Related papers: Necessary and sufficient conditions for consistent…
Predicting the ancestral sequences of a group of homologous sequences related by a phylogenetic tree has been the subject of many studies, and numerous methods have been proposed to this purpose. Theoretical results are available that show…
The structure of an evolving network contains information about its past. Extracting this information efficiently, however, is, in general, a difficult challenge. We formulate a fast and efficient method to estimate the most likely history…
This paper derives a unifying theorem establishing consistency results for a broad class of tree-based algorithms. It improves current results in two aspects. First of all, it can be applied to algorithms that vary from traditional Random…
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…
We consider a branching random walk with binary state space and index set $T^k$, the infinite rooted tree in which each node has k children (also known as the model of "broadcasting on a tree"). The root of the tree takes a random value 0…
In molecular systematics, evolutionary trees are reconstructed from sequences at the tips under simple models of site substitution. A central question is how much sequence data is required to reconstruct a tree accurately? The answer…
In this note we provide the necessary and sufficient conditions to uniquely reconstruct an oncogenetic tree.
Self-similar Markov trees constitute a remarkable family of random compact real trees carrying a decoration function that is positive on the skeleton. As the terminology suggests, they are self-similar objects that further satisfy a Markov…
We study (plane) tree-valued Markov chains $(T_n,n \geq 1)$ with uniform backward dynamics and show that they can be obtained by sampling from a real tree. As non--plane trees, every such Markov chain is represented by a weighted real tree.…
We study the problem of learning tree-structured Markov random fields (MRF) on discrete random variables with common support when the observations are corrupted by a $k$-ary symmetric noise channel with unknown probability of error. For…
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models,…
We present a computational model to reconstruct trees of ancestors for animals with sexual reproduction. Through a recursive algorithm combined with a random number generator, it is possible to reproduce the number of ancestors for each…
We consider phylogeny estimation under a two-state model of sequence evolution by site substitution on a tree. In the asymptotic regime where the sequence lengths tend to infinity, we show that for any fixed $k$ no statistically consistent…
We revisit the classical problem of approximating a stochastic differential equation by a discrete-time and discrete-space Markov chain. Our construction iterates Caratheodory's theorem over time to match the moments of the increments…
We destroy a finite tree of size $n$ by cutting its edges one after the other and in uniform random order. Informally, the associated cut-tree describes the genealogy of the connected components created by this destruction process. We…
We consider a family of random trees satisfying a Markov branching property. Roughly, this property says that the subtrees above some given height are independent with a law that depends only on their total size, the latter being either the…
Recurrence formulas are presented for studying the accuracy of the Fitch method for reconstructing the ancestral states in a given phylogenetic tree. As their applications, we analyze the convergence of the accuracy of reconstructing the…
We consider discrete-space continuous-time Markov models of reaction networks and provide sufficient conditions for the following stability condition to hold: each state in a closed, irreducible component of the state space is positive…
Phylogenetic trees constitute an interesting class of objects for stochastic processes due to the non-standard nature of the space they inhabit. In particular, many statistical applications require the construction of Markov processes on…
We study various types of consistency of honest decision trees and random forests in the regression setting. In contrast to related literature, our proofs are elementary and follow the classical arguments used for smoothing methods. Under…