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

The Random Dot Product Graph (RDPG) is a generative model for relational data, where nodes are represented via latent vectors in low-dimensional Euclidean space. RDPGs crucially postulate that edge formation probabilities are given by the…

A random dot product graph (RDPG) is a generative model for networks in which vertices correspond to positions in a latent Euclidean space and edge probabilities are determined by the dot products of the latent positions. We consider RDPGs…

Modeling of intricate relational patterns has become a cornerstone of contemporary statistical research and related data science fields. Networks, represented as graphs, offer a natural framework for this analysis. This paper extends the…

Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph. This paper proposes a generalisation of the latent position network model known as the random dot product graph, to allow…

A latent space model for a family of random graphs assigns real-valued vectors to nodes of the graph such that edge probabilities are determined by latent positions. Latent space models provide a natural statistical framework for graph…

We define a latent structure model (LSM) random graph as a random dot product graph (RDPG) in which the latent position distribution incorporates both probabilistic and geometric constraints, delineated by a family of underlying…

Can we learn the differential equations governing the evolution of a temporal network? We investigate this within Random Dot Product Graphs (RDPGs), where each network snapshot is generated from latent positions evolving under unknown…

We present a comprehensive extension of the latent position network model known as the random dot product graph to accommodate multiple graphs -- both undirected and directed -- which share a common subset of nodes, and propose a method for…

Latent-position random graph models usually treat the node set as fixed once the sample size is chosen, while graphon-based and random-measure constructions allow more randomness at the cost of weaker geometric interpretability. We…

Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…

Given a sequence of random (directed and weighted) graphs, we address the problem of online monitoring and detection of changes in the underlying data distribution. Our idea is to endow sequential change-point detection (CPD) techniques…

In this work we perform a detailed statistical analysis of topological and spectral properties of random geometric graphs (RGGs); a graph model used to study the structure and dynamics of complex systems embedded in a two dimensional space.…

Graph Neural Networks usually rely on the assumption that the graph topology is available to the network as well as optimal for the downstream task. Latent graph inference allows models to dynamically learn the intrinsic graph structure of…

Probabilistic dependency graphs (PDGs) are a flexible class of probabilistic graphical models, subsuming Bayesian Networks and Factor Graphs. They can also capture inconsistent beliefs, and provide a way of measuring the degree of this…

We study the multilayer random dot product graph (MRDPG) model, an extension of the random dot product graph to multilayer networks. To estimate the edge probabilities, we deploy a tensor-based methodology and demonstrate its superiority…

We connect two random graph models, the Popularity Adjusted Block Model (PABM) and the Generalized Random Dot Product Graph (GRDPG), by demonstrating that the PABM is a special case of the GRDPG in which communities correspond to mutually…

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…

Many real-world networks evolve dynamically over time and present different types of connections between nodes, often called layers. In this work, we propose a latent position model for these objects, called the dynamic multiplex random dot…

The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…

Latent space models play an important role in the modeling and analysis of network data. Under these models, each node has an associated latent point in some (typically low-dimensional) geometric space, and network formation is driven by…