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Stability and scalability in decision trees

Author

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  • Tomàs Aluja-Banet
  • Eduard Nafria

Abstract

Tree-based methods are statistical procedures for automatic learning from data, whose main applications are integrated into a data-mining environment for decision support systems. Here, we focus on two problems of decision trees: the stability of the rules obtained and their applicability to huge data sets. Since the tree-growing process is highly dependent on data, i.e. small fluctuations in data can cause big changes in the tree-growing process, we focused instead on the stability of the trees themselves. To this end we propose a series of data diagnostics to prevent internal instability in the tree-growing process before a particular split is made. Indeed, to be effective in actual managerial problems they must be applicable to massive amounts of stored data with maximum efficiency. For this reason we studied the theoretical complexity of such an algorithm. Finally, we present an algorithm that can cope with such problems, with linear cost upon the individuals, which can use a robust impurity measure as a splitting criterion. Copyright Physica-Verlag 2003

Suggested Citation

  • Tomàs Aluja-Banet & Eduard Nafria, 2003. "Stability and scalability in decision trees," Computational Statistics, Springer, vol. 18(3), pages 505-520, September.
    • Handle: RePEc:spr:compst:v:18:y:2003:i:3:p:505-520
    DOI: 10.1007/BF03354613
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    References listed on IDEAS

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    1. Ciampi, Antonio, 1991. "Generalized regression trees," Computational Statistics & Data Analysis, Elsevier, vol. 12(1), pages 57-78, August.
    2. G. V. Kass, 1980. "An Exploratory Technique for Investigating Large Quantities of Categorical Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(2), pages 119-127, June.
    3. Claudio Conversano & Francesco Mola & Roberta Siciliano, 2001. "Partitioning Algorithms and Combined Model Integration for Data Mining," Computational Statistics, Springer, vol. 16(3), pages 323-339, September.
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    2. Elena Ballante & Marta Galvani & Pierpaolo Uberti & Silvia Figini, 2021. "Polarized Classification Tree Models: Theory and Computational Aspects," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 481-499, October.

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