Related papers: Information geometry for phylogenetic trees
Phylogenetic trees and networks are leaf-labelled graphs used to model evolution. Display graphs are created by identifying common leaf labels in two or more phylogenetic trees or networks. The treewidth of such graphs is bounded as 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…
We consider the space of complete and separable metric spaces which are equipped with a probability measure. A notion of convergence is given based on the philosophy that a sequence of metric measure spaces converges if and only if all…
A model of genomic sequence evolution on a species tree should include not only a sequence substitution process, but also a coalescent process, since different sites may evolve on different gene trees due to incomplete lineage sorting.…
A geophylogeny is a phylogenetic tree (or dendrogram) where each leaf (e.g. biological taxon) has an associated geographic location (site). To clearly visualize a geophylogeny, the tree is typically represented as a crossing-free drawing…
The wealth of data being gathered about humans and their surroundings drives new machine learning applications in various fields. Consequently, more and more often, classifiers are trained using not only numerical data but also complex data…
New geometric and computational analyses of power-weighted shortest-path distances (PWSPDs) are presented. By illuminating the way these metrics balance density and geometry in the underlying data, we clarify their key parameters and…
While circular data occur in a wide range of scientific fields, the methodology for distributional modeling and probabilistic forecasting of circular response variables is rather limited. Most of the existing methods are built on the…
Bayesian inference for phylogenetics is a gold standard for computing distributions of phylogenies. It faces the challenging problem of. moving throughout the high-dimensional space of trees. However, hyperbolic space offers a low…
Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…
An increasing array of biomedical and computer vision applications requires the predictive modeling of complex data, for example images and shapes. The main challenge when predicting such objects lies in the fact that they do not comply to…
Phylogenetic trees elucidate evolutionary relationships among species, but phylogenetic inference remains challenging due to the complexity of combining continuous (branch lengths) and discrete parameters (tree topology). Traditional Markov…
Random forests are a statistical learning method widely used in many areas of scientific research because of its ability to learn complex relationships between input and output variables and also its capacity to handle high-dimensional…
This paper explores the Bergman geometry of bounded domains $\Omega$ in $\mathbb{C}^n$ through the lens of information geometry by introducing a mapping $\Phi: \Omega \rightarrow \mathcal{P}(\Omega)$, where $\mathcal{P}(\Omega)$ denotes a…
Phylogenetic trees are simple models of evolutionary processes. They describe conditionally independent divergent evolution of taxa from common ancestors. Phylogenetic trees commonly do not have enough flexibility to adequately model all…
Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…
Null models of binary phylogenetic trees are useful for testing hypotheses on real world phylogenies. In this paper we consider phylogenies as binary trees without edge lengths together with a sampling measure and encode them as algebraic…
Phylogenetic trees capture evolutionary relationships among species and reflect the forces that shaped them. While many studies rely on branch length information, the topology of phylogenetic trees (particularly their degree of imbalance)…
Topological phylogenetic trees can be assigned edge weights in several natural ways, highlighting different aspects of the tree. Here the rooted triple and quartet metrizations are introduced, and applied to formulate novel fast methods of…
Given an ensemble of randomized regression trees, it is possible to restructure them as a collection of multilayered neural networks with particular connection weights. Following this principle, we reformulate the random forest method of…