Related papers: Random ultrametric trees and applications
Phylogenetic tree shapes capture fundamental signatures of evolution. We consider ``ranked'' tree shapes, which are equipped with a total order on the internal nodes compatible with the tree graph. Recent work has established an elegant…
Distance-based methods such as UPGMA (Unweighted Pair Group Method with Arithmetic Mean) continue to play a significant role in phylogenetic research. We use polyhedral combinatorics to analyze the natural subdivision of the positive…
In a population with haploid reproduction any individual has a single parent in the previous generation. If all genealogical distances among pairs of individuals (generations from the closest common ancestor) are known it is possible to…
In this paper, we redesign and simplify an algorithm due to Remy et al. for the generation of rooted planar trees that satisfies a given partition of degrees. This new version is now optimal in terms of random bit complexity, up to a…
Rooted trees with probabilities are used to analyze properties of a variable length code. A bound is derived on the difference between the entropy rates of the code and a memoryless source. The bound is in terms of normalized informational…
The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…
We introduce new methods for phylogenetic tree quartet construction by using machine learning to optimize the power of phylogenetic invariants. Phylogenetic invariants are polynomials in the joint probabilities which vanish under a model of…
Random forests is a state-of-the-art supervised machine learning method which behaves well in high-dimensional settings although some limitations may happen when $p$, the number of predictors, is much larger than the number of observations…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
This paper addresses the problem of finding a representation of a subtree distance, which is an extension of the tree metric. We show that a minimal representation is uniquely determined by a given subtree distance, and give a linear time…
We give a de Finetti type representation for exchangeable random coalescent trees (formally described as semi-ultrametrics) in terms of sampling iid sequences from marked metric measure spaces. We apply this representation to define…
Random forests are a very effective and commonly used statistical method, but their full theoretical analysis is still an open problem. As a first step, simplified models such as purely random forests have been introduced, in order to shed…
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…
In the theoretical study of distributed communication networks, "history trees" are a discrete structure that naturally models the concept that anonymous agents become distinguishable upon receiving different sets of messages from…
Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…
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…
Nested (or reconciled) phylogenetic trees model co-evolutionary systems in which one evolutionary history is embedded within another. We introduce a geometric framework for such systems by defining $\sigma$-space, a moduli space of fully…
Suffix trees are one of the most versatile data structures in stringology, with many applications in bioinformatics. Their main drawback is their size, which can be tens of times larger than the input sequence. Much effort has been put into…
Tree rearrangement operations typically induce a metric on the space of phylogenetic trees. One important property of these metrics is the size of the neighbourhood, that is, the number of trees exactly one operation from a given tree. We…
We study the portraits of isometries of rooted trees - the labelling of the tree, at each vertex, by the permutation of its descendants - in terms of languages. We characterize regularly branched self-similar groups in terms of…