相关论文: When is Nontrivial Estimation Possible for Graphon…

Small subgraph counts can be used as summary statistics for large random graphs. We use the Stein-Chen method to derive Poisson approximations for the distribution of the number of subgraphs in the stochastic block model which are…

A class of models that have been widely used are the exponential random graph (ERG) models, which form a comprehensive family of models that include independent and dyadic edge models, Markov random graphs, and many other graph…

Estimating the matrix of connections probabilities is one of the key questions when studying sparse networks. In this work, we consider networks generated under the sparse graphon model and the in-homogeneous random graph model with missing…

We propose a general framework for modelling network data that is designed to describe aspects of non-exchangeable networks. Conditional on latent (unobserved) variables, the edges of the network are generated by their finite growth history…

Detection of correlation in a pair of random graphs is a fundamental statistical and computational problem that has been extensively studied in recent years. In this work, we consider a pair of correlated (sparse) stochastic block models…

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…

We give upper and lower bounds on the information-theoretic threshold for community detection in the stochastic block model. Specifically, let $k$ be the number of groups, $d$ be the average degree, the probability of edges between vertices…

We study the space complexity of sketching cuts and Laplacian quadratic forms of graphs. We show that any data structure which approximately stores the sizes of all cuts in an undirected graph on $n$ vertices up to a $1+\epsilon$ error must…

We are interested in recovering information on a stochastic block model from the subgraph discovered by an exploring random walk. Stochastic block models correspond to populations structured into a finite number of types, where two…

Recovering the random graph model from an observed collection of networks is known to present significant challenges in the setting, where the networks do not share a common node set and have different sizes. More specifically, the goal is…

The proliferation of models for networks raises challenging problems of model selection: the data are sparse and globally dependent, and models are typically high-dimensional and have large numbers of latent variables. Together, these…

Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new…

The graphon (W-graph), including the stochastic block model as a special case, has been widely used in modeling and analyzing network data. This random graph model is well-characterized by its graphon function, and estimation of the graphon…

The paper proposes the combination of stochastic blockmodels with smooth graphon models. The first allow for partitioning the set of individuals in a network into blocks which represent groups of nodes that presumably connect stochastically…

We study the problem of sketching an input graph, so that given the sketch, one can estimate the weight of any cut in the graph within factor $1+\epsilon$. We present lower and upper bounds on the size of a randomized sketch, focusing on…

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…

We propose a new hierarchy of semidefinite programming relaxations for inference problems. As test cases, we consider the problem of community detection in block models. The vertices are partitioned into $k$ communities, and a graph is…

Gaussian graphical models are widely utilized to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To…

Variational methods are extremely popular in the analysis of network data. Statistical guarantees obtained for these methods typically provide asymptotic normality for the problem of estimation of global model parameters under the…

In this paper, we present and analyze a simple and robust spectral algorithm for the stochastic block model with $k$ blocks, for any $k$ fixed. Our algorithm works with graphs having constant edge density, under an optimal condition on the…