Hybrid Bayesian estimation tree learning with discrete and fuzzy labels
Tóm tắt
Classical decision tree model is one of the classical machine learning models for its simplicity and effectiveness in applications. However, compared to the DT model, probability estimation trees (PETs) give a better estimation on class probability. In order to get a good probability estimation, we usually need large trees which are not desirable with respect to model transparency. Linguistic decision tree (LDT) is a PET model based on label semantics. Fuzzy labels are used for building the tree and each branch is associated with a probability distribution over classes. If there is no overlap between neighboring fuzzy labels, these fuzzy labels then become discrete labels and a LDT with discrete labels becomes a special case of the PET model. In this paper, two hybrid models by combining the naive Bayes classifier and PETs are proposed in order to build a model with good performance without losing too much transparency. The first model uses naive Bayes estimation given a PET, and the second model uses a set of small-sized PETs as estimators by assuming the independence between these trees. Empirical studies on discrete and fuzzy labels show that the first model outperforms the PET model at shallow depth, and the second model is equivalent to the naive Bayes and PET.
Tài liệu tham khảo
Quinlan J R. Induction of decision trees. Machine Learning, 1986, 1(1): 81–106
Olaru C, Wehenkel L. A complete fuzzy decision tree technique. Fuzzy Sets and Systems, 2003, 138(2): 221–254
Quinlan J R. C4. 5: programs for machine learning. Morgan Kaufmann, 1993
Baldwin J, Lawry J, Martin T. Mass assignment fuzzy ID3 with applications. In: Proceedings of the Unicom Workshop on Fuzzy Logic: Applications and Future Directions. 1997, 278–294
Janikow C Z. Fuzzy decision trees: issues and methods. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 1998, 28(1): 1–14
Huang Z, Gedeon T D, Nikravesh M. Pattern trees induction: a new machine learning method. IEEE Transactions on Fuzzy Systems, 2008, 16(4): 958–970
Qin B, Xia Y, Li F. Dtu: a decision tree for uncertain data. Advances in Knowledge Discovery and Data Mining, 2009: 4–15
Provost F, Domingos P. Tree induction for probability-based ranking. Machine Learning, 2003, 52(3): 199–215
Qin Z, Lawry J. Decision tree learning with fuzzy labels. Information Sciences, 2005, 172(1): 91–129
Qin Z, Lawry J. Prediction trees using linguistic modelling. In: Proceedings of World Congress of International Fuzzy Systems Association (IFSA-05), 2005
Qin Z, Lawry J. Prediction and query evaluation using linguistic decision trees. Applied Soft Computing, 2011, 11(5): 3916–3928
Lawry J. A framework for linguistic modelling. Artificial Intelligence, 2004, 155(1): 1–39
Elkan C. Naive bayesian learning. Technical Report CS97-557, Dept. of Computer Science and Engineering, UCSD, 1997
Blake C, Merz C J. UCI machine learning repository. http://www.ics.uci.edu/~mlearn/MLRepository.html
Zadeh L A. Fuzzy logic= computing with words. IEEE Transactions on Fuzzy Systems, 1996, 4(2): 103–111
Zadeh L A. The concept of a linguistic variable and its application to approximate reasoning-I. Information Sciences, 1975, 8(3): 199–249
Sufyan Beg M, Thint M, Qin Z. Pnl-enhanced restricted domain question answering system. In: Proceedings of the 2007 IEEE International Fuzzy Systems Conference. 2007, 1–7
Qin Z, Thint M, Beg M S. Deduction engine design for pnl-based question answering system. In: Proceedings of the 12th International Fuzzy Systems Association World Congress. 2007, 253–262
Lawry J. Modeling and reasoning with vague concepts. Springer, 2006
Lawry J, Shanahan J G, Ralescu A. Modelling with words: learning, fusion, and reasoning within a formal linguistic representation framework. Volume 2873. Springer, 2003
Qin Z, Lawry J. Lfoil: linguistic rule induction in the label semantics framework. Fuzzy Sets and Systems, 2008, 159(4): 435–448
Baldwin J F, Martin T P, Pilsworth B W. Fril-fuzzy and evidential reasoning in artificial intelligence. John Wiley & Sons, Inc., 1995
Zhang W, Qin Z. Dissimilarity measure of logical expressions. In: Proceedings of the 2010 International Conference on Machine Learning and Cybernetics (ICMLC). 2010, 199–203
Zhang W, Qin Z. Clustering data and imprecise concepts. In: Proceedings of the IEEE International Conference on Fuzzy Systems (FUZZ). 2011, 603–608
Jeffrey R C. The logic of decision. University of Chicago Press, 1990
Qin Z, Lawry J. Fuzziness and performance: an empirical study with linguistic decision trees. In: Proceedings of the 12th International Fuzzy Systems Association World Congress on Foundations of Fuzzy Logic and Soft Computing. 2007, 407–416
Randon N J, Lawry J. Classification and query evaluation using modelling with words. Information Sciences, 2006, 176(4): 438–464
Qin Z. Naive bayes classification given probability estimation trees. In: Proceedings of the 5th International Conference on Machine Learning and Applications, ICMLA’06. 2006, 34–42
Qin Z, Lawry J. Hybrid bayesian estimation trees based on label semantics. Lecture Notes in Computer Science, 2005, 896–907