Related papers: Memory effect in growing trees

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…

We show that to explain the growth of the citation network by preferential attachment (PA), one has to accept that individual nodes exhibit heterogeneous fitness values that decay with time. While previous PA-based models assumed either…

This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…

Counting the number of spanning trees in specific classes of graphs has attracted increasing attention in recent years. In this note, we present unified proofs and generalizations of several results obtained in the 2020s. The main method is…

Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…

This paper, dating from May 1991, contains preliminary (and unpublishable) notes on investigations about iteration trees. They will be of interest only to the specialist. In the first two sections I define notions of support and embeddings…

The chain-structured long short-term memory (LSTM) has showed to be effective in a wide range of problems such as speech recognition and machine translation. In this paper, we propose to extend it to tree structures, in which a memory cell…

Consider a tree network T, where each edge acts as an independent copy of a given channel M, and information is propagated from the root. For which T and M does the configuration obtained at level n of T typically contain significant…

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…

Although regression trees were originally designed for large datasets, they can profitably be used on small datasets as well, including those from replicated or unreplicated complete factorial experiments. We show that in the latter…

We study a new class of preferential attachment trees with \emph{self-reinforcement}. At each time, each vertex is assigned a weight equal to the cumulative sum over past times of an affine function of its degree. A new vertex attaches…

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…

Topology of exponential and scale-free trees and simple graphs is investigated numerically. The numbers of the nearest neighbors, the next-nearest neighbors, the next-next-nearest neighbors, the 4-th and the 5-th neighbors are calculated.…

Certain classes of problems, including perceptual data understanding, robotics, discovery, and learning, can be represented as incremental, dynamically constructed belief networks. These automatically constructed networks can be dynamically…

Neural networks with tree-based sentence encoders have shown better results on many downstream tasks. Most of existing tree-based encoders adopt syntactic parsing trees as the explicit structure prior. To study the effectiveness of…

Real growing networks like the WWW or personal connection based networks are characterized by a high degree of clustering, in addition to the small-world property and the absence of a characteristic scale. Appropriate modifications of the…

Tree-based data structures are ubiquitous across applications. Therefore, a multitude of different tree implementations exist. However, while these implementations are diverse, they share a tree structure as the underlying data structure.…

Why do we forget? Why do we remember things that never happened? The conventional answer points to biological hardware. We propose a different one: geometry. Here we show that high-dimensional embedding spaces, subjected to noise,…

In this paper, we consider the problem of reconstructing trees from traces in the tree edit distance model. Previous work by Davies et al. (2019) analyzed special cases of reconstructing labeled trees. In this work, we significantly expand…

There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied.…