Abstract
Besides a good prediction a classifier is to give an explanation how input data is related to the classification result. Decision trees are very popular classifiers and provide a good trade-off between accuracy and explainability for many scenarios. Its split decisions correspond to Boolean conditions on single attributes. In cases when for a class decision several attribute values interact gradually with each other, Boolean-logic-based decision trees are not appropriate. For such cases we propose a quantum-logic inspired decision tree (QLDT) which is based on sums and products on normalized attribute values. In contrast to decision trees based on fuzzy logic a QLDT obeys the rules of the Boolean algebra.
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Of course, there exist classification problems for which the decision tree based on Boolean logic fits perfectly.
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References
Aggarwal, C.C.: Data Mining: The Textbook. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-14142-8
Doshi-Velez, F., Kim, B.: Towards a rigorous science of interpretable machine learning. arXiv preprint arXiv:1702.08608 (2017)
Freitas, A.A.: Comprehensible classification models: a position paper. ACM SIGKDD Explor. Newsl. 15(1), 1–10 (2014)
Hüllermeier, E., Schmitt, I.: Non-additive utility functions: Choquet integral versus weighted DNF formulas. In: Gaul, W., Geyer-Schulz, A., Baba, Y., Okada, A. (eds.) German-Japanese Interchange of Data Analysis Results. SCDAKO, pp. 115–123. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-01264-3_10
Janikow, C.Z.: Fuzzy decision trees: issues and methods. IEEE Trans. Syst. Man Cybern. Part B (Cybernetics) 28(1), 1–14 (1998)
Jiménez, F., Martínez, C., Marzano, E., Palma, J.T., Sánchez, G., Sciavicco, G.: Multiobjective evolutionary feature selection for fuzzy classification. IEEE Trans. Fuzzy Syst. 27(5), 1085–1099 (2019)
Lundberg, S.M., Lee, S.I.: A unified approach to interpreting model predictions. In: Advances in Neural Information Processing Systems, vol. 30 (2017)
Mittelstaedt, P.: Quantum logic. In: PSA 1974, pp. 501–514. Springer, Cham (1976). https://doi.org/10.1007/978-94-010-1449-6_28
Mittelstaedt, P.: Quantum Logic. D. Reidel Publishing Company, Dordrecht (1978)
Olaru, C., Wehenkel, L.: A complete fuzzy decision tree technique. Fuzzy Sets Syst. 138(2), 221–254 (2003)
Schmitt, I.: Quantum query processing: unifying database querying and information retrieval. Citeseer (2006)
Schmitt, I.: QQL: a DB &IR query language. VLDB J. 17(1), 39–56 (2008)
Schmitt, I.: Incorporating weights into a quantum-logic-based query language. In: Aerts, D., Khrennikov, A., Melucci, M., Toni, B. (eds.) Quantum-Like Models for Information Retrieval and Decision-Making. SSTEAMH, pp. 129–143. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25913-6_7
Schmitt, I., Baier, D.: Logic based conjoint analysis using the commuting quantum query language. In: Algorithms from and for Nature and Life, pp. 481–489. Springer, Cham (2013). https://doi.org/10.1007/978-3-319-00035-0_49
Strumbelj, E., Kononenko, I.: An efficient explanation of individual classifications using game theory. J. Mach. Learn. Res. 11, 1–18 (2010)
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Schmitt, I. (2022). QLDT: A Decision Tree Based on Quantum Logic. In: Chiusano, S., et al. New Trends in Database and Information Systems. ADBIS 2022. Communications in Computer and Information Science, vol 1652. Springer, Cham. https://doi.org/10.1007/978-3-031-15743-1_28
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DOI: https://doi.org/10.1007/978-3-031-15743-1_28
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