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Why does Random Forest sample features at each split, not just once per tree?

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Answer

  • Per-split feature subsampling forces different trees to explore different features and different splits.
  • Without it, if one feature is very predictive, every tree would keep splitting on it near the root and become highly correlated — averaging correlated trees barely reduces variance.
  • Sampling features at each split de-correlates the ensemble.
  • Default maxfeatures  =  sqrt(d)\operatorname{max}_{\mathrm{features}}\; = \;\mathrm{sqrt}(d) for classification, d/3 for regression is a well-tested rule of thumb.
Check yourself — multiple choice
  • To make training slower
  • To de-correlate trees so averaging actually reduces variance
  • To reduce memory only
  • To bias trees toward specific features

Feature subsampling de-correlates trees, which is the point of the ensemble.

#random-forest#bagging#ensembles

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