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Influence Measures for CART Classification Trees

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  • Avner Bar-Hen
  • Servane Gey
  • Jean-Michel Poggi

Abstract

This paper deals with measuring the influence of observations on the results obtained with CART classification trees. To define the influence of individuals on the analysis, we use influence measures to propose criterions to quantify the sensitivity of the CART classification tree analysis. The proposals are based on predictions and use jackknife trees. The analysis is extended to the pruned sequences of CART trees to produce CART specific notions of influence. Using the framework of influence functions, distributional results are derived. A numerical example, the well known spam dataset, is presented to illustrate the notions developed throughout the paper. A real dataset relating the administrative classification of cities surrounding Paris, France, to the characteristics of their tax revenues distribution, is finally analyzed using the new influence-based tools. Copyright Classification Society of North America 2015

Suggested Citation

  • Avner Bar-Hen & Servane Gey & Jean-Michel Poggi, 2015. "Influence Measures for CART Classification Trees," Journal of Classification, Springer;The Classification Society, vol. 32(1), pages 21-45, April.
    • Handle: RePEc:spr:jclass:v:32:y:2015:i:1:p:21-45
    DOI: 10.1007/s00357-015-9172-4
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    References listed on IDEAS

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    1. Croux, Christophe & Joossens, Kristel, 2005. "Influence of observations on the misclassification probability in quadratic discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 384-403, October.
    2. Norm A. Campbell, 1978. "The Influence Function as an Aid in Outlier Detection in Discriminant Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 27(3), pages 251-258, November.
    3. Gey, Servane & Poggi, Jean-Michel, 2006. "Boosting and instability for regression trees," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 533-550, January.
    4. Bel, L. & Allard, D. & Laurent, J.M. & Cheddadi, R. & Bar-Hen, A., 2009. "CART algorithm for spatial data: Application to environmental and ecological data," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3082-3093, June.
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