU 2018. CCIS, vol. 854, pp. 748–759. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-91476-3_61

    Chapter  Google Scholar 

  7. Campagner, A., Ciucci, D.: Orthopartitions and soft clustering. Knowl. Based Syst. (Submitted)

    Google Scholar 

  8. Chow, C.: On optimum recognition error and reject tradeoff. IEEE Trans. Inform. Theory 16, 41–46 (1970)

    Article  Google Scholar 

  9. Ciucci, D.: Orthopairs: a simple and widely used way to model uncertainty. Fundamenta Informaticae 108, 287–304 (2011)

    MathSciNet  MATH  Google Scholar 

  10. Ciucci, D.: Orthopairs and granular computing. Granular Comput. 1, 159–170 (2016)

    Article  Google Scholar 

  11. Cortes, C., Vapnik, V.: Support-vector networks. Mach. Learn. 20(3), 273–297 (1995)

    MATH  Google Scholar 

  12. Daniel, W.W.: Applied Nonparametric Statistics. Duxbury Thomson Learning (1990)

    Google Scholar 

  13. Deo, R.: Machine learning in medicine. Circulation 132 (2015)

    Article  Google Scholar 

  14. Ellerman, D.: An introduction to logical entropy and its relation to Shannon entropy. Int. J. Semant. Comput. 7(2), 121–145 (2013)

    Article  Google Scholar 

  15. Feldman, K., Faust, L., Wu, X., Huang, C., Chawla, N.V.: Beyond volume: the impact of complex healthcare data on the machine learning pipeline. CoRR abs/1706.01513 (2017)

    Google Scholar 

  16. Ferri, C., Hernández-Orallo, J.: Cautious classifiers. In: ROC Analysis in Artificial Intelligence, 1st International Workshop, ROCAI-2004, pp. 27–36 (2004)

    Google Scholar 

  17. Goodfellow, I., Bengio, Y., Courville, A.: Deep Learning. MIT Press, Cambridge (2016)

    MATH  Google Scholar 

  18. Hajian, S., Bonchi, F., Castillo, C.: Algorithmic bias: from discrimination discovery to fairness-aware data mining. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 2125–2126, August 2016

    Google Scholar 

  19. Han, P.K., Klein, W.M., Arora, N.K.: Varieties of uncertainty in health care: a conceptual taxonomy. Med. Decis. Making 31(6), 828–838 (2011)

    Article  Google Scholar 

  20. Hechtlinger, Y., Póczos, B., Wasserman, L.A.: Cautious deep learning. arXiv/CoRR abs/1805.09460 (2018)

    Google Scholar 

  21. Hüllermeier, E.: Fuzzy sets in machine learning and data mining. Appl. Soft Comput. 11(2), 1493–1505 (2011)

    Article  Google Scholar 

  22. Hüllermeier, E.: Does machine learning need fuzzy logic? Fuzzy Sets Syst. 281, 292–299 (2015). Special Issue Celebrating the 50th Anniversary of Fuzzy Sets

    Article  MathSciNet  Google Scholar 

  23. Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques - Adaptive Computation and Machine Learning. The MIT Press, Cambridge (2009)

    Google Scholar 

  24. Kooi, T., et al.: Large scale deep learning for computer aided detection of mammographic lesions. Med. Image Anal. 35, 303–312 (2017)

    Article  Google Scholar 

  25. Li, J.D.: A two-step rejection procedure for testing multiple hypotheses. J. Stat. Plann. Infer. 138(6), 1521–1527 (2008)

    Article  MathSciNet  Google Scholar 

  26. Obermeyer, Z., Emanuel, E.J.: Predicting the future - big data, machine learning, and clinical medicine. N. Engl. J. Med. 375(13), 1216–1219 (2016)

    Article  Google Scholar 

  27. Pawlak, Z.: Rough sets. Int. J. Comput. Inform. Sci. 11(5), 341–356 (1982)

    Article  Google Scholar 

  28. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  29. Smets, P., Kennes, R.: The transferable belief model. Artif. Intell. 66(2), 191–234 (1994)

    Article  MathSciNet  Google Scholar 

  30. Svensson, C., Hübler, R., Figge, M.: Automated classification of circulating tumor cells and the impact of interobsever variability on classifier training and performance. J. Immunol. Res. 2015, 1–9 (2015)

    Article  Google Scholar 

  31. Yao, Y.: An outline of a theory of three-way decisions. In: Yao, J.T., Yang, Y., Słowiński, R., Greco, S., Li, H., Mitra, S., Polkowski, L. (eds.) RSCTC 2012. LNCS (LNAI), vol. 7413, pp. 1–17. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32115-3_1

    Chapter  Google Scholar 

  32. Zadeh, L.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Sistemistica e Comunicazione, University of Milano–Bicocca, Viale Sarca 336, 20126, Milan, Italy

    Andrea Campagner, Federico Cabitza & Davide Ciucci

  2. IRCCS Istituto Ortopedico Galeazzi, Via Galeazzi 4, 20161, Milan, Italy

    Federico Cabitza

  3. Deloitte Italia, Via Tortona 25, Milan, Italy

    Andrea Campagner

Authors
  1. Andrea Campagner
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  2. Federico Cabitza
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  3. Davide Ciucci
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Corresponding author

Correspondence to Davide Ciucci .

Editor information

Editors and Affiliations

  1. University of Debrecen, Debrecen, Hungary

    Tamás Mihálydeák

  2. Southwest Petroleum University, Chengdu, China

    Fan Min

  3. Chongqing University of Posts and Telecommunications, Chongqing, China

    Guoyin Wang

  4. Indian Institute of Technology Kanpur, Kanpur, India

    Mohua Banerjee

  5. Fujian Normal University, Fuzhou, China

    Ivo Düntsch

  6. University of Rzeszów, Rzeszow, Poland

    Zbigniew Suraj

  7. University of Milano-Bicocca, Milan, Italy

    Davide Ciucci

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Campagner, A., Cabitza, F., Ciucci, D. (2019). Three–Way Classification: Ambiguity and Abstention in Machine Learning. In: Mihálydeák, T., et al. Rough Sets. IJCRS 2019. Lecture Notes in Computer Science(), vol 11499. Springer, Cham. https://doi.org/10.1007/978-3-030-22815-6_22

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  • DOI: https://doi.org/10.1007/978-3-030-22815-6_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22814-9

  • Online ISBN: 978-3-030-22815-6

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