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二叉决策树生成算法的VC维上界 被引量:1

On Upper Bound of VC Dimension of Binary Decision Tree Algorithms
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摘要 在统计学习理论中 ,尤其对于分类问题 ,VC维扮演着中心作用。大多数常用算法的VC维未知。该文计算了二叉决策树生成算法的VC维上界 ,获得了定理 2 ,认为该上界随决策树的复杂度和节点可调参数个数的增大而提高。作为补充 ,还计算了单变量决策树非叶子节点的VC维上界 ,获得了定理 3。为了评估定理 2的数值结果 ,通过实验验证了有关的经验结论 ,发现它们在决策树复杂度较大时能够与实际符合。比较定理 2和经验结论发现两者存在较大的数值差别但是变化趋势相同。 VC dimension plays a central role in the Statistical Learning Theory especially for classification problems. Since there does not exist a universal method to calculate this combinatorial dimension, this value for most of the classification algorithms is still unknown. Binary decision tree algorithms for classification constitute a large family in the fields of machine learning, pattern recognition, and data mining. Investigating their VC dimension seems to be a helpful step towards further improvement of their generalization performance. For this purpose, the paper calculated, in theorem 2, an upper bound of VC dimension for binary decision tree algorithms, which rises as the complexity of resulting tree and the number of adjustable parameters at each node increases. To facilitate the calculation, only continuous attributes are considered here, and hypothesis function class of decision tree algorithms is considered as a continuously expending group of uniform Boolean formulas. As a supplement, upper bound of single non-leaf node of univariate decision tree algorithms is also calculated in theorem 3, which displays its special classification capability when compared with its multivariate counterpart. For the purpose of comparison, experiential conclusions on VC dimension of univirate decision tree algorithms are evaluated by experiments. They are found to be appropriate when complexity of the resulting tree is large enough. Based on this observation, a numerical comparison between the experiential value of VC dimension and the upper bound calculated by us was made. Although the numeric discrepancy between them is large, they display the same tendency. Possible origins of the exaggeration in the upper bound were discussed. Conclusions of the paper is helpful for us to understand the essential purpose of some techniques of improvement such as pruning a grown decision tree or imposing earlier-stop criteria in training, which are assumed to limit the VC dimension of the algorithm to a reasonable range and hence alleviate the serious problem of over training.
出处 《计算机仿真》 CSCD 2005年第2期74-78,126,共6页 Computer Simulation
关键词 决策树 统计学习理论 Decision tree Dimension Statistical learning theory
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参考文献10

  • 1边肇祺 张学工.模式识别(第二版)[M].北京:清华大学出版社,1999.224-227.
  • 2叶晨洲,杨杰,姚莉秀,陈念贻.采用重复剪辑近邻法提高决策树算法的性能[J].控制与决策,2003,18(1):96-98. 被引量:4
  • 3M Vidyasagar. A Theory of Learning and Generalization [M]. Great Britain: Springer, 1997.
  • 4V Vapnik. The Nature of Statistical Learning Theory (the second edition)[M].NewYork:Springer-Verlag1998(中译本张学工译统计学习理论的本质北京:清华大学出版社2000).
  • 5Simon Haykin. Neural Networks: A Comprehensive Foundation (2nd Edition ) [ M]. New Jersey: Prentice Hall, 1999.
  • 6Martin Anthony,Peter L.Bartlett. Neural Network Learning:Theoretical Foundations[M]. Cambridge: Cambridge University Press, 1999.
  • 7Apte Chidanand and Weiss Sholom. Data mining with decision trees and decision rules[J]. Future Generation Computer Systems, 1997, 13:197- 210.
  • 8Sreeramma K Murthy, Simon Kasif, Steven Salzberg. A System for Induction of Oblique Decision Trees[ J]. Journal of Artificial Intelligence Research, 1994,2:1 - 32.
  • 9Peter L Bartlett, Vitaly Maiorov. Almost Linear VC Dimension Bounds for Hecewise Polynomial Networks[M]. Advances in Neural Information Processing Systems 11(Edited by Michael S. Kearns,Sara A.Solla,David A.Cohn), Cambridge Massachusetts: MIT Press 1999:190 -196.
  • 10Peter Bartlett. Learning Theory and Generalization: Neural Networks and other Supervised Learning Techniques [ DB ] . http : //discus. anu. edu. au/~ bartlett/nips98/nipistutorial. html. 2003.

二级参考文献1

  • 1边肇祺 张学工.模式识别(第2版)[M].北京:清华大学出版社,1999..

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  • 1Isabelle Guyon & Andre Elisseeff.An Introduction to Variable and Feature Selection[J].Journal of Machine Learning Research.2003,3:1157-1182.
  • 2J R Quinlan.C4.5:Programs for Machine Learning[M].Morgan Kaufmann.1993
  • 3Bart Baesens,Rudy Setiono,Christophe Mues,Jan Vanthienen.Using Neural Network Rule Extraction and Decision Tables for Credit-Risk Evaluation[J].Management Science.March 2003,49(3):312-329
  • 4Marc Boulle,Khiops.A Statistical Discretization Method of Continuous Attributes[J].Machine Learning.2004,(55):53-69

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