Related papers: Mass distribution exponents for growing trees
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…
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…
We study the size and the lifetime distributions of scale-free random branching tree in which $k$ branches are generated from a node at each time step with probability $q_k\sim k^{-\gamma}$. In particular, we focus on finite-size trees in a…
We investigate approximating joint distributions of random processes with causal dependence tree distributions. Such distributions are particularly useful in providing parsimonious representation when there exists causal dynamics among…
The magnitude of Pearson correlation between two scalar random variables can be visually judged from the two-dimensional scatter plot of an independent and identically distributed sample drawn from the joint distribution of the two…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
Many of the distributed localization algorithms are based on relaxed optimization formulations of the localization problem. These algorithms commonly rely on first-order optimization methods, and hence may require many iterations or…
This study is dedicated to precise distributional analyses of the height of non-plane unlabelled binary trees ("Otter trees"), when trees of a given size are taken with equal likelihood. The height of a rooted tree of size $n$ is proved to…
Given any regularly varying dislocation measure, we identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application, we obtain continuum random tree limits of…
We develop a general statistical framework for the analysis and inference of large tree-structured data, with a focus on developing asymptotic goodness-of-fit tests. We first propose a consistent statistical model for binary trees, from…
We propose Partition Tree, a novel tree-based framework for conditional density estimation over general outcome spaces that supports both continuous and categorical variables within a unified formulation. Our approach models conditional…
Inspired by Stufler's recent probabilistic proof of Otter's asymptotic number of unlabeled trees, we revisit work of Palmer and Schwenk, and study unlabeled forests from a probabilistic point of view. We show that the number of trees in a…
The matrices of spanning rooted forests are studied as a tool for analysing the structure of networks and measuring their properties. The problems of revealing the basic bicomponents, measuring vertex proximity, and ranking from preference…
A set of general allometric scaling laws is derived for different systems represented by tree networks. The formulation postulates self-similar networks with an arbitrary number of branches developed in each generation, and with an…
Let $\mathcal{T}_n$ be the set of trees with $n$ vertices. Suppose that each tree in $\mathcal{T}_n$ is equally likely. We show that the number of different rooted trees of a tree equals $(\mu_r+o(1))n$ for almost every tree of…
Given a solution to a recursive distributional equation, a natural (and non-trivial) question is whether the corresponding recursive tree process is endogenous. That is, whether the random environment almost surely defines the tree process.…
We study the distribution regression problem assuming the distribution of distributions has a doubling measure larger than one. First, we explore the geometry of any distributions that has doubling measure larger than one and build a small…
Estimating phylogenetic trees is an important problem in evolutionary biology, environmental policy and medicine. Although trees are estimated, their uncertainties are discarded by mathematicians working in tree space. Here we explicitly…
We show that the Sibuya distribution and its non-critical relatives are relevant in the context of the recursive generation of both simply generated and increasing critical trees' and forests' progenies. A special class of generalized…
We consider two varieties of labeled rooted trees, and the probability that a vertex chosen from all vertices of all trees of a given size uniformly at random has a given rank. We prove that this probability converges to a limit as the tree…