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Graphs are a powerful tool for analyzing large data sets, but many real-world phenomena involve interactions that go beyond the simple pairwise relationships captured by a graph. In this paper we introduce and study a simple combinatorial…
The problem of comparing probability distributions is at the heart of many tasks in statistics and machine learning. Established comparison methods treat the standard setting that the distributions are supported in the same space. Recently,…
A central theme in phylogenetics is the reconstruction and analysis of evolutionary trees from a given set of data. To determine the optimal search methods for reconstructing trees, it is crucial to understand the size and structure of the…
A widely studied model for generating sequences is to ``evolve'' them on a tree according to a symmetric Markov process. We prove that model trees tend to be maximally ``far apart'' in terms of variational distance.
Regression trees are one of the oldest forms of AI models, and their predictions can be made without a calculator, which makes them broadly useful, particularly for high-stakes applications. Within the large literature on regression trees,…
Genomes and genes diversify during evolution; however, it is unclear to what extent genes still retain the relationship among species. Model species for molecular phylogenetic studies include yeasts and viruses whose genomes were sequenced…
Given natural limitations on the length DNA sequences, designing phylogenetic reconstruction methods which are reliable under limited information is a crucial endeavor. There have been two approaches to this problem: reconstructing partial…
Sequence segmentation is a well-studied problem, where given a sequence of elements, an integer K, and some measure of homogeneity, the task is to split the sequence into K contiguous segments that are maximally homogeneous. A classic…
Motivation: The construction of statistics for summarizing posterior samples returned by a Bayesian phylogenetic study has so far been hindered by the poor geometric insights available into the space of phylogenetic trees, and ad hoc…
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…
This paper presents two new deterministic algorithms for constructing consensus trees. Given an input of k phylogenetic trees with identical leaf label sets and n leaves each, the first algorithm constructs the majority rule (+) consensus…
Trees have long been used as a graphical representation of species relationships. However complex evolutionary events, such as genetic reassortments or hybrid speciations which occur commonly in viruses, bacteria and plants, do not fit into…
Ancestral sequence reconstruction is a key task in computational biology. It consists in inferring a molecular sequence at an ancestral species of a known phylogeny, given descendant sequences at the tip of the tree. In addition to its many…
Comparative analyses of phylogenetic trees typically require identical taxon sets, however, in practice, trees often include distinct but overlapping taxa. Pruning non-shared leaves discards phylogenetic signal, whereas tree completion can…
In this article the results of Waddell and Azad (2009) are extended. In particular, the geometric percentage mean standard deviation measure of the fit of distances to a phylogenetic tree is adjusted for the number of parameters fitted to…
In a population with haploid reproduction any individual has a single parent in the previous generation. If all genealogical distances among pairs of individuals (generations from the closest common ancestor) are known it is possible to…
Metagenomics is a powerful approach to study genetic content of environmental samples that has been strongly promoted by NGS technologies. To cope with massive data involved in modern metagenomic projects, recent tools [4, 39] rely on the…
We derive tractable criteria for the consistency of Bayesian tree reconstruction procedures, which constitute a central class of algorithms for inferring common ancestry among DNA sequence samples in phylogenetics. Our results encompass…
Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has…
k-means is a widely used clustering algorithm, but for $k$ clusters and a dataset size of $N$, each iteration of Lloyd's algorithm costs $O(kN)$ time. Although there are existing techniques to accelerate single Lloyd iterations, none of…