Related papers: Species tree inference from gene splits by Unroote…
We introduce equivariant tree models in algebraic statistics, which unify and generalise existing tree models such as the general Markov model, the strand symmetric model, and group based models. We focus on the ideals of such models. We…
Given a gene tree and a species tree, ancestral configurations represent the combinatorially distinct sets of gene lineages that can reach a given node of the species tree. They have been introduced as a data structure for use in the…
The paper attempts to validate the effectiveness of tree classifiers to classify tabla strokes especially the ones which are overlapping in nature. It uses decision tree, ID3 and random forest as classifiers. A custom made data sets of 650…
Species tree reconstruction is complicated by effects of Incomplete Lineage Sorting (ILS), commonly modeled by the multi-species coalescent model. While there has been substantial progress in developing methods that estimate a species tree…
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 study the influence of the seed in random trees grown according to the uniform attachment model, also known as uniform random recursive trees. We show that different seeds lead to different distributions of limiting trees from a total…
We study the problem of identifying the source of a diffusion spreading over a regular tree. When the degree of each node is at least three, we show that it is possible to construct confidence sets for the diffusion source with size…
We consider phylogeny estimation under a two-state model of sequence evolution by site substitution on a tree. In the asymptotic regime where the sequence lengths tend to infinity, we show that for any fixed $k$ no statistically consistent…
Phylogenetic data arising on two possibly different tree topologies might be mixed through several biological mechanisms, including incomplete lineage sorting or horizontal gene transfer in the case of different topologies, or simply…
A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density…
In this paper, we consider a tree inference problem motivated by the critical problem in single-cell genomics of reconstructing dynamic cellular processes from sequencing data. In particular, given a population of cells sampled from such a…
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,…
Designing flexible probabilistic models over tree topologies is important for developing efficient phylogenetic inference methods. To do that, previous works often leverage the similarity of tree topologies via hand-engineered heuristic…
Many fundamental statistical methods have become critical tools for scientific data analysis yet do not scale tractably to modern large datasets. This paper will describe very recent algorithms based on computational geometry which have…
We study the structure of genealogical trees associated with explosive Crump-Mode-Jagers branching processes (stopped at the explosion time), proving criteria for the associated tree to contain a node of infinite degree (a star) or an…
We consider in this paper the problem of discovering, via a traceroute algorithm, the topology of a network, whose graph is spanned by an infinite branching process. A subset of nodes is selected according to some criterion. As a measure of…
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…
Modeling the distribution of high dimensional data by a latent tree graphical model is a prevalent approach in multiple scientific domains. A common task is to infer the underlying tree structure, given only observations of its terminal…
Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of…
The sample frequency spectrum of a segregating site is the probability distribution of a sample of alleles from a genetic locus, conditional on observing the sample to have more than one clearly different phenotypes. We present a model for…