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Regularized impurity reduction: accurate decision trees with complexity guarantees.

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  • 1Division of Theoretical Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden.

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Summary
This summary is machine-generated.

This study enhances decision tree algorithms to guarantee smaller, more interpretable models. The new approach balances accuracy and complexity, offering theoretical guarantees for tree induction.

Keywords:
Approximation algorithmsDecision treesImpurity functionsSubmodularityTree complexity

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Area of Science:

  • Machine Learning
  • Data Mining
  • Artificial Intelligence

Background:

  • Decision trees are popular classification models known for accuracy and interpretability.
  • Model interpretability deteriorates as tree size increases.
  • Traditional algorithms lack theoretical guarantees for producing small trees.

Purpose of the Study:

  • To provide theoretical guarantees for producing smaller decision trees.
  • To enhance impurity-reduction functions for better complexity control.
  • To develop a tree-induction algorithm with approximation guarantees on complexity.

Main Methods:

  • Proposed a novel tree-induction algorithm with a logarithmic approximation guarantee on tree complexity.
  • Utilized a general family of impurity functions, including entropy and Gini-index.
  • Defined a greedy criterion balancing tree balance, cost-efficiency, and discriminative power.

Main Results:

  • The enhanced algorithm provides a tight logarithmic approximation factor for tree complexity.
  • Achieved an excellent balance between predictive accuracy and tree complexity.
  • Demonstrated effectiveness across binary and multi-class classification with non-uniform costs.

Conclusions:

  • The proposed enhancement successfully equips impurity functions with complexity guarantees.
  • The algorithm offers a practical solution for generating interpretable and accurate decision trees.
  • This work contributes to the theoretical understanding and practical application of decision tree induction.