Related papers: Rooted Trees with Probabilities Revisited

Let $T\_n$ denote the set of unrooted labeled trees of size $n$ and let $T\_n$ be a particular (finite, unlabeled) tree. Assuming that every tree of $T\_n$ is equally likely, it is shown that the limiting distribution as $n$ goes to…

Decision trees are a popular family of models due to their attractive properties such as interpretability and ability to handle heterogeneous data. Concurrently, missing data is a prevalent occurrence that hinders performance of machine…

Count data take on non-negative integer values and are challenging to properly analyze using standard linear-Gaussian methods such as linear regression and principal components analysis. Generalized linear models enable direct modeling of…

Let $t$ be a rooted tree and $n_i(t)$ the number of nodes in $t$ having $i$ children. The degree sequence $(n_i(t),i\geq 0)$ of $t$ satisfies $\sum_{i\ge 0} n_i(t)=1+\sum_{i\ge 0} in_i(t)=|t|$, where $|t|$ denotes the number of nodes in…

We consider root-finding algorithms for random rooted trees grown by uniform attachment. Given an unlabeled copy of the tree and a target accuracy $\varepsilon > 0$, such an algorithm outputs a set of nodes that contains the root with…

We prove a new formula for the generating function of multitype Cayley trees counted according to their degree distribution. Using this formula we recover and extend several enumerative results about trees. In particular, we extend some…

We explore a generating function trick which allows us to keep track of infinitely many statistics using finitely many variables, by recording their individual distributions rather than their joint distributions. Building on previous work…

We introduce a new model of random tree that grows like a random recursive tree, except at some exceptional "doubling events" when the tree is replaced by two copies of itself attached to a new root. We prove asymptotic results for the size…

In many modern applications, including analysis of gene expression and text documents, the data are noisy, high-dimensional, and unordered--with no particular meaning to the given order of the variables. Yet, successful learning is often…

This paper is concerned with the approximation of high-dimensional functions in a statistical learning setting, by empirical risk minimization over model classes of functions in tree-based tensor format. These are particular classes of…

We analyze a class of spatial random spanning trees built on a realization of a homogeneous Poisson point process of the plane. This tree has a simple radial structure with the origin as its root. We first use stochastic geometry arguments…

We provide a local probabilistic description of the limiting statistics of large preferential attachment trees in terms of the ordinary degree (number of neighbors) but augmented with information on leafdegree (number of neighbors that are…

Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attain low classification…

Understanding the structure of the Internet graph is a crucial step for building accurate network models and designing efficient algorithms for Internet applications. Yet, obtaining its graph structure is a surprisingly difficult task, as…

We consider random partitions of the vertex set of a given finite graph that can be sampled by means of loop-erased random walks stopped at a random exponential time of parameter $q>0$. The related random blocks tend to cluster nodes…

Probabilistic Time Series Forecasting (PTSF) plays a critical role in domains requiring accurate and uncertainty-aware predictions for decision-making. However, existing methods offer suboptimal distribution modeling and suffer from a…

Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…

Standard supervised learning procedures are validated against a test set that is assumed to have come from the same distribution as the training data. However, in many problems, the test data may have come from a different distribution. We…

We consider the decentralized binary hypothesis testing problem on trees of bounded degree and increasing depth. For a regular tree of depth t and branching factor k>=2, we assume that the leaves have access to independent and identically…

Regression models for supervised learning problems with a continuous target are commonly understood as models for the conditional mean of the target given predictors. This notion is simple and therefore appealing for interpretation and…