Related papers: Random Gaussian sums on trees

We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…

Let $X_i = {X_i(t), t \in T}$ be i.i.d. copies of a centered Gaussian process $X = {X(t), t \in T}$ with values in $\mathbb{R}^d$ defined on a separable metric space $T.$ It is supposed that $X$ is bounded. We consider the asymptotic…

We prove asymptotic normality for the number of fringe subtrees isomorphic to any given tree in uniformly random trees with given vertex degrees. As applications, we also prove corresponding results for random labelled trees with given…

For a complex number $\alpha$, we consider the sum of the $\alpha$th powers of subtree sizes in Galton--Watson trees conditioned to be of size $n$. Limiting distributions of this functional $X_n(\alpha)$ have been determined for $\Re\alpha…

We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…

We study the local limit of the fixed-point forest, a tree structure associated to a simple sorting algorithm on permutations. This local limit can be viewed as an infinite random tree that can be constructed from a Poisson point process…

We first consider the growth of trees by probabilistic attachment of new vertices to leaves. This leads to a growth model based on vertex clusters and probabilities assigned to clusters. This model turns out to be readily applicable to…

We propose a novel architecture for Graph Neural Networks that is inspired by the idea behind Tree Kernels of measuring similarity between trees by taking into account their common substructures, named fragments. By imposing a series of…

We consider the complex branching random walk on a dyadic tree with Gaussian weights on the boundary between the diffuse phase and the glassy phase. We study the branching random walk in the space of continuous functions and establish…

We demonstrate a method for proving precise concentration inequalities in uniformly random trees on $n$ vertices, where $n\geq1$ is a fixed positive integer. The method uses a bijection between mappings…

For each $n \ge 1$, let $\mathrm{d}^n=(d^{n}(i),1 \le i \le n)$ be a sequence of positive integers with even sum $\sum_{i=1}^n d^n(i) \ge 2n$. Let $(G_n,T_n,\Gamma_n)$ be uniformly distributed over the set of simple graphs $G_n$ with degree…

Tackling simulation optimization problems with non-convex objective functions remains a fundamental challenge in operations research. In this paper, we propose a class of random search algorithms, called Regular Tree Search, which…

A metric tree ($M$, $d$), also known as $\mathbb{R}$-trees or $T$-theory, is a metric space such that between any two points there is an unique arc and that arc is isometric to an interval in $\mathbb{R}$. In this paper after presenting…

Consider a uniformly sampled random $d$-regular graph on $n$ vertices. If $d$ is fixed and $n$ goes to $\infty$ then we can relate typical (large probability) properties of such random graph to a family of invariant random processes (called…

We consider growing random recursive trees in random environment, in which at each step a new vertex is attached (by an edge of a random length) to an existing tree vertex according to a probability distribution that assigns the tree…

This article describes a robust algorithm to estimate a conditional probability density f(t|x) as a non-parametric smooth regression function. It is based on a neural network and the Bayesian interpretation of the network output as a…

The generalised random graph contains $n$ vertices with positive i.i.d. weights. The probability of adding an edge between two vertices is increasing in their weights. We require the weight distribution to have finite second moments and…

For a given centered Gaussian process with stationary increments $\{X(t), t\geq 0\}$ and $c>0$, let $$ W_\gamma(t)=X(t)-ct-\gamma\inf_{0\leq s\leq t}\left(X(s)-cs\right), \quad t\geq 0$$ denote the $\gamma$-reflected process, where…

On a finite graph, there is a natural family of Boltzmann probability measures on cycle-rooted spanning forests, parametrized by weights on cycles. For a certain subclass of those weights, we construct Gibbs measures in infinite volume, as…

Let $X$ be a random variable with unknown mean and finite variance. We present a new estimator of the mean of $X$ that is robust with respect to the possible presence of outliers in the sample, provides tight sub-Gaussian deviation…