On the VC-dimension of univariate decision trees
AuthorYıldız, Olcay Taner
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CitationYıldız, O. T. (2012). On the VC-dimension of univariate decision trees. Paper present et the ICPRAM 2012 - Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods, 205-210. doi:10.5220/0003777202050210
In this paper, we give and prove lower bounds of the VC-dimension of the univariate decision tree hypothesis class. The VC-dimension of the univariate decision tree depends on the VC-dimension values of its subtrees and the number of inputs. In our previous work (Aslan et al., 2009), we proposed a search algorithm that calculates the VC-dimension of univariate decision trees exhaustively. Using the experimental results of that work, we show that our VC-dimension bounds are tight. To verify that the VC-dimension bounds are useful, we also use them to get VC-generalization bounds for complexity control using SRM in decision trees, i.e., pruning. Our simulation results shows that SRM-pruning using the VC-dimension bounds finds trees that are more accurate as those pruned using cross-validation.