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Automatic Construction of Decision Trees from Data: A MultiDisciplinary Survey
 Data Mining and Knowledge Discovery
, 1997
"... Decision trees have proved to be valuable tools for the description, classification and generalization of data. Work on constructing decision trees from data exists in multiple disciplines such as statistics, pattern recognition, decision theory, signal processing, machine learning and artificial ne ..."
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Cited by 146 (1 self)
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Decision trees have proved to be valuable tools for the description, classification and generalization of data. Work on constructing decision trees from data exists in multiple disciplines such as statistics, pattern recognition, decision theory, signal processing, machine learning and artificial neural networks. Researchers in these disciplines, sometimes working on quite different problems, identified similar issues and heuristics for decision tree construction. This paper surveys existing work on decision tree construction, attempting to identify the important issues involved, directions the work has taken and the current state of the art. Keywords: classification, treestructured classifiers, data compaction 1. Introduction Advances in data collection methods, storage and processing technology are providing a unique challenge and opportunity for automated data exploration techniques. Enormous amounts of data are being collected daily from major scientific projects e.g., Human Genome...
The role of Occam’s Razor in knowledge discovery
 Data Mining and Knowledge Discovery
, 1999
"... Abstract. Many KDD systems incorporate an implicit or explicit preference for simpler models, but this use of “Occam’s razor ” has been strongly criticized by several authors (e.g., Schaffer, 1993; Webb, 1996). This controversy arises partly because Occam’s razor has been interpreted in two quite di ..."
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Cited by 78 (3 self)
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Abstract. Many KDD systems incorporate an implicit or explicit preference for simpler models, but this use of “Occam’s razor ” has been strongly criticized by several authors (e.g., Schaffer, 1993; Webb, 1996). This controversy arises partly because Occam’s razor has been interpreted in two quite different ways. The first interpretation (simplicity is a goal in itself) is essentially correct, but is at heart a preference for more comprehensible models. The second interpretation (simplicity leads to greater accuracy) is much more problematic. A critical review of the theoretical arguments for and against it shows that it is unfounded as a universal principle, and demonstrably false. A review of empirical evidence shows that it also fails as a practical heuristic. This article argues that its continued use in KDD risks causing significant opportunities to be missed, and should therefore be restricted to the comparatively few applications where it is appropriate. The article proposes and reviews the use of domain constraints as an alternative for avoiding overfitting, and examines possible methods for handling the accuracy–comprehensibility tradeoff.
Theory and Applications of Agnostic PACLearning with Small Decision Trees
, 1995
"... We exhibit a theoretically founded algorithm T2 for agnostic PAClearning of decision trees of at most 2 levels, whose computation time is almost linear in the size of the training set. We evaluate the performance of this learning algorithm T2 on 15 common "realworld" datasets, and show that for mo ..."
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Cited by 75 (2 self)
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We exhibit a theoretically founded algorithm T2 for agnostic PAClearning of decision trees of at most 2 levels, whose computation time is almost linear in the size of the training set. We evaluate the performance of this learning algorithm T2 on 15 common "realworld" datasets, and show that for most of these datasets T2 provides simple decision trees with little or no loss in predictive power (compared with C4.5). In fact, for datasets with continuous attributes its error rate tends to be lower than that of C4.5. To the best of our knowledge this is the first time that a PAClearning algorithm is shown to be applicable to "realworld" classification problems. Since one can prove that T2 is an agnostic PAClearning algorithm, T2 is guaranteed to produce close to optimal 2level decision trees from sufficiently large training sets for any (!) distribution of data. In this regard T2 differs strongly from all other learning algorithms that are considered in applied machine learning, for w...
General and Efficient Multisplitting of Numerical Attributes
, 1999
"... . Often in supervised learning numerical attributes require special treatment and do not fit the learning scheme as well as one could hope. Nevertheless, they are common in practical tasks and, therefore, need to be taken into account. We characterize the wellbehavedness of an evaluation function, ..."
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Cited by 40 (7 self)
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. Often in supervised learning numerical attributes require special treatment and do not fit the learning scheme as well as one could hope. Nevertheless, they are common in practical tasks and, therefore, need to be taken into account. We characterize the wellbehavedness of an evaluation function, a property that guarantees the optimal multipartition of an arbitrary numerical domain to be defined on boundary points. Wellbehavedness reduces the number of candidate cut points that need to be examined in multisplitting numerical attributes. Many commonly used attribute evaluation functions possess this property; we demonstrate that the cumulative functions Information Gain and Training Set Error as well as the noncumulative functions Gain Ratio and Normalized Distance Measure are all wellbehaved. We also devise a method of finding optimal multisplits efficiently by examining the minimum number of boundary point combinations that is required to produce partitions which are optimal wit...
Simplifying Decision Trees: A Survey
, 1996
"... Induced decision trees are an extensivelyresearched solution to classification tasks. For many practical tasks, the trees produced by treegeneration algorithms are not comprehensible to users due to their size and complexity. Although many tree induction algorithms have been shown to produce simpl ..."
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Cited by 38 (5 self)
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Induced decision trees are an extensivelyresearched solution to classification tasks. For many practical tasks, the trees produced by treegeneration algorithms are not comprehensible to users due to their size and complexity. Although many tree induction algorithms have been shown to produce simpler, more comprehensible trees (or data structures derived from trees) with good classification accuracy, tree simplification has usually been of secondary concern relative to accuracy and no attempt has been made to survey the literature from the perspective of simplification. We present a framework that organizes the approaches to tree simplification and summarize and critique the approaches within this framework. The purpose of this survey is to provide researchers and practitioners with a concise overview of treesimplification approaches and insight into their relative capabilities. In our final discussion, we briefly describe some empirical findings and discuss the application of tree i...
Occam's Two Razors: The Sharp and the Blunt
 In Proceedings of the Fourth International Conference on Knowledge Discovery and Data Mining
, 1998
"... Occam's razor has been the subject of much controversy. This paper argues that this is partly because it has been interpreted in two quite different ways, the first of which (simplicity is a goal in itself) is essentially correct, while the second (simplicity leads to greater accuracy) is not. The p ..."
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Cited by 27 (3 self)
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Occam's razor has been the subject of much controversy. This paper argues that this is partly because it has been interpreted in two quite different ways, the first of which (simplicity is a goal in itself) is essentially correct, while the second (simplicity leads to greater accuracy) is not. The paper reviews the large variety of theoretical arguments and empirical evidence for and against the "second razor," and concludes that the balance is strongly against it. In particular, it builds on the case of (Schaffer, 1993) and (Webb, 1996) by considering additional theoretical arguments and recent empirical evidence that the second razor fails in most domains. A version of the first razor more appropriate to KDD is proposed, and we argue that continuing to apply the second razor risks causing significant opportunities to be missed. 1 Occam's Two Razors William of Occam's famous razor states that "Nunquam ponenda est pluralitas sin necesitate," which, approximately translated, means "En...
Intermediate Decision Trees
 In Proc. 14th Intl. Joint Conf. on Artificial Intelligence
, 1995
"... Intermediate decision trees are the subtrees of the full (unpruned) decision tree generated in a breadthfirst order. An extensive empirical investigation evaluates the classification error of intermediate decision trees and compares their performance to full and pruned trees. Empirical results were ..."
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Cited by 8 (1 self)
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Intermediate decision trees are the subtrees of the full (unpruned) decision tree generated in a breadthfirst order. An extensive empirical investigation evaluates the classification error of intermediate decision trees and compares their performance to full and pruned trees. Empirical results were generated using C4.5 with 66 databases from the UCI machine learning database repository. Results show that when attempting to minimize the error of the pruned tree produced by C4.5, the best intermediate tree performs significantly better in 46 of the 66 databases. These and other results question the effectiveness of decision tree pruning strategies and suggest further consideration of the full tree and its intermediates. Also, the results reveal specific properties satisfied by databases in which the intermediate full tree performs best. Such relationships improve guidelines for selecting appropriate inductive strategies based on domain properties. 1 Introduction Numerous decision tree ...
!()+, ./01 23456
, 1995
"... Computing the maximum bichromatic discrepancy is an interesting theoretical problem with important applications in computational learning theory, computational geometry and computer graphics. In this paper we give algorithms to compute the maximum bichromatic discrepancy for simple geometric ranges, ..."
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Computing the maximum bichromatic discrepancy is an interesting theoretical problem with important applications in computational learning theory, computational geometry and computer graphics. In this paper we give algorithms to compute the maximum bichromatic discrepancy for simple geometric ranges, including rectangles and halfspaces. In addition, we give extensions to other discrepancy problems. 1 Introduction The main theme of this paper is to present efficient algorithms that solve the problem of computing the maximum bichromatic discrepancy for axis oriented rectangles. This problem arises naturally in different areas of computer science, such as computational learning theory, computational geometry and computer graphics ([Ma], [DG]), and has applications in all these areas. In computational learning theory, the problem of agnostic PAClearning with simple geometric hypotheses can be reduced to the problem of computing the maximum bichromatic discrepancy for simple geometric ra...