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VC-dimension of univariate decision trees.

Olcay Taner Yildiz

    IEEE Transactions on Neural Networks and Learning Systems
    |January 17, 2015
    PubMed
    Summary

    This study establishes lower bounds for Vapnik-Chervonenkis (VC)-dimension in univariate decision trees. These bounds aid in pruning decision trees for improved accuracy, outperforming cross-validation methods.

    Area of Science:

    • Machine Learning
    • Computational Learning Theory

    Background:

    • The Vapnik-Chervonenkis (VC)-dimension is a key measure of the capacity of a hypothesis class.
    • Understanding the VC-dimension of decision trees is crucial for analyzing their generalization ability.
    • Univariate decision trees offer a fundamental model for classification tasks.

    Purpose of the Study:

    • To derive and prove lower bounds for the VC-dimension of univariate decision tree hypothesis classes.
    • To demonstrate the tightness of these bounds for simple decision tree structures.
    • To apply these VC-dimension bounds for structural risk minimization (SRM) in decision tree pruning.

    Main Methods:

    • Development of a search algorithm to exhaustively calculate the VC-dimension of univariate decision trees.

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  • Theoretical analysis to establish lower bounds based on subtree VC-dimensions and input counts.
  • Implementation of SRM pruning using derived VC-dimension bounds for complexity control.

    • Main Results:

    • The paper provides proven lower bounds for the VC-dimension of univariate decision trees.
    • The derived bounds are shown to be tight for simple decision tree structures.
    • Structural risk minimization pruning utilizing VC-dimension bounds yields more accurate trees compared to cross-validation pruning.

    Conclusions:

    • The established lower bounds for VC-dimension are effective for analyzing univariate decision trees.
    • VC-dimension-based SRM pruning is a viable and accurate method for decision tree complexity control.
    • This work contributes to a deeper theoretical understanding and practical application of decision tree generalization bounds.