Related papers: Estimating the history of a random recursive tree
In this paper we consider high dimension models based on dependent observations defined through autoregressive processes. For such models we develop an adaptive efficient estimation method via the robust sequential model selection…
We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of $\mathbb{R}$. An order-$1$ autoregressive model in this context is to be understood as a Markov…
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…
We use the framework of multivariate regular variation to analyse the extremal behaviour of preferential attachment models. To this end, we follow a directed linear preferential attachment model for a random, heavy-tailed number of steps in…
We examine a discrete random recursive tree growth process that, at each time step, either adds or deletes a node from the tree with probability $p$ and $1-p$, respectively. Node addition follows the usual uniform attachment model. For node…
In this work we consider random two-colourings of random linear preferential attachment trees, which includes random recursive trees, random plane-oriented recursive trees, random binary search trees, and a class of random $d$-ary trees.…
We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…
Due to their efficiency and small size, decision trees and random forests are popular machine learning models used for classification on resource-constrained systems. In such systems, the available execution time for inference in a random…
In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of…
In this paper we develop a new machine learning estimator for ordered choice models based on the random forest. The proposed Ordered Forest flexibly estimates the conditional choice probabilities while taking the ordering information…
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
We consider the minimum spanning tree problem with predictions, using the weight-arrival model, i.e., the graph is given, together with predictions for the weights of all edges. Then the actual weights arrive one at a time and an…
We introduce a quantitative method to compare arbitrary pairs of graph centrality measures, based on the ordering of vertices induced by them. The proposed method is conceptually simple, mathematically elegant, and allows for a quantitative…
The Jordan center of a graph is defined as a vertex whose maximum distance to other nodes in the graph is minimal, and it finds applications in facility location and source detection problems. We study properties of the Jordan Center in the…
We consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the l1-constraint. It is…
Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen randomly proportionally to its weight. Under some assumptions on the sequence of…
In the problem of online unweighted interval selection, the objective is to maximize the number of non-conflicting intervals accepted by the algorithm. In the conventional online model of irrevocable decisions, there is an Omega(n) lower…
We study the growth of a time-ordered rooted tree by probabilistic attachment of new vertices to leaves. We construct a likelihood function of the leaves based on the connectivity of the tree. We take such connectivity to be induced by the…
A new approach called ABRF (the attention-based random forest) and its modifications for applying the attention mechanism to the random forest (RF) for regression and classification are proposed. The main idea behind the proposed ABRF…
The spread of infectious disease in a human community or the proliferation of fake news on social media can be modeled as a randomly growing tree-shaped graph. The history of the random growth process is often unobserved but contains…