Related papers: Pruning, cut trees, and the reconstruction problem
In a deterministic or random tree, a notion of ancestral diversity can be defined as follows. Sample independently $n$ groups of $k$ leaves and count the number $N_n(k)$ of distinct most recent common ancestors of each of the groups. As $n$…
Given a general critical or sub-critical branching mechanism and its associated L\'evy continuum random tree, we consider a pruning procedure on this tree using a Poisson snake. It defines a fragmentation process on the tree. We compute the…
We introduce and study a model of plane random trees generalizing the famous Bienaym\'e--Galton--Watson model but where births and deaths are locally correlated. More precisely, given a random variable $(B,H)$ with values in $\{1,2,3,…
In [Aldous,Pitman,1998] a tree-valued Markov chain is derived by pruning off more and more subtrees along the edges of a Galton-Watson tree. More recently, in [Abraham,Delmas,2012], a continuous analogue of the tree-valued pruning dynamics…
Recently, much attention has been given to understanding recombination events along a chromosome in a variety of field. For instance, many population genetics problems are limited by the inaccuracy of inferred evolutionary histories of…
We examine how recently documented, fundamental phenomena in deep learning models subject to pruning are affected by changes in the pruning procedure. Specifically, we analyze differences in the connectivity structure and learning dynamics…
Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population \cite{nature_01}. This result brings our attention again to a math problem related to inbreeding family trees…
We tackle the challenging problem of creating full and accurate three dimensional reconstructions of botanical trees with the topological and geometric accuracy required for subsequent physical simulation, e.g. in response to wind forces.…
Inference problems in graphical models are often approximated by casting them as constrained optimization problems. Message passing algorithms, such as belief propagation, have previously been suggested as methods for solving these…
Due to their long-standing reputation as excellent off-the-shelf predictors, random forests continue remain a go-to model of choice for applied statisticians and data scientists. Despite their widespread use, however, until recently, little…
Background. The supertree problem, i.e., the task of finding a common refinement of a set of rooted trees is an important topic in mathematical phylogenetics. The special case of a common leaf set $L$ is known to be solvable in linear time.…
We propose a principled method for autoencoding with random forests. Our strategy builds on foundational results from nonparametric statistics and spectral graph theory to learn a low-dimensional embedding of the model that optimally…
Recent advances in the sparse neural network literature have made it possible to prune many large feed forward and convolutional networks with only a small quantity of data. Yet, these same techniques often falter when applied to the…
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
We prove that a uniform, rooted unordered binary tree with $n$ vertices has the Brownian continuum random tree as its scaling limit for the Gromov-Hausdorff topology. The limit is thus, up to a constant factor, the same as that of uniform…
We consider a discrete-time Markov chain, called fragmentation process, that describes a specific way of successively removing objects from a linear arrangement. The process arises in population genetics and describes the ancestry of the…
We study the graph structure of large random dissections of polygons sampled according to Boltzmann weights, which encompasses the case of uniform dissections or uniform $p$-angulations. As their number of vertices $n$ goes to infinity, we…
We perform a pruning procedure on a L\'evy tree and instead of throwing away the removed sub-tree, we regraft it on a given branch (not related to the L\'evy tree). We prove that the tree constructed by regrafting is distributed as the…
Combinatorial trees can be used to represent genealogies of asexual individuals. These individuals can be endowed with birth and death times, to obtain a so-called `chronological tree'. In this work, we are interested in the continuum…
We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob-Martin compactification; it also gives a representation of the limit in…