Related papers: Probabilistic Methods in the Study of Topological …
Three types of explicit estimators are proposed here to estimate the loss rates of the links in a network of the tree topology. All of them are derived by the maximum likelihood principle and proved to be either asymptotic unbiased or…
The multispecies coalescent model describes the generation of gene trees from a rooted metric species tree, and thus provides a framework for the inference of species trees from sampled gene trees. We prove that the STAR method of Liu et…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
The global structure of the minimal spanning tree (MST) is expected to be universal for a large class of underlying random discrete structures. However, very little is known about the intrinsic geometry of MSTs of most standard models, and…
The spanning tree heuristic is a commonly adopted procedure in network inference and estimation. It allows one to generalize an inference method developed for trees, which is usually based on a statistically rigorous approach, to a…
Random forests are ensemble methods which grow trees as base learners and combine their predictions by averaging. Random forests are known for their good practical performance, particularly in high dimensional set-tings. On the theoretical…
The eccentric sequence of a connected graph $G$ is the nondecreasing sequence of the eccentricities of its vertices. The Wiener index of $G$ is the sum of the distances between all unordered pairs of vertices of $G$. The unique trees that…
We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…
The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths),…
Random Forest (RF) is a powerful supervised learner and has been popularly used in many applications such as bioinformatics. In this work we propose the guided random forest (GRF) for feature selection. Similar to a feature selection method…
Random Forests and related tree-based methods are popular for supervised learning from table based data. Apart from their ease of parallelization, their classification performance is also superior. However, this performance, especially…
Gene trees are evolutionary trees representing the ancestry of genes sampled from multiple populations. Species trees represent populations of individuals -- each with many genes -- splitting into new populations or species. The coalescent…
We discuss a notion of convergence for binary trees that is based on subtree sizes. In analogy to recent developments in the theory of graphs, posets and permutations we investigate some general aspects of the topology, such as a…
We give a Large Deviation Principle (LDP) with explicit rate function for the distribution of vertex degrees in plane trees, a combinatorial model of RNA secondary structures. We calculate the typical degree distributions based on nearest…
We consider the task of learning Ising models when the signs of different random variables are flipped independently with possibly unequal, unknown probabilities. In this paper, we focus on the problem of robust estimation of…
Continuing the recent work of L. Zhong and K. Xu [MATCH Commun. Math. Comput. Chem.71(2014) 627-642], we determine inequalities among several vertex-degree-based topological indices; first geometric-arithmetic index(GA), augmented Zagreb…
We characterize and study variable importance (VIMP) and pairwise variable associations in binary regression trees. A key component involves the node mean squared error for a quantity we refer to as a maximal subtree. The theory naturally…
One regards spaces of trees as stratified spaces, to study distributions of phylogenetic trees. Stratified spaces with may have cycles, however spaces of trees with a fixed number of leafs are contractible. Spaces of trees with three leafs,…
We study the properties of random walks on complex trees. We observe that the absence of loops reflects in physical observables showing large differences with respect to their looped counterparts. First, both the vertex discovery rate and…
We investigated testing the likelihood of a phylogenetic tree by comparison to its subtree pruning and regrafting (SPR) neighbors, with or without re-optimizing branch lengths. This is inspired by aspects of Bayesian significance tests, and…