Related papers: Graph space: using both geometric and probabilisti…
Causal discovery aims to recover graphs that represent causal relations among given variables from observations, and new methods are constantly being proposed. Increasingly, the community raises questions about how much progress is made,…
Graph analytics can lead to better quantitative understanding and control of complex networks, but traditional methods suffer from high computational cost and excessive memory requirements associated with the high-dimensionality and…
Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…
In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have…
This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…
Graph-based tests are a class of non-parametric two-sample tests useful for analyzing high-dimensional data. The test statistics are constructed from similarity graphs (such as K-minimum spanning tree), and consequently, their performance…
Generative models for graphs have been typically committed to strong prior assumptions concerning the form of the modeled distributions. Moreover, the vast majority of currently available models are either only suitable for characterizing…
Graph similarity search is a common and fundamental operation in graph databases. One of the most popular graph similarity measures is the Graph Edit Distance (GED) mainly because of its broad applicability and high interpretability.…
Reeb graphs are structural descriptors that capture shape properties of a topological space from the perspective of a chosen function. In this work we define a combinatorial metric for Reeb graphs of orientable surfaces in terms of the cost…
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…
In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated…
Sparse exchangeable graphs on $\mathbb{R}_+$, and the associated graphex framework for sparse graphs, generalize exchangeable graphs on $\mathbb{N}$, and the associated graphon framework for dense graphs. We develop the graphex framework as…
When we represent a network of sensors in Euclidean space by a graph, there are two distances between any two nodes that we may consider. One of them is the Euclidean distance. The other is the distance between the two nodes in the graph,…
The shortest-path, commute time, and diffusion distances on undirected graphs have been widely employed in applications such as dimensionality reduction, link prediction, and trip planning. Increasingly, there is interest in using…
We consider the testing and estimation of change-points -- locations where the distribution abruptly changes -- in a data sequence. A new approach, based on scan statistics utilizing graphs representing the similarity between observations,…
A metric graph is a 1-dimensional stratified metric space consisting of vertices and edges or loops glued together. Metric graphs can be naturally used to represent and model data that take the form of noisy filamentary structures, such as…
We investigate the estimation of the perimeter of a set by a graph cut of a random geometric graph. For $\Omega \subset D = (0,1)^d$, with $d \geq 2$, we are given $n$ random i.i.d. points on $D$ whose membership in $\Omega$ is known. We…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
Statistical inference on graphs is a burgeoning field in the applied and theoretical statistics communities, as well as throughout the wider world of science, engineering, business, etc. In many applications, we are faced with the reality…
Data are often represented as graphs. Many common tasks in data science are based on distances between entities. While some data science methodologies natively take graphs as their input, there are many more that take their input in…