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Phylogenetic trees (i.e. evolutionary trees, additive trees or X-trees) play a key role in the processes of modeling and representing species evolution. Genome evolution of a given group of species is usually modeled by a species…

Several structural learning algorithms for staged tree models, an asymmetric extension of Bayesian networks, have been defined. However, they do not scale efficiently as the number of variables considered increases. Here we introduce the…

Model averaging methods have become an increasingly popular tool for improving predictions and dealing with model uncertainty, especially in Bayesian settings. Recently, frequentist model averaging methods such as information theoretic and…

We estimate the size of a labelled tree by comparing the amount of (labelled) nodes with the size of the set of labels. Roughly speaking, a exponentially big labelled tree, is any labelled tree that has an exponential gap between its size,…

Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to ``classic'' decision trees with constant values in their leaves, model trees can use linear…

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…

Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo (MCMC) with simple proposal mechanisms. This hinders exploration efficiency and often requires long runs to deliver accurate posterior estimates. In this paper,…

Phylogenetic Diversity (PD) is a prominent quantitative measure of the biodiversity of a collection of present-day species (taxa). This measure is based on the evolutionary distance among the species in the collection. Loosely speaking, if…

The matrix factor model has drawn growing attention for its advantage in achieving two-directional dimension reduction simultaneously for matrix-structured observations. In this paper, we propose a simple iterative least squares algorithm…

We propose a novel method for the inference of phylogenetic trees that utilises point configurations on hyperbolic space as its optimisation landscape. Each taxon corresponds to a point of the point configuration, while the evolutionary…

In modern data analysis, random sampling is an efficient and widely-used strategy to overcome the computational difficulties brought by large sample size. In previous studies, researchers conducted random sampling which is according to the…

We define a new balance index for rooted phylogenetic trees based on the symmetry of the evolutive history of every set of 4 leaves. This index makes sense for multifurcating trees and it can be computed in time linear in the number of…

We consider a class of simple, non-trivial models of evolving weighted scale-free networks. The network evolution in these models is determined by attachment of new vertices to ends of preferentially chosen weighted edges. Resulting…

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…

The existence of exponential dichotomies has been well-established as a powerful tool to study existence, stability, and bifurcations of coherent structures. Currently, the application of exponential dichotomies to elliptic problems posed…

Phylogenetic trees are used to model evolution: leaves are labelled to represent contemporary species ("taxa") and interior vertices represent extinct ancestors. Informally, convex characters are measurements on the contemporary species in…

The reconstruction of phylogenetic networks is an important but challenging problem in phylogenetics and genome evolution, as the space of phylogenetic networks is vast and cannot be sampled well. One approach to the problem is to solve the…

In phylogenetics, tree-based networks are used to model and visualize the evolutionary history of species where reticulate events such as horizontal gene transfer have occurred. Formally, a tree-based network $N$ consists of a phylogenetic…

We present the partial evolutionary tensor neural networks (pETNNs), a novel framework for solving time-dependent partial differential equations with high accuracy and capable of handling high-dimensional problems. Our architecture…

In high-dimensional statistics, the Lasso is a cornerstone method for simultaneous variable selection and parameter estimation. However, its reliance on the squared loss function renders it highly sensitive to outliers and heavy-tailed…