Related papers: Asymptotic Normality for Multivariate Random Fores…
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…
We prove that the number of crossings in a random labelled tree with vertices in convex position is asymptotically Gaussian with mean $ n^2/6$ and variance $ n^3/45$. A similar result is proved for points in general position under mild…
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…
We propose a computationally efficient alternative to generalized random forests (GRFs) for estimating heterogeneous effects in large dimensions. While GRFs rely on a gradient-based splitting criterion, which in large dimensions is…
Random forests have become an established tool for classification and regression, in particular in high-dimensional settings and in the presence of complex predictor-response relationships. For bounded outcome variables restricted to the…
The issue of estimating residual variance in regression models has experienced relatively little attention in the machine learning community. However, the estimate is of primary interest in many practical applications, e.g. as a primary…
Random forests are among the most popular classification and regression methods used in industrial applications. To be effective, the parameters of random forests must be carefully tuned. This is usually done by choosing values that…
We propose a theoretical study of two realistic estimators of conditional distribution functions and conditional quantiles using random forests. The estimation process uses the bootstrap samples generated from the original dataset when…
In this paper we study the asymptotic normality in high-dimensional linear regression. We focus on the case where the covariance matrix of the regression variables has a KMS structure, in asymptotic settings where the number of predictors,…
Random forests are a statistical learning method widely used in many areas of scientific research because of its ability to learn complex relationships between input and output variables and also its capacity to handle high-dimensional…
Regression trees and their ensemble methods are popular methods for nonparametric regression: they combine strong predictive performance with interpretable estimators. To improve their utility for locally smooth response surfaces, we study…
In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of…
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…
Random forests is a state-of-the-art supervised machine learning method which behaves well in high-dimensional settings although some limitations may happen when $p$, the number of predictors, is much larger than the number of observations…
A multivariable measurement error model $AX \approx B$ is considered. Here $A$ and $B$ are input and output matrices of measurements and $X$ is a rectangular matrix of fixed size to be estimated. The errors in $[A,B]$ are row-wise…
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 work develops formal statistical inference procedures for machine learning ensemble methods. Ensemble methods based on bootstrapping, such as bagging and random forests, have improved the predictive accuracy of individual trees, but…
We consider a multivariate functional measurement error model $AX\approx B$. The errors in $[A,B]$ are uncorrelated, row-wise independent, and have equal (unknown) variances. We study the total least squares estimator of $X$, which, in the…
The Distributional Random Forest (DRF) is a recently introduced Random Forest algorithm to estimate multivariate conditional distributions. Due to its general estimation procedure, it can be employed to estimate a wide range of targets such…
We investigate the statistics of trees grown from some initial tree by attaching links to preexisting vertices, with attachment probabilities depending only on the valence of these vertices. We consider the asymptotic mass distribution that…