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Random forests are a learning algorithm proposed by Breiman (2001) which combines several randomized decision trees and aggregates their predictions by averaging. Despite its wide usage and outstanding practical performance, little is known about the mathematical properties of the procedure. This disparity between theory and practice originates in the… (More)

- Gérard Biau, Erwan Scornet
- 2015

The random forest algorithm, proposed by L. Breiman in 2001, has been extremely successful as a general-purpose classification and regression method. The approach, which combines several randomized decision trees and aggregates their predictions by averaging, has shown excellent performance in settings where the number of variables is much larger than the… (More)

- Erwan Scornet
- J. Multivariate Analysis
- 2016

The last decade has witnessed a growing interest in random forest models which are recognized to exhibit good practical performance, especially in high-dimensional settings. On the theoretical side, however, their predictive power remains largely unexplained, thereby creating a gap between theory and practice. The aim of this paper is twofold. Firstly, we… (More)

- Erwan Scornet
- IEEE Transactions on Information Theory
- 2016

Random forests are ensemble methods which grow trees as base learners and combine their predictions by averaging. Random forests are known for their good practical performance, particularly in high-dimensional settings. On the theoretical side, several studies highlight the potentially fruitful connection between the random forests and the kernel methods.… (More)

- Gérard Biau, Erwan Scornet, Johannes Welbl
- ArXiv
- 2016

Given an ensemble of randomized regression trees, it is possible to restructure them as a collection of multilayered neural networks with particular connection weights. Following this principle, we reformulate the random forest method of Breiman (2001) into a neural network setting, and in turn propose two new hybrid procedures that we call neural random… (More)

- ERWAN SCORNET, GÉRARD BIAU
- 2015

Random forests are a learning algorithm proposed by Breiman [Mach. Learn. 45 (2001) 5–32] that combines several randomized decision trees and aggregates their predictions by averaging. Despite its wide usage and outstanding practical performance, little is known about the mathematical properties of the procedure. This disparity between theory and practice… (More)

Technical Lemma 1. Assume that (H1) is satisfied and that L ≡ 0 for all cuts in some given cell A. Then the regression function m is constant on A. Proof of Technical Lemma 1. We start by proving the result in dimension p = 1. Letting A = [a, b] (0 ≤ a < b ≤ 1), and recalling that = − 1 (b − a) 2 b a m(t)dt 2 + 1 (b − a)(z − a) z a m(t)dt 2 + 1 (b − a)(b −… (More)

We establish the consistency of an algorithm of Mondrian Forest [LRT14, LRT16], a randomized classification algorithm that can be implemented online. First, we amend the original Mondrian Forest algorithm proposed in [LRT14], that considers a fixed lifetime parameter. Indeed, the fact that this parameter is fixed actually hinders statistical consistency of… (More)

- Elsa Bernard, Yunlong Jiao, Erwan Scornet, Veronique Stoven, Thomas Walter, Jean-Philippe Vert
- Molecular informatics
- 2017

The development of high-throughput in vitro assays to study quantitatively the toxicity of chemical compounds on genetically characterized human-derived cell lines paves the way to predictive toxicogenetics, where one would be able to predict the toxicity of any particular compound on any particular individual. In this paper we present a machine… (More)

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