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VC-dimension of univariate decision trees
IEEE Transactions on Neural Networks and Learning Systems
|January 17, 2015
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.
- 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.
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