Related papers: Nested Recursions, Simultaneous Parameters and Tre…
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…
One of the fundamental principles of contemporary linguistics states that language processing requires the ability to extract recursively nested tree structures. However, it remains unclear whether and how this code could be implemented in…
In this paper we present novel algorithmic techniques with a O(H(N)+N/H(N)) time complexity for performing several types of queries and updates on general rooted trees, binary search trees and lists of size N. For rooted trees we introduce…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…
This paper presents both a proof method and a result. The proof method presented is particularly suitable for uniformly proving families of identities satisfied by a family of recursive sequences. To illustrate the method, we study the…
The Raney numbers $R_{p,r}(n)$ are a two-parameter generalization of the Catalan numbers that were introduced by Raney in his investigation of functional composition patterns \cite{Raney}. We give a new combinatorial interpretation for all…
We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…
Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…
Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…
We present a general setting for structure-sequence comparison in a large class of RNA structures that unifies and generalizes a number of recent works on specific families on structures. Our approach is based on tree decomposition of…
K-nearest neighbor (kNN) search has wide applications in many areas, including data mining, machine learning, statistics and many applied domains. Inspired by the success of ensemble methods and the flexibility of tree-based methodology, we…
This paper proposes a new algorithm for learning accurate tree-based models while ensuring the existence of recourse actions. Algorithmic Recourse (AR) aims to provide a recourse action for altering the undesired prediction result given by…
Trees are useful entities allowing to model data structures and hierarchical relationships in networked decision systems ubiquitously. An ordered tree is a rooted tree where the order of the subtrees (children) of a node is significant. In…
This paper presents a new approach for trees-based regression, such as simple regression tree, random forest and gradient boosting, in settings involving correlated data. We show the problems that arise when implementing standard…
This paper proves that two differently defined rooted binary trees are isomorphic. The first tree is one associated to a version of Farey sequences where the vertices correspond to the open intervals formed by two successive terms in the…
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…
This paper studies the problem of estimating the order of arrival of the vertices in a random recursive tree. Specifically, we study two fundamental models: the uniform attachment model and the linear preferential attachment model. We…
We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob-Martin compactification; it also gives a representation of the limit in…
A uniform recursive tree on $n$ vertices is a random tree where each possible $(n-1)!$ labeled recursive rooted tree is selected with equal probability. In this paper we introduce and study weighted trees, a non-uniform recursive tree model…