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Phylogenetic networks are a generalization of phylogenetic trees that allow for the representation of non-treelike evolutionary events, like recombination, hybridization, or lateral gene transfer. In a recent series of papers devoted to the…
In graph theory, a tree is one of the more popular families of graphs with a wide range of applications in computer science as well as many other related fields. While there are several distance measures over the set of all trees, we…
Regression forests have long delivered state-of-the-art accuracy, often outperforming regression trees and even neural networks, but they suffer from limited interpretability as ensemble methods. In this work, we revisit forest pruning, an…
Understanding generalization and robustness of machine learning models fundamentally relies on assuming an appropriate metric on the data space. Identifying such a metric is particularly challenging for non-Euclidean data such as graphs.…
Compatibility of unrooted phylogenetic trees is a well studied problem in phylogenetics. It asks to determine whether for a set of k input trees there exists a larger tree (called a supertree) that contains the topologies of all k input…
Phylogenetic networks are a special type of graph which generalize phylogenetic trees and that are used to model non-treelike evolutionary processes such as recombination and hybridization. In this paper, we consider {\em unrooted}…
Hybridization networks are representations of evolutionary histories that allow for the inclusion of reticulate events like recombinations, hybridizations, or lateral gene transfers. The recent growth in the number of hybridization network…
A merge tree is a fundamental topological structure used to capture the sub-level set (and similarly, super-level set) topology in scalar data analysis. The interleaving distance is a theoretically sound, stable metric for comparing merge…
Metrics on rooted phylogenetic trees are integral to a number of areas of phylogenetic analysis. Cluster-similarity metrics have recently been introduced in order to limit skew in the distribution of distances, and to ensure that trees in…
Learning about the relationship between distance to landmarks and events and phenomena of interest is a multi-faceted problem, as it may require taking into account multiple dimensions, including: spatial position of landmarks, timing of…
We introduce a scale-free method for testing the proportionality of branch lengths between two phylogenetic trees that have the same topology and contain the same set of taxa. This method scales both trees to a total length of 1 and sums up…
In this paper, we investigate the computational complexity of subgraph reconfiguration problems in directed graphs. More specifically, we focus on the problem of reconfiguring arborescences in a digraph, where an arborescence is a directed…
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…
Typing methods are widely used in the surveillance of infectious diseases, outbreaks investigation and studies of the natural history of an infection. And their use is becoming standard, in particular with the introduction of High…
Constrained forest problems form a class of graph problems where specific connectivity requirements for certain cuts within the graph must be satisfied by selecting the minimum-cost set of edges. The prize-collecting version of these…
We propose a procedure to build a decision tree which approximates the performance of complex machine learning models. This single approximation tree can be used to interpret and simplify the predicting pattern of random forests (RFs) and…
Recent years have witnessed a surge of biological interest in the minimum spanning tree (MST) problem for its relevance to automatic model construction using the distances between data points. Despite the increasing use of MST algorithms…
The Neighbor-Joining algorithm is a popular distance-based phylogenetic method that computes a tree metric from a dissimilarity map arising from biological data. Realizing dissimilarity maps as points in Euclidean space, the algorithm…
The early development of a zygote can be mathematically described by a developmental tree. To compare developmental trees of different species, we need to define distances on trees. If children cells after a division are not…
Phylogenetic networks are used to represent the evolutionary history of species. They are versatile when compared to traditional phylogenetic trees, as they capture more complex evolutionary events such as hybridization and horizontal gene…