Related papers: On the asymptotics of random forests

In this paper we study asymptotic properties of random forests within the framework of nonlinear time series modeling. While random forests have been successfully applied in various fields, the theoretical justification has not been…

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…

This paper derives a unifying theorem establishing consistency results for a broad class of tree-based algorithms. It improves current results in two aspects. First of all, it can be applied to algorithms that vary from traditional Random…

Random forests are a very effective and commonly used statistical method, but their full theoretical analysis is still an open problem. As a first step, simplified models such as purely random forests have been introduced, in order to shed…

Random forests remain among the most popular off-the-shelf supervised learning algorithms. Despite their well-documented empirical success, however, until recently, few theoretical results were available to describe their performance and…

As a testament to their success, the theory of random forests has long been outpaced by their application in practice. In this paper, we take a step towards narrowing this gap by providing a consistency result for online random forests.

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…

Random forests have proven to be reliable predictive algorithms in many application areas. Not much is known, however, about the statistical properties of random forests. Several authors have established conditions under which their…

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…

In a multivariate nonparametric regression setting we construct explicit asymptotic uniform confidence bands for centered purely random forests. Since the most popular example in this class of random forests, namely the uniformly centered…

We give examples of data-generating models under which Breiman's random forest may be extremely slow to converge to the optimal predictor or even fail to be consistent. The evidence provided for these properties is based on mostly intuitive…

Random forests are a scheme proposed by Leo Breiman in the 2000's for building a predictor ensemble with a set of decision trees that grow in randomly selected subspaces of data. Despite growing interest and practical use, there has been…

As a flexible nonparametric learning tool, the random forests algorithm has been widely applied to various real applications with appealing empirical performance, even in the presence of high-dimensional feature space. Unveiling the…

Inspired by Stufler's recent probabilistic proof of Otter's asymptotic number of unlabeled trees, we revisit work of Palmer and Schwenk, and study unlabeled forests from a probabilistic point of view. We show that the number of trees in a…

Random forests are a powerful method for non-parametric regression, but are limited in their ability to fit smooth signals, and can show poor predictive performance in the presence of strong, smooth effects. Taking the perspective of random…

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…

We study various types of consistency of honest decision trees and random forests in the regression setting. In contrast to related literature, our proofs are elementary and follow the classical arguments used for smoothing methods. Under…

Tree-based ensemble methods, as Random Forests and Gradient Boosted Trees, have been successfully used for regression in many applications and research studies. Furthermore, these methods have been extended in order to deal with uncertainty…

The classes of tree permutations and forest permutations were defined by Acan and Hitczenko (2016). We study random permutations of a given length from these classes, and in particular the number of occurrences of a fixed pattern in one of…

Regression trees and random forests are popular and effective non-parametric estimators in practical applications. A recent paper by Athey and Wager shows that the random forest estimate at any point is asymptotically Gaussian; in this…