Related papers: Phylogenetic network models as graphical models

This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…

Phylogenetics begins with reconstructing biological family trees from genetic data. Since Nature is not limited to tree-like histories, we use networks to organize our data, and have discovered new polytopes, metric spaces, and simplicial…

A phylogenetic network is a directed acyclic graph that visualises an evolutionary history containing so-called reticulations such as recombinations, hybridisations or lateral gene transfers. Here we consider the construction of a simplest…

Directed acyclic graphs (DAGs) are directed graphs in which there is no path from a vertex to itself. DAGs are an omnipresent data structure in computer science and the problem of counting the DAGs of given number of vertices and to sample…

Phylogenetic networks are directed acyclic graphs that depict the genomic evolution of related taxa. Reticulation nodes in such networks (nodes with more than one parent) represent reticulate evolutionary events, such as recombination,…

Semidirected networks have received interest in evolutionary biology as the appropriate generalization of unrooted trees to networks, in which some but not all edges are directed. Yet these networks lack proper theoretical study. We define…

Since the advent of modern bioinformatics, the challenging, multifaceted problem of reconstructing phylogenetic history from biological sequences has hatched perennial statistical and algorithmic innovation. Studies of the phylogenetic…

In many situations, it would be useful to know not just the best phylogenetic tree for a given data set, but the collection of high-quality trees. This goal is typically addressed using Bayesian techniques, however, current Bayesian methods…

One strategy for reconstruction of phylogenetic networks is to solve the phylogenetic network problem, which involves inferring phylogenetic trees first and subsequently computing the smallest phylogenetic network that displays all the…

We consider the problem of learning the underlying causal structure among a set of variables, which are assumed to follow a Bayesian network or, more specifically, a linear recursive structural equation model (SEM) with the associated…

Phylogenetic networks are used to represent evolutionary scenarios in biology and linguistics. To find the most probable scenario, it may be necessary to compare candidate networks, to distinguish different networks, and to see when one…

We study a distributed learning problem in which learning agents are embedded in a directed acyclic graph (DAG). There is a fixed and arbitrary distribution over feature/label pairs, and each agent or vertex in the graph is able to directly…

Directed acyclic graph (DAG) models are widely used to represent causal relationships among random variables in many application domains. This paper studies a special class of non-Gaussian DAG models, where the conditional variance of each…

Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many…

A Bayesian Network (BN) is a probabilistic model that represents a set of variables using a directed acyclic graph (DAG). Current algorithms for learning BN structures from data focus on estimating the edges of a specific DAG, and often…

A directed acyclic graph (DAG) partially represents the conditional independence structure among observations of a system if the local Markov condition holds, that is, if every variable is independent of its non-descendants given its…

In the process of building (structural learning) a probabilistic graphical model from a set of observed data, the directional, cyclic dependencies between the random variables of the model are often found. Existing graphical models such as…

A directed phylogenetic network is tree-child if every non-leaf vertex has a child that is not a reticulation. As a class of directed phylogenetic networks, tree-child networks are very useful from a computational perspective. For example,…

Biomolecular networks have already found great utility in characterizing complex biological systems arising from pair-wise interactions amongst biomolecules. Here, we review how graph theoretical approaches can be applied not only for a…

Phylogenetic mixtures model the inhomogeneous molecular evolution commonly observed in data. The performance of phylogenetic reconstruction methods where the underlying data is generated by a mixture model has stimulated considerable recent…