Related papers: Stochastic safety radius on Neighbor-Joining metho…
A variety of algorithms have been proposed for reconstructing trees that show the evolutionary relationships between species by comparing differences in genetic data across present-day taxa. If the leaf-to-leaf distances in a tree can be…
The popular neighbor-joining (NJ) algorithm used in phylogenetics is a greedy algorithm for finding the balanced minimum evolution (BME) tree associated to a dissimilarity map. From this point of view, NJ is ``optimal'' when the algorithm…
Balanced minimum evolution (BME) is a statistically consistent distance-based method to reconstruct a phylogenetic tree from an alignment of molecular data. In 2000, Pauplin showed that the BME method is equivalent to optimizing a linear…
In 2007, Eickmeyer et al. showed that the tree topologies outputted by the Neighbor-Joining (NJ) algorithm and the balanced minimum evolution (BME) method for phylogenetic reconstruction are each determined by a polyhedral subdivision of…
This paper introduces constNJ, the first algorithm for phylogenetic reconstruction of sets of trees with constrained pairwise rooted subtree-prune regraft (rSPR) distance. We are motivated by the problem of constructing sets of trees which…
Distance-based approaches in phylogenetics such as Neighbor-Joining are a fast and popular approach for building trees. These methods take pairs of sequences from them construct a value that, in expectation, is additive under a stochastic…
A common assumption in multiple scientific applications is that the distribution of observed data can be modeled by a latent tree graphical model. An important example is phylogenetics, where the tree models the evolutionary lineages of a…
The Neighbor-Joining algorithm is a popular distance-based phylogenetic method that computes a tree metric from a dissimilarity map arising from biological data. Realizing dissimilarity maps as points in Euclidean space, the algorithm…
Recent theoretical work has demonstrated that Neighbor Joining applied to concatenated DNA sequences is a statistically consistent method of species tree reconstruction. This brief note compares the accuracy of this approach to other…
The widely used model for evolutionary relationships is a bifurcating tree with all taxa/observations placed at the leaves. This is not appropriate if the taxa have been densely sampled across evolutionary time and may be in a direct…
For a tree with the given sequence of vertex degrees the spectral radius of its terminal distance matrix is shown to be bounded from below by the the average row sum of the terminal distance matrix of the, so called, BFS-tree (also known as…
The Neighbor-Joining algorithm is a recursive procedure for reconstructing trees that is based on a transformation of pairwise distances between leaves. We present a generalization of the neighbor-joining transformation, which uses…
We consider the stochastic geometry model where the location of each node is a random point in a given metric space, or the existence of each node is uncertain. We study the problems of computing the expected lengths of several…
Consider~\(n\) nodes~\(\{X_i\}_{1 \leq i \leq n}\) independently distributed in the unit square~\(S,\) each according to a distribution~\(f.\) Nodes~\(X_i\) and~\(X_j\) are joined by an edge if the Euclidean distance~\(d(X_i,X_j)\) is less…
We study the inference of network archaeology in growing random geometric graphs. We consider the root finding problem for a random nearest neighbor tree in dimension $d \in \mathbb{N}$, generated by sequentially embedding vertices…
Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and…
Distance-based phylogenetic algorithms attempt to solve the NP-hard least squares phylogeny problem by mapping an arbitrary dissimilarity map representing biological data to a tree metric. The set of all dissimilarity maps is a Euclidean…
The problem of reconstructing evolutionary trees or phylogenies is of great interest in computational biology. A popular model for this problem assumes that we are given the set of leaves (current species) of an unknown binary tree and the…
Stochastic localization is a pathwise analysis technique originating from convex geometry. This paper explores certain algorithmic aspects of stochastic localization as a computational tool. First, we unify various existing stochastic…
Recent years have witnessed a surge of biological interest in the minimum spanning tree (MST) problem for its relevance to automatic model construction using the distances between data points. Despite the increasing use of MST algorithms…