Related papers: Does freezing impede the growth of random recursiv…

This article describes a new system for induction of oblique decision trees. This system, OC1, combines deterministic hill-climbing with two forms of randomization to find a good oblique split (in the form of a hyperplane) at each node of a…

We consider linear preferential attachment random trees with additive fitness, where fitness is defined as the random initial vertex attractiveness. We show that when the fitness distribution has positive bounded support, the weak local…

We consider root-finding algorithms for random rooted trees grown by uniform attachment. Given an unlabeled copy of the tree and a target accuracy $\varepsilon > 0$, such an algorithm outputs a set of nodes that contains the root with…

We study a random tree, which was introduced by Ajazi et al. as part of a model of a neuronal network. Realising a scaling relation for the law of the tree, we can use elementary techniques to derive asymptotic results on the geometry as…

A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step $t=1,2,\ldots$, with probability $\pi_1>0$ a new vertex with one…

We study the effect of temperature shift on aging phenomena in the Random Energy Model (REM). From calculation on the correlation function and simulation on the Zero-Field-Cooled magnetization, we find that the REM satisfies a scaling…

We consider linear preferential attachment trees, and show that they can be regarded as random split trees in the sense of Devroye (1999), although with infinite potential branching. In particular, this applies to the random recursive tree…

Random forests are a statistical learning technique that use bootstrap aggregation to average high-variance and low-bias trees. Improvements to random forests, such as applying Lasso regression to the tree predictions, have been proposed in…

Random forest (RF) methodology is one of the most popular machine learning techniques for prediction problems. In this article, we discuss some cases where random forests may suffer and propose a novel generalized RF method, namely…

We study two models of discrete height functions, that is, models of random integer-valued functions on the vertices of a tree. First, we consider the random homomorphism model, in which neighbours must have a height difference of exactly…

We introduce and study a model of percolation with constant freezing (PCF) where edges open at constant rate 1, and clusters freeze at rate \alpha independently of their size. Our main result is that the infinite volume process can be…

We provide a uniform upper bound on the minimal drift so that the one-per-site frog model on a $d$-ary tree is recurrent. To do this, we introduce a subprocess that couples across trees with different degrees. Finding couplings for frog…

The last decade has shed some light on theoretical properties such as their consistency for regression tasks. In the current paper, we propose a new class of very simple learners based on so-called naive trees. These naive trees partition…

Additive models, such as produced by gradient boosting, and full interaction models, such as classification and regression trees (CART), are widely used algorithms that have been investigated largely in isolation. We show that these models…

In this paper we propose using the principle of boosting to reduce the bias of a random forest prediction in the regression setting. From the original random forest fit we extract the residuals and then fit another random forest to these…

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…

The class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In this paper, we provide a better combinatorial characterization of this specific family of…

We investigate properties of trees of height $\omega_1$ and their preservation under subcomplete forcing. We show that subcomplete forcing cannot add a new branch to an $\omega_1$-tree. We introduce fragments of subcompleteness which are…

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…

We study fragmentation of a random recursive tree into a forest by repeated removal of nodes. The initial tree consists of N nodes and it is generated by sequential addition of nodes with each new node attaching to a randomly-selected…