# Random Forests

@article{Breiman2001RandomF, title={Random Forests}, author={L. Breiman}, journal={Machine Learning}, year={2001}, volume={45}, pages={5-32} }

Random forests are a combination of tree predictors such that each tree depends on the values of a random vector sampled independently and with the same distribution for all trees in the forest. The generalization error for forests converges a.s. to a limit as the number of trees in the forest becomes large. The generalization error of a forest of tree classifiers depends on the strength of the individual trees in the forest and the correlation between them. Using a random selection of features…

## 72,768 Citations

### Ensemble of optimal trees, random forest and random projection ensemble classification

- Computer Science, Environmental ScienceAdv. Data Anal. Classif.
- 2020

This work investigates the idea of integrating trees that are accurate and diverse and uses out-of-bag observations as a validation sample from the training bootstrap samples, to choose the best trees based on their individual performance and assess these trees for diversity using the Brier score on an independent validation sample.

### of optimal trees, random forest and random projection ensemble classiﬁcation.

- Computer Science, Environmental Science
- 2022

The idea of integrating trees that are accurate and diverse are investigated, to choose the best trees based on their individual performance and then assess these trees for diversity using the Brier score on an independent validation sample.

### Effects of stopping criterion on the growth of trees in regression random forests

- Computer ScienceThe New England Journal of Statistics in Data Science
- 2022

This work has developed a straightforward method for incorporating weights into the random forest analysis of survey data and demonstrates that generalization error under the proposed approach is competitive to that attained from the original random forest approach when data have large random error variability.

### An Ensemble of Optimal Trees for Classification and Regression (OTE)

- Computer Science, Environmental Science
- 2016

This work investigates the idea of integrating trees that are accurate and diverse and utilizes out-of-bag observation as validation sample from the training bootstrap samples to choose the best trees based on their individual performance and then assess these trees for diversity using Brier score.

### Improvement of randomized ensembles of trees for supervised learning in very high dimension

- Computer Science
- 2011

Empirical experiments show that the combination of the monotone LASSO with features extracted from tree ensembles leads at the same time to a drastic reduction of the number of features and can improve the accuracy with respect to unpruned ensembleles of trees.

### On the selection of decision trees in Random Forests

- Computer Science2009 International Joint Conference on Neural Networks
- 2009

It is shown that better subsets of decision trees can be obtained even using a sub-optimal classifier selection method, which proves that “classical” RF induction process, for which randomized trees are arbitrary added to the ensemble, is not the best approach to produce accurate RF classifiers.

### Trees Weighting Random Forest Method for Classifying High-Dimensional Noisy Data

- Computer Science2010 IEEE 7th International Conference on E-Business Engineering
- 2010

This paper presents a new approach to solve the problem of noisy trees in random forest through weighting the trees according to their classification ability, named Trees Weighting Random Forest (TWRF).

### Random Forests and Decision Trees Classifiers : Effects of Data Quality on the Learning Curve

- Computer Science
- 2006

It appeared that random forests and individual decision trees have different sensitivities to those perturbation factors, but counterintuitively random forests show a greater sensitivity to noise than decision trees for this parameter.

### Is rotation forest the best classifier for problems with continuous features?

- Computer ScienceArXiv
- 2018

It is demonstrated that on large problems rotation forest can be made an order of magnitude faster without significant loss of accuracy, and it is maintained that without any domain knowledge to indicate an algorithm preference, rotation forest should be the default algorithm of choice for problems with continuous attributes.

### Analysis of purely random forests bias

- Computer Science, MathematicsArXiv
- 2014

Under some regularity assumptions on the regression function, it is shown that the bias of an infinite forest decreases at a faster rate (with respect to the size of each tree) than a single tree, and infinite forests attain a strictly better risk rate than single trees.

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