Related papers: Likelihood-Based Root State Reconstruction on a Tr…
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…
Likelihood-based methods are widely considered the best approaches for reconstructing ancestral states. Although much effort has been made to study properties of these methods, previous works often assume that both the tree topology and…
We consider the branch-length estimation problem on a bifurcating tree: a character evolves along the edges of a binary tree according to a two-state symmetric Markov process, and we seek to recover the edge transition probabilities from…
Reconstructing evolutionary trees from molecular sequence data is a fundamental problem in computational biology. Stochastic models of sequence evolution are closely related to spin systems that have been extensively studied in statistical…
Diffusion processes on trees are commonly used in evolutionary biology to model the joint distribution of continuous traits, such as body mass, across species. Estimating the parameters of such processes from tip values presents challenges…
We consider the problem of inferring an ancestral state from observations at the leaves of a tree, assuming the state evolves along the tree according to a two-state symmetric Markov process. We establish a general branching rate condition…
We analyse a maximum-likelihood approach for combining phylogenetic trees into a larger `supertree'. This is based on a simple exponential model of phylogenetic error, which ensures that ML supertrees have a simple combinatorial description…
Sum-Product Networks with complex probability distribution at the leaves have been shown to be powerful tractable-inference probabilistic models. However, while learning the internal parameters has been amply studied, learning complex leaf…
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…
It is common in phylogenetics to have some, perhaps partial, information about the overall evolutionary tree of a group of organisms and wish to find an evolutionary tree of a specific gene for those organisms. There may not be enough…
The evolution of aligned DNA sequence sites is generally modeled by a Markov process operating along the edges of a phylogenetic tree. It is well known that the probability distribution on the site patterns at the tips of the tree…
Maximum likelihood estimators are used extensively to estimate unknown parameters of stochastic trait evolution models on phylogenetic trees. Although the MLE has been proven to converge to the true value in the independent-sample case, we…
A Brownian motion tree (BMT) model is a Gaussian model whose associated set of covariance matrices is linearly constrained according to common ancestry in a phylogenetic tree. We study the complexity of inferring the maximum likelihood (ML)…
We apply the theory of markov random fields on trees to derive a phase transition in the number of samples needed in order to reconstruct phylogenies. We consider the Cavender-Farris-Neyman model of evolution on trees, where all the inner…
Ancestral maximum likelihood (AML) is a method that simultaneously reconstructs a phylogenetic tree and ancestral sequences from extant data (sequences at the leaves). The tree and ancestral sequences maximize the probability of observing…
Consider an information source generating a symbol at the root of a tree network whose links correspond to noisy communication channels, and broadcasting it through the network. We study the problem of reconstructing the transmitted symbol…
A central task in the study of molecular sequence data from present-day species is the reconstruction of the ancestral relationships. The most established approach to tree reconstruction is the maximum likelihood (ML) method. In this…
A major task of evolutionary biology is the reconstruction of phylogenetic trees from molecular data. The evolutionary model is given by a Markov chain on a tree. Given samples from the leaves of the Markov chain, the goal is to reconstruct…
The study of Markov processes and broadcasting on trees has deep connections to a variety of areas including statistical physics, graphical models, phylogenetic reconstruction, Markov Chain Monte Carlo, and community detection in random…
Motivated by the theory of spin-glasses in physics, we study the so-called reconstruction problem for the related distributions on the tree, and on the sparse random graph $G(n,d/n)$. Both cases, reduce naturally to studying broadcasting…