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The minimal number of rooted subtree prune and regraft (rSPR) operations needed to transform one phylogenetic tree into another one induces a metric on phylogenetic trees - the rSPR-distance. The rSPR-distance between two phylogenetic trees…
For an arbitrary tree we investigate the problems of constructing a maximum matching which minimizes or maximizes the cardinality of a maximum matching of the graph obtained from original one by its removal and present corresponding…
Given a set $X$ of species, a phylogenetic tree is an unrooted binary tree whose leaves are bijectively labelled by $X$. Such trees can be used to show the way species evolve over time. One way of understanding how topologically different…
Understanding the evolution of a set of genes or species is a fundamental problem in evolutionary biology. The problem we study here takes as input a set of trees describing {possibly discordant} evolutionary scenarios for a given set of…
Random Forests (RF) and Extreme Gradient Boosting (XGBoost) are two of the most widely used and highly performing classification and regression models. They aggregate equally weighted CART trees, generated randomly in RF or sequentially in…
Given two phylogenetic trees with the $\{1, \ldots, n\}$ leaf-set the maximum agreement subtree problem asks what is the maximum size of the subset $A \subseteq \{1, \ldots, n\}$ such that the two trees are equivalent when restricted to…
We prove polynomial upper and lower bounds on the expected size of the maximum agreement subtree of two random binary phylogenetic trees under both the uniform distribution and Yule-Harding distribution. This positively answers a question…
The ancestral maximum-likelihood and phylogeography problems are two fundamental problems involving evolutionary studies. The ancestral maximum-likelihood problem involves identifying a rooted tree alongside internal node sequences that…
In recent years, significant progress has been made on algorithms for learning optimal decision trees, primarily in the context of binary features. Extending these methods to continuous features remains substantially more challenging due to…
Bayesian inference is now a leading technique for reconstructing phylogenetic trees from aligned sequence data. In this short note, we formally show that the maximum posterior tree topology provides a statistically consistent estimate of a…
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…
We develop and analyze methods for computing provably optimal {\em maximum a posteriori} (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex…
We propose an algorithm named best-scored random forest for binary classification problems. The terminology "best-scored" means to select the one with the best empirical performance out of a certain number of purely random tree candidates…
Here we present a new fixed parameter tractable algorithm to compute the hybridization number r of two rooted binary phylogenetic trees on taxon set X in time (6r)^r.poly(n), where n=|X|. The novelty of this approach is that it avoids the…
Reticulate events play an important role in determining evolutionary relationships. The problem of computing the minimum number of such events to explain discordance between two phylogenetic trees is a hard computational problem. Even for…
In the Properly Colored Spanning Tree problem, we are given an edge-colored undirected graph and the goal is to find a properly colored spanning tree, i.e., a spanning tree in which any two adjacent edges have distinct colors. The problem…
Phylogenetic trees play a key role in the reconstruction of evolutionary relationships. Typically, they are derived from aligned sequence data (like DNA, RNA, or proteins) by using optimization criteria like, e.g., maximum parsimony (MP).…
Sequence alignment is common nowadays as it is used in many fields to determine how closely two sequences are related and at times to see how little they differ. In computational biology / Bioinformatics, there are many algorithms developed…
We derive ensembles of decision trees through a nonparametric Bayesian model, allowing us to view random forests as samples from a posterior distribution. This insight provides large gains in interpretability, and motivates a class of…
Machine Learning has attracted considerable attention throughout the past decade due to its potential to solve far-reaching tasks, such as image classification, object recognition, anomaly detection, and data forecasting. A standard…