English
Related papers

Related papers: Recursive construction of continuum random trees

200 papers

We give an explicit construction of the scaling limit of the minimum spanning tree of the complete graph. The limit object is described using a recursive construction involving the convex minorants of a Brownian motion with parabolic drift…

Probability · Mathematics 2023-07-25 Nicolas Broutin , Jean-François Marckert

Oblique decision trees combine the transparency of trees with the power of multivariate decision boundaries, but learning high-quality oblique splits is NP-hard, and practical methods still rely on slow search or theory-free heuristics. We…

Machine Learning · Computer Science 2026-05-01 Hongyi Li , Han Lin , Jun Xu

This paper proposes a bidirectional rapidly-exploring random trees (RRT) algorithm to solve the motion planning problem for hybrid systems. The proposed algorithm, called HyRRT-Connect, propagates in both forward and backward directions in…

Robotics · Computer Science 2025-04-16 Nan Wang , Ricardo G. Sanfelice

Inspired by [4] we present a new algorithm for uniformly random generation of ordered trees in which all occuring outdegrees can be specified by a given sequence of numbers. The method can be used for random generation of binary or n-ary…

Discrete Mathematics · Computer Science 2021-12-30 Aleksander Kiryk

We propose a computationally efficient alternative to generalized random forests (GRFs) for estimating heterogeneous effects in large dimensions. While GRFs rely on a gradient-based splitting criterion, which in large dimensions is…

Machine Learning · Statistics 2025-06-18 David Fleischer , David A. Stephens , Archer Y. Yang

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…

Statistics Theory · Mathematics 2015-08-11 Erwan Scornet , Gérard Biau , Jean-Philippe Vert

We prove an invariance principle for a general class of continuous time critical branching processes with finite variance (non-local) branching mechanism. We show that the genealogical trees, viewed as random compact metric measure spaces,…

Probability · Mathematics 2026-01-12 Emma Horton , Ellen Powell

We study protected nodes in various classes of random rooted trees by putting them in the general context of fringe subtrees introduced by Aldous (1991). Several types of random trees are considered: simply generated trees (or conditioned…

Probability · Mathematics 2013-10-03 Luc Devroye , Svante Janson

We consider the model of random trees introduced by Devroye [SIAM J. Comput. 28 (1999) 409-432]. The model encompasses many important randomized algorithms and data structures. The pieces of data (items) are stored in a randomized fashion…

Probability · Mathematics 2012-11-05 Nicolas Broutin , Cecilia Holmgren

Rooted, weighted continuum random trees are used to describe limits of sequences of random discrete trees. Formally, they are random quadruples $(\mathcal{T},d,r,p)$, where $(\mathcal{T},d)$ is a tree-like metric space, $r\in\mathcal{T}$ is…

Probability · Mathematics 2021-01-29 Noah Forman

Generalized Chinese Remainder Theorem (CRT) is a well-known approach to solve ambiguity resolution related problems. In this paper, we study the robust CRT reconstruction for multiple numbers from a view of statistics. To the best of our…

Other Statistics · Statistics 2019-09-04 Hanshen Xiao , Nan Du , Zhikang T. Wang , Guoqiang Xiao

We consider a model of random tree growth, where at each time unit a new vertex is added and attached to an already existing vertex chosen at random. The probability with which a vertex with degree $k$ is chosen is proportional to $w(k)$,…

Probability · Mathematics 2007-05-23 Anna Rudas , Balint Toth , Benedek Valko

This paper presents a novel algorithm, called MRRT, which uses multiple rapidly-exploring random trees for fast online replanning of autonomous vehicles in dynamic environments with moving obstacles. The proposed algorithm is built upon the…

Robotics · Computer Science 2021-04-23 Zongyuan Shen , James P. Wilson , Ryan Harvey , Shalabh Gupta

In this paper, we study a parallel version of Galton-Watson processes for the random generation of tree-shaped structures. Random trees are useful in many situations (testing, binary search, simulation of physics phenomena,...) as attests…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-06-22 Olivier Bodini , Camille Coti , Julien David

We study a random fragmentation process and its associated random tree. The process has earlier been studied by Dean and Majumdar (J. Phys. A: Math. Gen., vol. 35, L501--L507), who found a phase transition: the number of fragmentations is…

Probability · Mathematics 2007-05-23 S. Janson , R. Neininger

The properties of randomly evolving special trees having defined and analyzed already in two earlier papers (arXiv:cond-mat/0205650 and arXiv:cond-mat/0211092) have been investigated in the case when the continuous time parameter converges…

Statistical Mechanics · Physics 2007-05-23 L. Pal

Previous algorithms for constructing regression tree models for longitudinal and multiresponse data have mostly followed the CART approach. Consequently, they inherit the same selection biases and computational difficulties as CART. We…

Machine Learning · Statistics 2013-05-28 Wei-Yin Loh , Wei Zheng

We apply a tree-based methodology to solve new, very broadly defined families of nested recursions of the general form R(n)=sum_{i=1}^k R(n-a_i-sum_{j=1}^p R(n-b_{ij})), where a_i are integers, b_{ij} are natural numbers, and k,p are…

Combinatorics · Mathematics 2018-08-09 Abraham Isgur , Vitaly Kuznetsov , Mustazee Rahman , Stephen Tanny

Reverse search is a convenient method for enumerating structured objects, that can be used both to address theoretical issues and to solve data mining problems. This method has already been successfully developed to handle unordered trees.…

Discrete Mathematics · Computer Science 2022-05-13 Florian Ingels , Romain Azaïs

In the past several years a wide range of methods for the construction of regression trees and other estimators based on the recursive partitioning of samples have appeared in the statistics literature. Many applications involve data…

Methodology · Statistics 2014-07-07 Daniell Toth , John Eltinge