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Give decision trees to represent the following boolean functions:
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(a) A A -B (b) A V [ B A C ] (c) A X O R B (d) [ A A B] v [C A Dl
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Consider the following set of training examples: Instance Classification a1
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( a ) What is the entropy of this collection of training examples with respect to the
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target function classification (b) What is the information gain of a2 relative to these training examples 33 True or false: If decision tree D2 is an elaboration of tree Dl, then D l is moregeneral-than D2 Assume D l and D2 are decision trees representing arbitrary boolean functions, and that D2 is an elaboration of D l if ID3 could extend D l into D2 If true, give a proof; if false, a counterexample (More-general-than is defined in 2) 34 ID3 searches for just one consistent hypothesis, whereas the CANDIDATEELIMINATION algorithm finds all consistent hypotheses Consider the correspondence between these two learning algorithms ( a ) Show the decision tree that would be learned by ID3 assuming it is given the four training examples for the Enjoy Sport target concept shown in Table 21 of 2 (b) What is the relationship between the learned decision tree and the version space (shown in Figure 23 of 2) that is learned from these same examples Is the learned tree equivalent to one of the members of the version space (c) Add the following training example, and compute the new decision tree This time, show the value of the information gain for each candidate attribute at each step in growing the tree
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( d ) Suppose we wish to design a learner that (like ID3) searches a space of decision
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tree hypotheses and (like CANDIDATE-ELIMINATION) all hypotheses confinds sistent with the data In short, we wish to apply the CANDIDATE-ELIMINATION algorithm to searching the space of decision tree hypotheses Show the S and G sets that result from the first training example from Table 21 Note S must contain the most specific decision trees consistent with the data, whereas G must contain the most general Show how the S and G sets are refined by thesecond training example (you may omit syntactically distinct trees that describe the same concept) What difficulties do you foresee in applying CANDIDATE-ELIMINATION to a decision tree hypothesis space
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m 3 DECISION TREE LEARNING
Fayyad, U M, & Irani, K B (1992) On the handling of continuous-valued attributes in decision tree generation Machine Learning, 8, 87-102 Fayyad, U M, & Irani, K B (1993) Multi-interval discretization of continuous-valued attributes for classification learning In R Bajcsy (Ed), Proceedings of the 13th International Joint Conference on ArtiJcial Intelligence (pp 1022-1027) Morgan-Kaufmann Fayyad, U M, Weir, N, & Djorgovski, S (1993) SKICAT: A machine learning system for automated cataloging of large scale sky surveys Proceedings of the Tenth International Conference on Machine Learning (pp 112-1 19) Amherst, MA: Morgan Kaufmann Fisher, D H, and McKusick, K B (1989) An empirical comparison of ID3 and back-propagation Proceedings of the Eleventh International Joint Conference on A (pp 788-793) Morgan 1 Kaufmann Fnedman, J H (1977) A recursive partitioning decision rule for non-parametric classification IEEE Transactions on Computers @p 404408) Hunt, E B (1975) Art$cial Intelligence New Yorc Academic Press Hunt, E B, Marin, J, & Stone, P J (1966) Experiments in Induction New York: Academic Press Kearns, M, & Mansour, Y (1996) On the boosting ability of top-down decision tree learning algorithms Proceedings of the 28th ACM Symposium on the Theory of Computing New York: ACM Press Kononenko, I, Bratko, I, & Roskar, E (1984) Experiments in automatic learning of medical diagnostic rules (Technical report) Jozef Stefan Institute, Ljubljana, Yugoslavia Lopez de Mantaras, R (1991) A distance-based attribute selection measure for decision tree induction Machine Learning, 6(1), 81-92 Malerba, D, Floriana, E, & Semeraro, G (1995) A further comparison of simplification methods for decision tree induction In D Fisher & H Lenz (Eds), Learningfrom data: AI and statistics Springer-Verlag Mehta, M, Rissanen, J, & Agrawal, R (1995) MDL-based decision tree pruning Proceedings of the First International Conference on Knowledge Discovery and Data Mining (pp 216-221) Menlo Park, CA: AAAI Press Mingers, J (1989a) An empirical comparison of selection measures for decision-tree induction Machine Learning, 3(4), 319-342 Mingers, J (1989b) An empirical comparison of pruning methods for decision-tree induction Machine Learning, 4(2), 227-243 Murphy, P M, & Pazzani, M J (1994) Exploring the decision forest: An empirical investigation of Occam's razor in decision tree induction Journal of Artijicial Intelligence Research, 1, 257-275 Murthy, S K, Kasif, S, & Salzberg, S (1994) A system for induction of oblique decision trees Journal of Art$cial Intelligence Research, 2, 1-33 Nunez, M (1991) The use of background knowledge in decision tree induction Machine Learning, 6(3), 23 1-250 Pagallo, G, & Haussler, D (1990) Boolean feature discovery in empirical learning Machine Learning, 5, 71-100 Qulnlan, J R (1979) Discovering rules by induction from large collections of examples In D Michie (Ed), Expert systems in the micro electronic age Edinburgh Univ Press Qulnlan, J R (1983) Learning efficient classification procedures and their application to chess end games In R S Michalski, J G Carbonell, & T M Mitchell (Eds), Machine learning: An artificial intelligence approach San Matw, CA: Morgan Kaufmann Qulnlan, J R (1986) Induction of decision trees Machine Learning, 1(1), 81-106 Qulnlan, J R (1987) Rule induction with statistical data-a comparison with multiple regression Journal of the Operational Research Society, 38,347-352 Quinlan, JR (1988) An empirical comparison of genetic and decision-tree classifiers Proceedings of the Fifrh International Machine Learning Conference (135-141) San Matw, CA: Morgan Kaufmann Quinlan, JR (1988b) Decision trees and multi-valued attributes In Hayes, Michie, & Richards (Eds), Machine Intelligence 1 1 , (pp 305-318) Oxford, England: Oxford University Press
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