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it is possible to add branches to the tree that improve performance on the training examples while decreasing performance on other instances outside this set Methods for post-pruning the decision tree are therefore important to avoid overfitting in decision tree learning (and other inductive inference methods that employ a preference bias) A large variety of extensions to the basic ID3 algorithm has been developed by different researchers These include methods for post-pruning trees, handling real-valued attributes, accommodating training examples with missing attribute values, incrementally refining decision trees as new training examples become available, using attribute selection measures other than information gain, and considering costs associated with instance attributes Among the earliest work on decision tree learning is Hunt's Concept Learning System (CLS) (Hunt et al 1966) and Friedman and Breiman's work resulting in the CART system (Friedman 1977; Breiman et al 1984) Quinlan's ID3 system (Quinlan 1979, 1983) forms the basis for the discussion in this chapter Other early work on decision tree learning includes ASSISTANT (Kononenko et al 1984; Cestnik et al 1987) Implementations of decision tree induction algorithms are now commercially available on many computer platforms For further details on decision tree induction, an excellent book by Quinlan (1993) discusses many practical issues and provides executable code for C45 Mingers (1989a) and Buntine and Niblett (1992) provide two experimental studies comparing different attribute-selection measures Mingers (1989b) and Malerba et al (1995) provide studies of different pruning strategies Experiments comparing decision tree learning and other learning methods can be found in numerous papers, including (Dietterich et al 1995; Fisher and McKusick 1989; Quinlan 1988a; Shavlik et al 1991; Thrun et al 1991; Weiss and Kapouleas 1989)

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Give decision trees to represent the following boolean functions:

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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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After closing the user interface design assistant window you will be back in the main installer setup window. Just click on the Build button. You will be prompted for a name for the package. This is the name that the user will see below the Package installer icon when he comes to install your program. Click OK, and the build process will begin. This should take a few seconds, and all being well, you will see a message confirming success (Figure 15 17).

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

Breiman, L, Friedman, J H, Olshen, R A, & Stone, P 1 (1984) ClassiJicationand regression trees Belmont, CA: Wadsworth International Group Brodley, C E, & Utgoff, P E (1995) Multivariate decision trees Machine Learning, 19, 45-77 Buntine, W, & Niblett, T (1992) A further comparison of splitting rules for decision-tree induction Machine Learning, 8, 75-86 Cestnik, B, Kononenko, I, & Bratko, I (1987) ASSISTANT-86: A knowledge-elicitation tool for sophisticated users In I Bratko & N LavraE (Eds), Progress in machine learning Bled, Yugoslavia: Sigma Press Dietterich, T G, Hild, H, & Bakiri, G (1995) A comparison of ID3 and BACKPROPAGATION for English text-to-speech mapping Machine Learning, 18(1), 51-80 Dietterich, T G, Kearns, M, & Mansour, Y (1996) Applying the weak learning framework to understand and improve C45 Proceedings of the 13th International Conference on Machine Learning (pp 96104) San Francisco: Morgan Kaufmann Fayyad, U M (1991) On the induction of decision trees for multiple concept leaning, (PhD dissertation) EECS Department, University of Michigan

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