Related papers: Low-Complexity and Consistent Graphon Estimation f…
We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…
We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…
Graphons offer a powerful framework for modeling large-scale networks, yet estimation remains challenging. We propose a novel approach that leverages a low-rank additive representation, yielding both a low-rank connection probability matrix…
Estimating the probabilities of linkages in a network has gained increasing interest in recent years. One popular model for network analysis is the exchangeable graph model (ExGM) characterized by a two-dimensional function known as a…
Quantifying the complexity of large graphs requires measures that extend beyond predefined structural features and scale efficiently with graph size. This work adopts a generative perspective, modeling large networks as exchangeable graphs…
Exchangeable graph models (ExGM) subsume a number of popular network models. The mathematical object that characterizes an ExGM is termed a graphon. Finding scalable estimators of graphons, provably consistent, remains an open issue. In…
We study nonparametric methods for the setting where multiple distinct networks are observed on the same set of nodes. Such samples may arise in the form of replicated networks drawn from a common distribution, or in the form of…
Graphons, as limit objects of dense graph sequences, play a central role in the statistical analysis of network data. However, existing graphon estimation methods often struggle with scalability to large networks and resolution-independent…
We study graphons as a non-parametric generalization of stochastic block models, and show how to obtain compactly represented estimators for sparse networks in this framework. Our algorithms and analysis go beyond previous work in several…
We propose a class of methods for graphon estimation based on exploiting connections with nonparametric regression. The idea is to construct an ordering of the nodes in the network, similar in spirit to Chan and Airoldi (2014). However,…
Network complexity has been studied for over half a century and has found a wide range of applications. Many methods have been developed to characterize and estimate the complexity of networks. However, there has been little research with…
In this work, we propose to train a graph neural network via resampling from a graphon estimate obtained from the underlying network data. More specifically, the graphon or the link probability matrix of the underlying network is first…
A graphon is a limiting object used to describe the behaviour of large networks through a function that captures the probability of edge formation between nodes. Although the merits of graphons to describe large and unlabelled networks are…
Non-parametric approaches for analyzing network data based on exchangeable graph models (ExGM) have recently gained interest. The key object that defines an ExGM is often referred to as a graphon. This non-parametric perspective on network…
This paper focuses on the comparison of networks on the basis of statistical inference. For that purpose, we rely on smooth graphon models as a nonparametric modeling strategy that is able to capture complex structural patterns. The graphon…
We study low-rank estimation of an unknown sparse graphon from sampled network data under operator-norm loss, motivated by targeted interventions in graphon games. Starting from the observed adjacency matrix, we construct low-rank…
We propose a nonparametric framework for the analysis of networks, based on a natural limit object termed a graphon. We prove consistency of graphon estimation under general conditions, giving rates which include the important practical…
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…
Exchangeable random graphs, which include some of the most widely studied network models, have emerged as the mainstay of statistical network analysis in recent years. Graphons, which are the central objects in graph limit theory, provide a…
Many real world network problems often concern multivariate nodal attributes such as image, textual, and multi-view feature vectors on nodes, rather than simple univariate nodal attributes. The existing graph estimation methods built on…