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About 10,000 papers for “Random tree”

Super-Tree Random Measures

Hassan Allouba, Rick Durrett, John Hawkes et al. · 1996

. We use supercritical branching processes with random walk steps of geometrically decreasing size to construct random measures. Special cases of our construction give close relatives of the super-(spherically symmetric stable) processes. However, other cases can produce measures with very smooth densities in any dimension. 1. Introduction and Statement of Results Let fp k : k 2 Ng be a probability distribution on f1; 2; : : :g with p 1 ! 1. Let ¯ = P k kp k (? 1) and suppose P k k 2 p k ! 1. In this paper we will use a branching process with offspring distribution fp k g to construct random measures using the following recipe: (i) We start at time 0 with the "progenitor," one individual of generation 0, who immediately splits into k individuals (of generation 1) with probability p k . (ii) The jth individual of generation n is displaced from its parent by an amount a n X n;j where the X n;j are i.i.d. random vectors in R d and the a n are positive numbers. (iii) We assign mas...

Cited by 0

Random tree-weighted graphs

Louigi Addario‐Berry, Jordan Barrett · arXiv (Cornell University) · 2020

For each $n \ge 1$, let $\mathrm{d}^n=(d^{n}(i),1 \le i \le n)$ be a sequence of positive integers with even sum $\sum_{i=1}^n d^n(i) \ge 2n$. Let $(G_n,T_n,Γ_n)$ be uniformly distributed over the set of simple graphs $G_n$ with degree sequence $\mathrm{d}^n$, endowed with a spanning tree $T_n$ and rooted along an oriented edge $Γ_n$ of $G_n$ which is not an edge of $T_n$. Under a finite variance assumption on degrees in $G_n$, we show that, after rescaling, $T_n$ converges in distribution to the Brownian continuum random tree as $n \to \infty$. Our main tool is a new version of Pitman's additive coalescent (https://doi.org/10.1006/jcta.1998.2919), which can be used to build both random trees with a fixed degree sequence, and random tree-weighted graphs with a fixed degree sequence. As an input to the proof, we also derive a Poisson approximation theorem for the number of loops and multiple edges in the superposition of a fixed graph and a random graph with a given degree sequence sampled according to the configuration model; we find this to be of independent interest.

Cited by 0Open access

Uncovering a Random Tree

Hackl, Benjamin, Panholzer, Alois, Wagner, Stephan · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2022

We consider the process of uncovering the vertices of a random labeled tree according to their labels. First, a labeled tree with n vertices is generated uniformly at random. Thereafter, the vertices are uncovered one by one, in order of their labels. With each new vertex, all edges to previously uncovered vertices are uncovered as well. In this way, one obtains a growing sequence of forests. Three particular aspects of this process are studied in this extended abstract: first the number of edges, which we prove to converge to a stochastic process akin to a Brownian bridge after appropriate rescaling. Second, the connected component of a fixed vertex, for which different phases are identified and limiting distributions determined in each phase. Lastly, the largest connected component, for which we also observe a phase transition.

Cited by 0Open access

The semi-random tree process

Sofiya Burova, Lyuben Lichev · arXiv (Cornell University) · 2022

The online semi-random graph process is a one-player game which starts with the empty graph on $n$ vertices. At every round, a player (called Builder) is presented with a vertex $v$ chosen uniformly at random and independently from previous rounds, and constructs an edge of their choice that is incident to $v$. Inspired by recent advances on the semi-random graph process, we define a family of generalised online semi-random models. We analyse a particular instance that shares similar features with the original semi-random graph process and determine the hitting times of the classical graph properties minimum degree $k$, $k$-connectivity, containment of a perfect matching, a Hamiltonian cycle and an $H$-factor for a fixed graph $H$ possessing an additional tree-like property. Along the way, we derive a few consequences of the famous Aldous-Broder algorithm that may be of independent interest.

Cited by 3Open access

Parking on a Random Tree

Dehling, H., Fleurke, S. R., Kuelske, C. · arXiv (Cornell University) · 2007

Consider an infinite tree with random degrees, i.i.d. over the sites, with a prescribed probability distribution with generating function G(s). We consider the following variation of Renyi's parking problem, alternatively called blocking RSA: at every vertex of the tree a particle (or car) arrives with rate one. The particle sticks to the vertex whenever the vertex and all of its nearest neighbors are not occupied yet. We provide an explicit expression for the so-called parking constant in terms of the generating function.

Cited by 0Open access

PERT - perfect random tree ensembles

Adele Cutler, Guohua Zhao · 2001

Ensemble classifiers originated in the machine learning community. They work by fitting many individual classifiers and combining them by weighted or unweighted voting. The ensemble classifier is often much more accurate than the individual classifiers from which it is built. In fact, ensemble classifiers are among the most accurate general-purpose classifiers available. We introduce a new ensemble method, PERT, in which each individual classifier is a perfectly-fit classification tree with random selection of splits. Compared to other ensemble methods, PERT is very fast to fit. Given the randomness of the split selection, PERT is surprisingly accurate. Calculations suggest that one reason why PERT works so well is that although the individual tree classifiers are extremely weak, they are almost uncorrelated. The simple probabilistic nature of the classifier lends itself to theoretical analysis. We show that PERT is fitting a continuous posterior probability surface for each class. As such, it can be viewed as a classification-via-regression procedure that fits a continuous interpolating surface. In theory, this surface could be found using a one-shot procedure.

Cited by 0

A Logarithmic Random Access Tree

Tom Morgan · 2007

Making a data structure that performs like a dynamic array but functions in logarithmic time for all operations is the goal, but is by no means a trivial one. The obvious solution is to use a tree of some sort, but how? By using a binary tree in which values are stored at the leaf nodes and each node keeps track of how many leaves there are below it, we can quickly achieve logarithmic random access, insertion and deletion in the average case but all operations are linear on the worst case. To balance the tree, a self-balancing binary search tree like a Red Black Tree or a Splay Tree is used. These trees are always balanced and by using their balancing mechanisms and changing them to use the random access system described above, the goal is reached.

Cited by 0

The Continuum Random Tree III

David Aldous · The Annals of Probability · 1993

Let $(\mathscr{R}(k), k \geq 1)$ be random trees with $k$ leaves, satisfying a consistency condition: Removing a random leaf from $\mathscr{R}(k)$ gives $\mathscr{R}(k - 1)$. Then under an extra condition, this family determines a random continuum tree $\mathscr{L}$, which it is convenient to represent as a random subset of $l_1$. This leads to an abstract notion of convergence in distribution, as $n \rightarrow \infty$, of (rescaled) random trees $\mathscr{J}_n$ on $n$ vertices to a limit continuum random tree $\mathscr{L}$. The notion is based upon the assumption that, for fixed $k$, the subtrees of $\mathscr{J}_n$ determined by $k$ randomly chosen vertices converge to $\mathscr{R}(k)$. As our main example, under mild conditions on the offspring distribution, the family tree of a Galton-Watson branching process, conditioned on total population size equal to $n$, can be rescaled to converge to a limit continuum random tree which can be constructed from Brownian excursion.

Cited by 435Open access

THE CONTINUUM RANDOM TREE .1.

ALDOUS, D · eScholarship (California Digital Library) · 1991

Exact and asymptotic results for the uniform random labelled tree on n vertices have been studied extensively by combinatorialists.Here we treat asymptotics from a modern stochastic process viewpoint.There are three limit processes.One is an infinite discrete tree.The other two are most naturally represented as continuous two-dimensional fractal tree-like subsets of the infinite-dimensional space 11.One is compact; the other is unbounded and self-similar.The proofs are based upon a simple algorithm for generating the finite random tree and upon weak convergence arguments.Distributional properties of these limit processes will be discussed in a sequel.

Cited by 6Open access

Tree-matchings in random graphs

Luczak, T., Rucinski, A. (Uniwersytet Adama Mickiewicza, Poznan (Poland). Dept. of Discrete Mathematics), Bonn Univ. (Germany). Sonderforschungsbereich 303 - Information und die Koordination Wirtschaftlicher Aktivitaeten · OpenGrey (Institut de l'Information Scientifique et Technique) · 1987

Available from Bibliothek des Instituts fuer Weltwirtschaft, ZBW, Duesternbrook Weg 120, D-24105 Kiel C 161153 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische Informationsbibliothek

Cited by 0

Random boosting and random^2 forests -- A random tree depth injection approach

Tobias Markus Krabel, Thi Ngoc Tien Tran, Andreas Groll et al. · arXiv (Cornell University) · 2020

The induction of additional randomness in parallel and sequential ensemble methods has proven to be worthwhile in many aspects. In this manuscript, we propose and examine a novel random tree depth injection approach suitable for sequential and parallel tree-based approaches including Boosting and Random Forests. The resulting methods are called \emph{Random Boost} and \emph{Random$^2$ Forest}. Both approaches serve as valuable extensions to the existing literature on the gradient boosting framework and random forests. A Monte Carlo simulation, in which tree-shaped data sets with different numbers of final partitions are built, suggests that there are several scenarios where \emph{Random Boost} and \emph{Random$^2$ Forest} can improve the prediction performance of conventional hierarchical boosting and random forest approaches. The new algorithms appear to be especially successful in cases where there are merely a few high-order interactions in the generated data. In addition, our simulations suggest that our random tree depth injection approach can improve computation time by up to 40%, while at the same time the performance losses in terms of prediction accuracy turn out to be minor or even negligible in most cases.

Cited by 0Open access

A Tree in a Random Forest

Junzhe Zhu · IDEALS (University of Illinois Urbana-Champaign) · 2019

We web-scraped 450000+ comments from New York Times, applied a LDA model to analyze their topic distribution, and manually marked these topics. We then derived a Random Decision Tree Forest of 100 regression trees, with more than 1100 nodes in each tree, in order to infer audience engagement (indicated by comment length) from topic distribution for each comment. The visualization of the tree helped us determine the importance of each topic in terms of how it affects audience's attention.

Cited by 0Open access

Empirical distribution of random tree scores.

Brett Trost (140006), Jason Kindrachuk (200521), Pekka Määttänen (491174) et al. · Figshare · 2016

<p>Ten thousand random matrices were created from the matrix used to create the sample dendrogram in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080837#pone-0080837-g001" target="_blank">Figure 1</a> by randomly rearranging the peptide intensity values within each sample. For each score that was given to at least one random tree, the frequency of that score is indicated.</p>

Cited by 0Open access

Mining Software Defects using Random tree

Antony Rosewelt, Sampathkumar Vajeravelu · 2011

A relevant sub area of reverse engineering is identification of modules requiring re engineering, which focuses on predicting faulty modules. To this end, predicting faulty modules may use any available source of information such as source code and documentation. Similarly, the identified abstractions may take different forms such as module breakdown, structurecharts, entity-relationship diagrams, and software metric specifications. In this paper it is proposed to investigate the classification accuracy of random tree algorithms for software defect prediction.

Cited by 1