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Risk bounds for purely uniformly random forests

Robin Genuer 1, 2 
2 SELECT - Model selection in statistical learning
Inria Saclay - Ile de France, LMO - Laboratoire de Mathématiques d'Orsay
Abstract : Random forests, introduced by Leo Breiman in 2001, are a very effective statistical method. The complex mechanism of the method makes theoretical analysis difficult. Therefore, a simplified version of random forests, called purely random forests, which can be theoretically handled more easily, has been considered. In this paper we introduce a variant of this kind of random forests, that we call purely uniformly random forests. In the context of regression problems with a one-dimensional predictor space, we show that both random trees and random forests reach minimax rate of convergence. In addition, we prove that compared to random trees, random forests improve accuracy by reducing the estimator variance by a factor of three fourths.
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Submitted on : Tuesday, June 15, 2010 - 2:13:20 PM
Last modification on : Sunday, June 26, 2022 - 11:51:53 AM
Long-term archiving on: : Wednesday, September 15, 2010 - 8:32:54 PM

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  • HAL Id : inria-00492231, version 1
  • ARXIV : 1006.2980

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Robin Genuer. Risk bounds for purely uniformly random forests. [Research Report] RR-7318, INRIA. 2010, pp.19. ⟨inria-00492231⟩

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