Related papers: Pruning of CRT-sub-trees
The mating of trees approach to Schramm-Loewner evolution (SLE) in the random geometry of Liouville quantum gravity (LQG) has been recently developed by Duplantier-Miller-Sheffield (2014). In this paper we consider the mating of trees…
Decision trees with binary splits are popularly constructed using Classification and Regression Trees (CART) methodology. For binary classification and regression models, this approach recursively divides the data into two near-homogenous…
We use the Mass Transport Principle to analyze the local recursion governing the resolvent $(A-z)^{-1}$ of the adjacency operator of unimodular random trees. In the limit where the complex parameter $z$ approaches a given location $\lambda$…
We study high-dimensional Ornstein--Uhlenbeck processes driven by L\'evy noise and consider drift matrices that decompose into a low-rank plus sparse component, capturing a few latent factors together with a sparse network of direct…
We consider a conditioned Galton-Watson tree and prove an estimate of the number of pairs of vertices with a given distance, or, equivalently, the number of paths of a given length. We give two proofs of this result, one probabilistic and…
We provide simplified proofs for the asymptotic distribution of the number of cuts required to cut down a Galton-Watson tree with critical, finite-variance offspring distribution, conditioned to have total progeny $n$. Our proof is based on…
We propose a method for cutting down a random recursive tree that focuses on its higher degree vertices. Enumerate the vertices of a random recursive tree of size $n$ according to a decreasing order of their degrees; namely, let…
In this paper we are concerned with contact processes with random edge weights on rooted regular trees. We assign i.i.d weights on each edge on the tree and assume that an infected vertex infects its healthy neighbor at rate proportional to…
This work builds upon the recent monograph [5] on self-similar Markov trees. A self-similar Markov tree is a random real tree equipped with a function from the tree to $[0,\infty)$ that we call the decoration. Here, we construct local time…
The basis of this paper is the elementary observation that the $n$-step descendant distribution of any Galton-Watson process satisfies a discrete Smoluchowski coagulation equation with multiple coalescence. Using this we obtain necessary…
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…
The metric dimension of a graph $G$ is the minimal size of a subset $R$ of vertices of $G$ that, upon reporting their graph distance from a distingished (source) vertex $v^\star$, enable unique identification of the source vertex $v^\star$…
This paper considers magnitude, asymptotics and duration of drawdowns for some L\'{e}vy processes. First, we revisit some existing results on the magnitude of drawdowns for spectrally negative L\'{e}vy processes using an approximation…
We present an implementation and an experimental evaluation of an algorithm that, given a connected graph G (represented by adjacency lists), estimates in sublinear time, with a relative error, the Minimum Spanning Tree Weight of G; the…
We code Galton-Walton trees by a continuous height process, in order to give a precise meaning to the convergence of forests of trees. This allows us to establish the convergence of the forest of genealogical trees of the branching process…
Top-down induction of decision trees has been observed to suffer from the inadequate functioning of the pruning phase. In particular, it is known that the size of the resulting tree grows linearly with the sample size, even though the…
The weighted tree augmentation problem (WTAP) is a fundamental network design problem. We are given an undirected tree $G = (V,E)$, an additional set of edges $L$ called links and a cost vector $c \in \mathbb{R}^L_{\geq 1}$. The goal is to…
We study composition-valued continuous-time Markov chains that appear naturally in the framework of Chinese Restaurant Processes (CRPs). As time evolves, new customers arrive (up-step) and existing customers leave (down-step) at suitable…
As the size of transformer-based models continues to grow, fine-tuning these large-scale pretrained vision models for new tasks has become increasingly parameter-intensive. Parameter-efficient learning has been developed to reduce the…
In the first part of this paper we give easy and intuitive proofs for the small value probabilities of the martingale limit of a supercritical Galton-Watson process in both the Schr\"oder and the B\"ottcher case. These results are…