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Assume we are given a set of items from a general metric space, but we neither have access to the representation of the data nor to the distances between data points. Instead, suppose that we can actively choose a triplet of items (A,B,C)…
A compositional tree refers to a tree structure on a set of random variables where each random variable is a node and composition occurs at each non-leaf node of the tree. As a generalization of compositional data, compositional trees…
A random forest is a popular tool for estimating probabilities in machine learning classification tasks. However, the means by which this is accomplished is unprincipled: one simply counts the fraction of trees in a forest that vote for a…
Tree-based ensemble methods such as random forests, gradient-boosted trees, and Bayesianadditive regression trees have been successfully used for regression problems in many applicationsand research studies. In this paper, we study ensemble…
Random Forest (Breiman, 2001) is a successful and widely used regression and classification algorithm. Part of its appeal and reason for its versatility is its (implicit) construction of a kernel-type weighting function on training data,…
Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…
Trees are useful entities allowing to model data structures and hierarchical relationships in networked decision systems ubiquitously. An ordered tree is a rooted tree where the order of the subtrees (children) of a node is significant. In…
Random forests is a common non-parametric regression technique which performs well for mixed-type unordered data and irrelevant features, while being robust to monotonic variable transformations. Standard random forests, however, do not…
Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
Recent studies have adopted an approach of selecting accurate and diverse trees based on individual or collective performance within an ensemble for classification and regression problems. This work follows in the wake of these…
This paper presents a new approach for trees-based regression, such as simple regression tree, random forest and gradient boosting, in settings involving correlated data. We show the problems that arise when implementing standard…
The perspective of developing trustworthy AI for critical applications in science and engineering requires machine learning techniques that are capable of estimating their own uncertainty. In the context of regression, instead of estimating…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…
Label ranking aims to learn a mapping from instances to rankings over a finite number of predefined labels. Random forest is a powerful and one of the most successful general-purpose machine learning algorithms of modern times. In this…
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…
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
Random Forests and related tree-based methods are popular for supervised learning from table based data. Apart from their ease of parallelization, their classification performance is also superior. However, this performance, especially…
Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…