Related papers: Phase transition in the sample complexity of likel…
Many biological studies involve inferring the evolutionary history of a sample of individuals from a large population and interpreting the reconstructed tree. Such an ascertained tree typically represents only a small part of a…
Label shift refers to the phenomenon where the prior class probability p(y) changes between the training and test distributions, while the conditional probability p(x|y) stays fixed. Label shift arises in settings like medical diagnosis,…
Quartet Reconstruction, the task of recovering a phylogenetic tree from smaller trees on four species called \textit{quartets}, is a well-studied problem in theoretical computer science with far-reaching connections to statistics, graph…
The evolution of molecular and phenotypic traits is commonly modelled using Markov processes along a phylogeny. This phylogeny can be a tree, or a network if it includes reticulations, representing events such as hybridization or admixture.…
In many interesting cases the reconstruction of a correct phylogeny is blurred by high mutation rates and/or horizontal transfer events. As a consequence a divergence arises between the true evolutionary distances and the differences…
We observe $n$ sequences at each of $m$ sites, and assume that they have evolved from an ancestral sequence that forms the root of a binary tree of known topology and branch lengths, but the sequence states at internal nodes are unknown.…
Data analysis in science, e.g., high-energy particle physics, is often subject to an intractable likelihood if the observables and observations span a high-dimensional input space. Typically the problem is solved by reducing the…
We derive sharp thresholds for exact recovery of communities in a weighted stochastic block model, where observations are collected in the form of a weighted adjacency matrix, and the weight of each edge is generated independently from a…
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…
Phylogenetic network is an evolutionary model that uses a rooted directed acyclic graph (instead of a tree) to model an evolutionary history of species in which reticulate events (e.g., hybrid speciation or horizontal gene transfer)…
Phylogenetic trees describe the evolutionary history of a group of present-day species from a common ancestor. These trees are typically reconstructed from aligned DNA sequence data. In this paper we analytically address the following…
In this article we consider the problem of choosing an optimal sampling scheme for the regression problem simultaneously with that of model selection. We consider a batch type approach and an on-line approach following algorithms recently…
Attempting to recognize a tree inside a phylogenetic network is a fundamental undertaking in evolutionary analysis. In the last few years, therefore, tree-based phylogenetic networks, which are defined by a spanning tree called a…
The latent stochastic block model is a flexible and widely used statistical model for the analysis of network data. Extensions of this model to a dynamic context often fail to capture the persistence of edges in contiguous network…
A phylogenetic variety is an algebraic variety parameterized by a statistical model of the evolution of biological sequences along a tree. Understanding this variety is an important problem in the area of algebraic statistics with…
In this article, we consider a Branching Random Walk on the real line. The genealogical structure is assumed to be given through a supercritical branching process in the i.i.d. environment and satisfies the Kesten-Stigum condition. The…
Reticulate evolutionary processes result in phylogenetic histories that cannot be modeled using a tree topology. Here, we apply methods from topological data analysis to molecular sequence data with reticulations. Using a simple example, we…
We investigate the optimization landscape of maximum likelihood estimation (MLE) for the Cavender-Farris-Neyman (CFN) model, a two-state latent tree model fundamental to statistical phylogenetics and the ferromagnetic Ising model. Although…
The manifold hypothesis says that natural high-dimensional data lie on or around a low-dimensional manifold. The recent success of statistical and learning-based methods in very high dimensions empirically supports this hypothesis,…
Mutation rate variation across loci is well known to cause difficulties, notably identifiability issues, in the reconstruction of evolutionary trees from molecular sequences. Here we introduce a new approach for estimating general…