相关论文: A distance based test on random trees

The goal of this paper is to study the similarity between sequences using a distance between the \emph{context} trees associated to the sequences. These trees are defined in the framework of \emph{Sparse Probabilistic Suffix Trees} (SPST),…

Stochastic branching processes are a classical model for describing random trees, which have applications in numerous fields including biology, physics, and natural language processing. In particular, they have recently been proposed to…

We consider the simple random walk on the infinite cluster of the Bernoulli bond percolation of trees, and investigate the relation between the speed of the simple random walk and the retaining probability p by studying three classes of…

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…

In this article, we focus on Bienaym\'e-Galton-Watson processes with linear-fractional offspring distributions. At a fixed generation, we consider a sample of the individuals alive, drawn in two different ways: either through Bernoulli…

Energy distance is a statistical distance between the distributions of random variables, which characterizes the equality of the distributions. Utilizing the energy distance, we develop a nonparametric test for the diagonal symmetry, which…

Understanding the evolution of a set of genes or species is a fundamental problem in evolutionary biology. The problem we study here takes as input a set of trees describing {possibly discordant} evolutionary scenarios for a given set of…

We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution,…

In many domains, data measurements can naturally be associated with the leaves of a tree, expressing the relationships among these measurements. For example, companies belong to industries, which in turn belong to ever coarser divisions…

The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption…

We investigate some aspects of the problem of the estimation of birth distributions (BD) in multi-type Galton-Watson trees (MGW) with unobserved types. More precisely, we consider two-type MGW called spinal-structured trees. This kind of…

We study properties of the harmonic measure of balls in typical large discrete trees. For a ball of radius $n$ centered at the root, we prove that, although the size of the boundary is of order $n$, most of the harmonic measure is supported…

This work briefly explores the possibility of approximating spatial distance (alternatively, similarity) between data points using the Isolation Forest method envisioned for outlier detection. The logic is similar to that of isolation: the…

Random forest is effective for prediction tasks but the randomness of tree generation hinders interpretability in feature importance analysis. To address this, we proposed DT-Sampler, a SAT-based method for measuring feature importance in…

Despite widespread interest and practical use, the theoretical properties of random forests are still not well understood. In this paper we contribute to this understanding in two ways. We present a new theoretically tractable variant of…

Markov networks are frequently used in sciences to represent conditional independence relationships underlying observed variables arising from a complex system. It is often of interest to understand how an underlying network differs between…

In this paper, we consider the problem of testing the equality of two multivariate distributions based on geometric graphs constructed using the interpoint distances between the observations. These include the tests based on the minimum…

We consider the number of nodes in the levels of unlabelled rooted random trees and show that the stochastic process given by the properly scaled level sizes weakly converges to the local time of a standard Brownian excursion. Furthermore…

The reliability of a phylogenetic inference method from genomic sequence data is ensured by its statistical consistency. Bayesian inference methods produce a sample of phylogenetic trees from the posterior distribution given sequence data.…

We consider growing random recursive trees in random environment, in which at each step a new vertex is attached (by an edge of a random length) to an existing tree vertex according to a probability distribution that assigns the tree…