Related papers: Random recursive trees: A boundary theory approach

The problems of model and variable selections for classification trees are jointly considered. A penalized criterion is proposed which explicitly takes into account the number of variables, and a risk bound inequality is provided for the…

Regression trees are a popular machine learning algorithm that fit piecewise constant models by recursively partitioning the predictor space. This paper focuses on statistical inference for a data-dependent model obtained from a fitted…

We consider the continuous-time version of the random digital search tree, and construct a coupling with a border aggregation model as studied in Thacker and Volkov (2018), showing a relation between the height of the tree and the time…

We consider the genealogy tree for a critical branching process conditioned on non-extinction. We enumerate vertices in each generation of the tree so that for each two generations one can define a monotone map describing the…

We consider the tributary structure of Howard's drainage model studied by Gangopadhyay et. al. Conditional on the event that the tributary survives up to time $n$, we show that, as a sequence of random metric spaces, scaled tributary…

Theoretical background and an implementation of the (p)-group generation algorithm by Newman and O'Brien are used to provide computational evidence of a new type of periodically repeating patterns in pruned descendant trees of finite…

The Doob transform technique enables the study of a killed random walk (KRW) via a random walk (RW) with transition probabilities tilted by a discrete massive harmonic function. The main contribution of this paper is to transfer this…

The Aldous--Broder algorithm provides a way of sampling a uniformly random spanning tree for finite connected graphs using simple random walk. Namely, start a simple random walk on a connected graph and stop at the cover time. The tree…

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…

This paper studies the convex isotonic regression with generalized order restrictions induced by a directed tree. The proposed model covers various intriguing optimization problems with shape or order restrictions, including the generalized…

We consider a continuous-time random walk on a regular tree of finite depth and study its favorite points among the leaf vertices. For the walk started from a leaf vertex and stopped upon hitting the root we prove that, in the limit as as…

The random split tree introduced by Devroye (1999) is considered. We derive a second order expansion for the mean of its internal path length and furthermore obtain a limit law by the contraction method. As an assumption we need the…

We study questions inspired by Erd\H os' celebrated distance problems with dot products in lieu of distances, and for more than a single pair of points. In particular, we study point configurations present in large finite point sets in the…

The motivation for this paper is the study of the phase transition for recurrence/transience of a class of self-interacting random walks on trees, which includes the once-reinforced random walk. For this purpose, we define a quantity, that…

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…

There is an unproven duality theory hypothesizing that random discrete trees and their poissonized embeddings in continuous time share fundamental properties. We give additional evidence in favor of this theory by showing that several…

A complete representation of the Martin boundary of killed random walks on the quadrant ${\mathbb{N}}^*\times{\mathbb{N}}^*$ is obtained. It is proved that the corresponding full Martin compactification of the quadrant…

Machine learning on trees has been mostly focused on trees as input to algorithms. Much less research has investigated trees as output, which has many applications, such as molecule optimization for drug discovery, or hint generation for…

Termination property of functions is an important issue in computability theory. In this paper, we show that repeated iterations of a function can induce an order amongst the elements of its domain set. Hasse diagram of the poset, thus…

We consider the problem of embedding the Steiner points of a Steiner tree with given topology into the rectilinear plane. Thereby, the length of the path between a distinguished terminal and each other terminal must not exceed given length…