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Despite the widespread application of latent factor analysis, existing methods suffer from the following weaknesses: requiring the number of factors to be known, lack of theoretical guarantees for learning the model structure, and…
Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…
We study \emph{local computation algorithms (LCAs)} for constructing spanning trees. In this setting, the goal is to locally determine, for each edge $ e \in E $, whether it belongs to a spanning tree $ T $ of the input graph $ G $, where $…
We investigate numerically and analytically Potts models on ``thin'' random graphs -- generic Feynman diagrams, using the idea that such models may be expressed as the N --> 1 limit of a matrix model. The thin random graphs in this limit…
We study bond percolation of the Cayley tree (CT) by focusing on the probability distribution function (PDF) of a local variable, namely, the size of the cluster including a selected vertex. Because the CT does not have a dominant bulk…
Developing a robust algorithm for automatic individual tree crown (ITC) detection from laser scanning datasets is important for tracking the responses of trees to anthropogenic change. Such approaches allow the size, growth and mortality of…
We study the scaling limit of random forest with prescribed degree sequence in the regime that the largest tree consists of all but a vanishing fraction of nodes. We give a description of the limit of the forest consisting of the small…
We consider critical percolation on Galton-Watson trees and prove quenched analogues of classical theorems of critical branching processes. We show that the probability critical percolation reaches depth $n$ is asymptotic to a…
The mathematical analysis of random phylogenetic networks via analytic and algorithmic methods has received increasing attention in the past years. In the present work we introduce branching process methods to their study. This approach…
Let $T$ be a random tree taken uniformly at random from the family of labelled trees on $n$ vertices. In this note, we provide bounds for $c(n)$, the number of sub-trees of $T$ that hold asymptotically almost surely. With computer support…
We consider a continuous-time branching random walk on a multidimensional lattice with two types of particles and an infinite number of initial particles. The main results are devoted to the study of the generating function and the limiting…
We study the limiting degree distribution of the vertex splitting model introduced in \cite{DDJS:2009}. This is a model of randomly growing ordered trees, where in each time step the tree is separated into two components by splitting a…
We consider the probability that a spanning tree chosen uniformly at random from a graph can be partitioned into a fixed number $k$ of trees of equal size by removing $k-1$ edges. In that case, the spanning tree is called {\em splittable}.…
Accurately assessing a patient's risk of a given event is essential in making informed treatment decisions. One approach is to stratify patients into two or more distinct risk groups with respect to a specific outcome using both clinical…
We study a configuration model on bipartite planar maps in which, given $n$ even integers, one samples a planar map with $n$ faces uniformly at random with these face degrees. We prove that when suitably rescaled, such maps always admit…
We consider a uniform spanning tree in a $\delta$-square grid approximation of a planar domain $\Omega$. For given integer $n\ge 2$, we condition the tree on the following $n$-arm event: we pick $n$ branches, emanating from $n$ points…
We consider a variant of treewidth that we call clique-partitioned treewidth in which each bag is partitioned into cliques. This is motivated by the recent development of FPT-algorithms based on similar parameters for various problems. With…
Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…
In this work, we adapt a method based on multiple hypothesis tracking (MHT) that has been shown to give state-of-the-art vessel segmentation results in interactive settings, for the purpose of extracting trees. Regularly spaced tubular…
Replica symmetry breaking postulates that near optima of spin glass Hamiltonians have an ultrametric structure. Namely, near optima can be associated to leaves of a tree, and the Euclidean distance between them corresponds to the distance…