CONSISTENCY FOR A SIMPLE MODEL OF RANDOM FORESTS

By Leo Breiman. 2004

214 citations recorded by the source corpus.

Subfields: Statistics and Probability, Statistical Learning Theory

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Citations in the corpus

Analysis of a Random Forests Model (2010, methodology): “In the present paper, we go one step further into random forests by working out and solidifying the properties of a model suggested by Breiman in [12].”
Generalized random forests (2016, methodology): “The main substantive difference between the random forests of Breiman (2001) relative to other non-parametric regression techniques is their use of recursive partitioning on subsamples to generate these weights αi(x). Motivated by the empirical success of regression forests across several applicatio”
Estimation and Inference of Heterogeneous Treatment Effects using Random Forests (2015, background): “…bounded away from and infinity; however, we assume uniformity for simpler exposition. by, amongothers, Biau (2012), Biau,Devroye, andLugosi (2008), Breiman (2004), Breiman et al. (1984), Meinshausen (2006), Scornet, Biau, and Vert (2015), Wager and Walther (2015), and Zhu, Zeng, and Kosorok…”
Consistency of Random Forests (2014, background): “This was followed by a technical note (Breiman, 2004), that focuses on a stylized version of the original algorithm.”
Variable selection using random forests (2010, result): “Purely random forests have been introduced by Cutler et al. (2001) for classiﬁcation problems and then studied by Breiman (2004), but the results are somewhat preliminary.”
Understanding Random Forests: From Theory to Practice (2014, result): “84 random forests Interestingly, and corroborating results of [Breiman, 2004], this work also highlights the fact that performance of random forests only depends on the number r of relevant variables, and not on p, making the method robust to overfitting.”
Analysis of purely random forests bias (2014, methodology): “8.2 Comparison with other random forest models Another random forest model has been suggested by Breiman (2004) and was more precisely analyzed by Biau (2012).”
Adaptive Concentration of Regression Trees, with Application to Random Forests (2015, background): “Several authors have studied the theoretical properties of trees and forests in order to explain their performance [1, 5, 6, 9, 14, 19, 28, 31, 33, 37, 38, 39, 45].”
Understanding variable importances in forests of randomized trees (2013, background): “Zhao (2000), Breiman (2004), Biau et al. (2008); Biau (2012), Meinshausen (2006) and Lin and Jeon (2006) investigated simplified to very realistic variants of these algorithms and proved the consistency of those variants.”
A random forest guided tour (2015, methodology): “The rates of convergence of centered forests are discussed in Breiman (2004) and Biau (2012).”
On Oblique Random Forests (2011, background): “They often do well with little parameter tuning [16], and are able to identify relevant feature subsets even in the presence of a large amount of irrelevant predictors [6, 21, 25, 2].”
Narrowing the Gap: Random Forests In Theory and In Practice (2013, methodology): “Random forests (Breiman, 2001) were originally conceived as a method of combining several CART (Breiman et al., 1984) style decision trees using bagging (Breiman, 1996). Their early development was influenced by the random subspace method of Ho (1998), the approach of random split selection from Die”
On the layered nearest neighbour estimate, the bagged nearest neighbour estimate and the random forest method in regression and classification (2010, methodology): “However, as pointed out by Lin and Jeon [18], no matter what splitting strategy is used, if the nodes of the individual trees define rectangular cells, then a random forest with k = 1 can be viewed as a weighted LNN regression estimate (see also Breiman [9]).”
Consistency of Random Forests and Other Averaging Classifiers (2008, background): “Such greedy forests were introduced by Breiman [5, 6] and have shown excellent performance in many applications.”
A comparison of random forest and its Gini importance with standard chemometric methods for the feature selection and classification of spectral data (2009, methodology): “As a classifier, random forest performs an implicit feature selection, using a small subset of "strong variables" for the classification only [27], leading to its superior performance on high dimensional data.”
Consistency of Online Random Forests (2013, background): “This was followed by the ﬁrst consistency result in this area from Breiman (2004), who proves consistency of a simpli-ﬁed model of the random forests used in practice.”
Quantile Regression Forests (2006, methodology): “Consistency for random forests (when approximating the conditional mean) has been shown for a simplified model of random forests in (Breiman, 2004), together with an analysis of convergence rates.”