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In this report we present two new ways of enforcing monotone constraints in regression and classification trees. One yields better results than the current LightGBM, and has a similar computation time. The other one yields even better…

Systematic sampling is often used to select plot locations for forest inventory estimation. However, it is not possible to derive a design-unbiased variance estimator for a systematic sample using one random start. As a result, many forest…

Random forests are an ensemble method relevant for many problems, such as regression or classification. They are popular due to their good predictive performance (compared to, e.g., decision trees) requiring only minimal tuning of…

We present the analysis of two recently proposed noise reduction techniques, Hutch++ and XTrace, both based on inexact deflation. These methods were proven to have a better asymptotic convergence to the solution than the classical…

We prove a lower bound on the number of spanning two-forests in a graph, in terms of the number of vertices, edges, and spanning trees. This implies an upper bound on the average cut size of a random two-forest. The main tool is an identity…

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…

Most computational models of dependency syntax consist of distributions over spanning trees. However, the majority of dependency treebanks require that every valid dependency tree has a single edge coming out of the ROOT node, a constraint…

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…

Feature subsampling is a core component of random forests and other ensemble methods. While recent theory suggests that this randomization acts solely as a variance reduction mechanism analogous to ridge regularization, these results…

In this paper we suggest a modification of the regression-based variance reduction approach recently proposed in Belomestny et al. This modification is based on the stratification technique and allows for a further significant variance…

We study a dynamic version of the implicit trace estimation problem. Given access to an oracle for computing matrix-vector multiplications with a dynamically changing matrix A, our goal is to maintain an accurate approximation to A's trace…

Throughout the last decade, random forests have established themselves as among the most accurate and popular supervised learning methods. While their black-box nature has made their mathematical analysis difficult, recent work has…

We propose a new method for performing multiscale analysis of functions defined on the vertices of a finite connected weighted graph. Our approach relies on a random spanning forest to downsample the set of vertices, and on approximate…

Tree-based methods are powerful nonparametric techniques in statistics and machine learning. However, their effectiveness, particularly in finite-sample settings, is not fully understood. Recent applications have revealed their surprising…

This paper proposes FREEtree, a tree-based method for high dimensional longitudinal data with correlated features. Popular machine learning approaches, like Random Forests, commonly used for variable selection do not perform well when there…

Random Forests (RFs) are widely used Machine Learning models in low-power embedded devices, due to their hardware friendly operation and high accuracy on practically relevant tasks. The accuracy of a RF often increases with the number of…

A novel approach for non-intrusive uncertainty propagation is proposed. Our approach overcomes the limitation of many traditional methods, such as generalised polynomial chaos methods, which may lack sufficient accuracy when the quantity of…

In model-free deep reinforcement learning (RL) algorithms, using noisy value estimates to supervise policy evaluation and optimization is detrimental to the sample efficiency. As this noise is heteroscedastic, its effects can be mitigated…

Three types of explicit estimators are proposed here to estimate the loss rates of the links in a network of the tree topology. All of them are derived by the maximum likelihood principle and proved to be either asymptotic unbiased or…

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…