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The Effect of Splitting on Random Forests.

Hemant Ishwaran1

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|September 19, 2017
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Summary
This summary is machine-generated.

Weighted splitting rules in random forests (RF) adapt to both signal and noise, improving performance. End-cut splits are beneficial in deep trees, unlike in single trees, enhancing RF robustness and efficiency.

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CARTend-cut preferencelaw of the iterated logarithmsplit-pointsplitting rule

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Area of Science:

  • Machine Learning
  • Data Science
  • Computational Statistics

Background:

  • Random forests (RF) are powerful ensemble learning methods.
  • Splitting rules determine how trees are constructed within RF.
  • The impact of different splitting rules on RF performance is not fully understood.

Purpose of the Study:

  • To systematically study the effect of splitting rules on random forests (RF) for regression and classification.
  • To analyze a class of weighted splitting rules, including CART weighted variance and Gini index splitting.
  • To investigate the adaptive properties of these rules to signal and noise.

Main Methods:

  • Analysis of weighted splitting rules, including CART weighted variance and Gini index splitting.
  • Theoretical arguments for the utility of end-cut splits in deeply grown trees.
  • Comparison of weighted, unweighted, heavy-weighted, and pure random splitting rules.
  • Introduction of a hybrid method combining random split-point selection with weighted splitting.

Main Results:

  • Weighted splitting rules exhibit adaptive properties to both signal and noise.
  • For noisy variables, weighted splitting favors end-cut splits, which are beneficial in deep RFs.
  • Weighted variance splitting effectively identifies points of curvature for strong variables.
  • Unweighted, heavy-weighted, and pure random splitting rules are less effective than weighted rules.

Conclusions:

  • Weighted splitting rules offer superior adaptivity to signal and noise compared to other methods.
  • End-cut splitting in RFs, contrary to single trees, aids in handling noise and maximizing sample size.
  • A novel hybrid method provides computational efficiency while retaining the adaptive benefits of weighted splitting.