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The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…

Reachability analysis is a powerful tool when it comes to capturing the behaviour, thus verifying the safety, of autonomous systems. However, general-purpose methods, such as Hamilton-Jacobi approaches, suffer from the curse of…

Regression trees have emerged as a preeminent tool for solving real-world regression problems due to their ability to deal with nonlinearities, interaction effects and sharp discontinuities. In this article, we rather study regression trees…

Joint distributions over many variables are frequently modeled by decomposing them into products of simpler, lower-dimensional conditional distributions, such as in sparsely connected Bayesian networks. However, automatically learning such…

Hierarchical tree structures are common in many real-world systems, from tree roots and branches to neuronal dendrites and biologically inspired artificial neural networks, as well as in technological networks for organizing and searching…

The decision tree ensembles use a single data feature at each node for splitting the data. However, splitting in this manner may fail to capture the geometric properties of the data. Thus, oblique decision trees generate the oblique…

Random forests are considered a cornerstone in machine learning for their robustness and versatility. Despite these strengths, their conventional centralized training is ill-suited for the modern landscape of data that is often distributed,…

We introduce WildWood (WW), a new ensemble algorithm for supervised learning of Random Forest (RF) type. While standard RF algorithms use bootstrap out-of-bag samples to compute out-of-bag scores, WW uses these samples to produce improved…

The positioning of this research falls within the scalar-on-function classification literature, a field of significant interest across various domains, particularly in statistics, mathematics, and computer science. This study introduces an…

In recent years, deep learning has been at the center of analytics due to its impressive empirical success in analyzing complex data objects. Despite this success, most of the existing tools behave like black-box machines, thus the…

In recent years, non-parametric methods utilizing random walks on graphs have been used to solve a wide range of machine learning problems, but in their simplest form they do not scale well due to the quadratic complexity. In this paper, a…

Sampling-based motion planners perform exceptionally well in robotic applications that operate in high-dimensional space. However, most works often constrain the planning workspace rooted at some fixed locations, do not adaptively reason on…

Existing ordinal trees and random forests typically use scores that are assigned to the ordered categories, which implies that a higher scale level is used. Versions of ordinal trees are proposed that take the scale level seriously and…

The paper attempts to validate the effectiveness of tree classifiers to classify tabla strokes especially the ones which are overlapping in nature. It uses decision tree, ID3 and random forest as classifiers. A custom made data sets of 650…

This paper introduces a novel tree-based model, Learning Hyperplane Tree (LHT), which outperforms state-of-the-art (SOTA) tree models for classification tasks on several public datasets. The structure of LHT is simple and efficient: it…

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…

We investigate active learning by pairwise similarity over the leaves of trees originating from hierarchical clustering procedures. In the realizable setting, we provide a full characterization of the number of queries needed to achieve…

This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency. Most commonly-used model selection methods fail to consistently recover the true model when…

Recursive partitioning is the core of several statistical methods including CART, random forest, and boosted trees. Despite the popularity of tree based methods, to date, there did not exist methods for combining multiple trees into a…

This paper is concerned with the approximation of high-dimensional functions in a statistical learning setting, by empirical risk minimization over model classes of functions in tree-based tensor format. These are particular classes of…