Related papers: Asymptotic Theory for Random Forests

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 have become an important tool for improving accuracy in regression and classification problems since their inception by Leo Breiman in 2001. In this paper, we revisit a historically important random forest model originally…

Random forest is a classification algorithm well suited for microarray data: it shows excellent performance even when most predictive variables are noise, can be used when the number of variables is much larger than the number of…

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…

Random forests are popular methods for regression and classification analysis, and many different variants have been proposed in recent years. One interesting example is the Mondrian random forest, in which the underlying constituent trees…

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…

We prove asymptotic normality for the number of fringe subtrees isomorphic to any given tree in uniformly random trees with given vertex degrees. As applications, we also prove corresponding results for random labelled trees with given…

Although the methods of bagging and random forests are some of the most widely used prediction methods, relatively little is known about their algorithmic convergence. In particular, there are not many theoretical guarantees for deciding…

Let $T\_n$ denote the set of unrooted labeled trees of size $n$ and let $T\_n$ be a particular (finite, unlabeled) tree. Assuming that every tree of $T\_n$ is equally likely, it is shown that the limiting distribution as $n$ goes to…

The random forest (RF) algorithm has become a very popular prediction method for its great flexibility and promising accuracy. In RF, it is conventional to put equal weights on all the base learners (trees) to aggregate their predictions.…

We seek decision rules for prediction-time cost reduction, where complete data is available for training, but during prediction-time, each feature can only be acquired for an additional cost. We propose a novel random forest algorithm to…

Random Forest has become one of the most popular tools for feature selection. Its ability to deal with high-dimensional data makes this algorithm especially useful for studies in neuroimaging and bioinformatics. Despite its popularity and…

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…

In this paper, error estimates of classification Random Forests are quantitatively assessed. Based on the initial theoretical framework built by Bates et al. (2023), the true error rate and expected error rate are theoretically and…

Hash codes are a very efficient data representation needed to be able to cope with the ever growing amounts of data. We introduce a random forest semantic hashing scheme with information-theoretic code aggregation, showing for the first…

We demonstrate that adaptively controlling the size of individual regression trees in a random forest can improve predictive performance, contrary to the conventional wisdom that trees should be fully grown. A fast pruning algorithm,…

It was recently demonstrated that two machine-learning architectures, reservoir computing and time-delayed feed-forward neural networks, can be exploited for detecting the Earth's anomaly magnetic field immersed in overwhelming complex…

Despite widespread interest and practical use, the theoretical properties of random forests are still not well understood. In this paper we contribute to this understanding in two ways. We present a new theoretically tractable variant of…

We introduce a modification of Random Forests to estimate functions when unobserved confounding variables are present. The technique is tailored for high-dimensional settings with many observed covariates. We use spectral deconfounding…

Quantile Regression Forests (QRF) are widely used for non-parametric conditional quantile estimation, yet statistical inference for variable importance measures remains challenging due to the non-smoothness of the loss function and the…