Related papers: Hoppe trees, random recursive sets and their baryc…
We present new insights into causal inference in the context of Heterogeneous Treatment Effects by proposing natural variants of Random Forests to estimate the key conditional distributions. To achieve this, we recast Breiman's original…
We consider various classes of Motzkin trees as well as lambda-terms for which we derive asymptotic enumeration results. These classes are defined through various restrictions concerning the unary nodes or abstractions, respectively: We…
We study the problem of model aggregation within the Wasserstein space for probability measures on the real line. Given a fixed finite collection of candidate probability models, we consider the associated class of Wasserstein barycenters…
Accessibility percolation is a new type of percolation problem inspired by evolutionary biology. To each vertex of a graph a random number is assigned and a path through the graph is called accessible if all numbers along the path are in…
A new synthesis scheme is proposed to effectively generate a random vector with prescribed joint density that induces a (latent) Gaussian tree structure. The quality of synthesis is measured by total variation distance between the…
Random forests are popular methods for regression and classification analysis, and many different variants have been proposed in recent years. One interesting example is the Mondrian random forest, in which the underlying constituent trees…
Consider an information source generating a symbol at the root of a tree network whose links correspond to noisy communication channels, and broadcasting it through the network. We study the problem of reconstructing the transmitted symbol…
We study the number of random records in an arbitrary split tree (or equivalently, the number of random cuttings required to eliminate the tree). We show that a classical limit theorem for convergence of sums of triangular arrays to…
Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…
Inside the discipline of graph theory exists an extension known as the hypergraph. This generalization of graphs includes vertices along with hyperedges consisting of collections of two or more vertices. One well-studied application of this…
In a multivariate nonparametric regression setting we construct explicit asymptotic uniform confidence bands for centered purely random forests. Since the most popular example in this class of random forests, namely the uniformly centered…
An elliptic random matrix $X$ is a square matrix whose $(i,j)$-entry $X_{ij}$ is independent of the rest of the entries except possibly $X_{ji}$. Elliptic random matrices generalize Wigner matrices and non-Hermitian random matrices with…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
The random Fibonacci chain is a generalisation of the classical Fibonacci substitution and is defined as the rule mapping $0\mapsto 1$ and $1 \mapsto 01$ with probability $p$ and $1 \mapsto 10$ with probability $1-p$ for $0<p<1$ and where…
Peca suggested in a recent paper on the arxiv to consider binary butterfly trees and their Horton-Strahler numbers. The trees are obtained by glueing two binary trees together in a special way; the results are again binary trees but with a…
We present a new approach to the following meta-problem: given a quantitative property of trees, design a type system such that the desired property for the tree generated by an infinitary ground lambda-term corresponds to some property of…
We introduce an extension of the P\'olya tree approach for constructing distributions on the space of probability measures. By using optional stopping and optional choice of splitting variables, the construction gives rise to random…
The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…
This article is motivated by the following satisfiability question: pick uniformly at random an and/or Boolean expression of length n, built on a set of k_n Boolean variables. What is the probability that this expression is satisfiable?…
In this paper we show that all infinite trees which have bounded coordination and whose surface is negligible with respect to the volume in the limit of large distances (so that they can be embedded in a finite-dimensional euclidean space)…