Related papers: Dimensional reduction for the general Markov model…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate…
It is known that the Kimura 3ST model of sequence evolution on phylogenetic trees can be extended quite naturally to arbitrary split systems. However, this extension relies heavily on mathematical peculiarities of the K3ST model, and…
In the last decade, some algebraic tools have been successfully applied to phylogenetic reconstruction. These tools are mainly based on the knowledge of equations describing algebraic varieties associated to phylogenetic trees evolving…
Recently there has been renewed interest in phylogenetic inference methods based on phylogenetic invariants, alongside the related Markov invariants. Broadly speaking, both these approaches give rise to polynomial functions of sequence site…
Many of the stochastic models used in inference of phylogenetic trees from biological sequence data have polynomial parameterization maps. The image of such a map --- the collection of joint distributions for a model --- forms the model…
The general Markov plus invariable sites (GM+I) model of biological sequence evolution is a two-class model in which an unknown proportion of sites are not allowed to change, while the remainder undergo substitutions according to a Markov…
Modelling the substitution of nucleotides along a phylogenetic tree is usually done by a hidden Markov process. This allows to define a distribution of characters at the leaves of the trees and one might be able to obtain polynomial…
Dimension reduction is a common strategy to study non-linear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of…
We studied how to obtain a distribution for the number of ancestors in species of sexual reproduction. Present models concentrate on the estimation of distributions repetitions of ancestors in genealogical trees. It has been shown that is…
A calculational framework is proposed for phylogenetics, using nonlocal quantum field theories in hypercubic geometry. Quadratic terms in the Hamiltonian give the underlying Markov dynamics, while higher degree terms represent branching…
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models,…
In general, cellular phenotypes, as measured by concentrations of cellular components, involve large degrees of freedom. However, recent measurement has demonstrated that phenotypic changes resulting from adaptation and evolution in…
Phylogenetic invariants are certain polynomials in the joint probability distribution of a Markov model on a phylogenetic tree. Such polynomials are of theoretical interest in the field of algebraic statistics and they are also of practical…
The evolution of aligned DNA sequence sites is generally modeled by a Markov process operating along the edges of a phylogenetic tree. It is well known that the probability distribution on the site patterns at the tips of the tree…
We consider novel phylogenetic models with rate matrices that arise via the embedding of a progenitor model on a small number of character states, into a target model on a larger number of character states. Adapting representation-theoretic…
Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method…
Phylogenetic networks provide a means of describing the evolutionary history of sets of species believed to have undergone hybridization or gene flow during their evolution. The mutation process for a set of such species can be modeled as a…
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…
In recent years, a number of methods have been developed to infer complex demographic histories, especially historical population size changes, from genomic sequence data. Coalescent Hidden Markov Models have proven to be particularly…
This thesis develops and expands upon known techniques of mathematical physics relevant to the analysis of the popular Markov model of phylogenetic trees required in biology to reconstruct the evolutionary relationships of taxonomic units…