相关论文: Statistical inference on random dot product graphs…

A random geometric graph (RGG) with kernel $K$ is constructed by first sampling latent points $x_1,\ldots,x_n$ independently and uniformly from the $d$-dimensional unit sphere, then connecting each pair $(i,j)$ with probability $K(\langle…

Data generation is a fundamental research problem in data management due to its diverse use cases, ranging from testing database engines to data-specific applications. However, real-world entities often involve complex interactions that…

Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank…

Graph partitioning (GP), a.k.a. community detection, is a classic problem that divides nodes of a graph into densely-connected blocks. From a perspective of graph signal processing, we find that graph Laplacian with a negative correction…

We provide new connectivity results for {\em vertex-random graphs} or {\em random annulus graphs} which are significant generalizations of random geometric graphs. Random geometric graphs (RGG) are one of the most basic models of random…

We prove a central limit theorem for the components of the eigenvectors corresponding to the $d$ largest eigenvalues of the normalized Laplacian matrix of a finite dimensional random dot product graph. As a corollary, we show that for…

Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for…

Graph signal processing (GSP) is a key tool for satisfying the growing demand for information processing over networks. However, the success of GSP in downstream learning and inference tasks is heavily dependent on the prior identification…

Random geometric graphs (RGGs) offer a powerful tool for analyzing the geometric and dependence structures in real-world networks. For example, it has been observed that RGGs are a good model for protein-protein interaction networks. In…

Understanding the decisions of tree-based ensembles and their relationships is pivotal for machine learning model interpretation. Recent attempts to mitigate the human-in-the-loop interpretation challenge have explored the extraction of the…

The problem of unsupervised learning node embeddings in graphs is one of the important directions in modern network science. In this work we propose a novel framework, which is aimed to find embeddings by \textit{discriminating…

Joint network topology inference represents a canonical problem of jointly learning multiple graph Laplacian matrices from heterogeneous graph signals. In such a problem, a widely employed assumption is that of a simple common component…

Joint spectral embeddings facilitate analysis of multiple network data by simultaneously mapping vertices in each network to points in Euclidean space where statistical inference is then performed. In this work, we consider one such joint…

This contribution proposes a new approach towards developing a class of probabilistic methods for classifying attributed graphs. The key concept is random attributed graph, which is defined as an attributed graph whose nodes and edges are…

We study randomly coloured graphs embedded into Euclidean space, whose vertex sets are infinite, uniformly discrete subsets of finite local complexity. We construct the appropriate ergodic dynamical systems, explicitly characterise ergodic…

This paper studies how close random graphs are typically to their expectations. We interpret this question through the concentration of the adjacency and Laplacian matrices in the spectral norm. We study inhomogeneous Erd\"os-R\'enyi random…

Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…

Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…

Many real-world datasets have an underlying dynamic graph structure, where entities and their interactions evolve over time. Machine learning models should consider these dynamics in order to harness their full potential in downstream…

Statistical inference on graphs often proceeds via spectral methods involving low-dimensional embeddings of matrix-valued graph representations, such as the graph Laplacian or adjacency matrix. In this paper, we analyze the asymptotic…