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

Inhomogeneous random graph models encompass many network models such as stochastic block models and latent position models. We consider the problem of statistical estimation of the matrix of connection probabilities based on the…

Network analysis is becoming one of the most active research areas in statistics. Significant advances have been made recently on developing theories, methodologies and algorithms for analyzing networks. However, there has been little…

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…

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 studies the problem of estimating the grahpon model - the underlying generating mechanism of a network. Graphon estimation arises in many applications such as predicting missing links in networks and learning user preferences in…

Graphon estimation has been one of the most fundamental problems in network analysis and has received considerable attention in the past decade. From the statistical perspective, the minimax error rate of graphon estimation has been…

We explicitly quantify the empirically observed phenomenon that estimation under a stochastic block model (SBM) is hard if the model contains classes that are similar. More precisely, we consider estimation of certain functionals of random…

In the present paper we consider a dynamic stochastic network model. The objective is estimation of the tensor of connection probabilities $\Lambda$ when it is generated by a Dynamic Stochastic Block Model (DSBM) or a dynamic graphon. In…

Local dependence random graph models are a class of block models for network data which allow for dependence among edges under a local dependence assumption defined around the block structure of the network. Since being introduced by…

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…

The Stochastic Block Model (Holland et al., 1983) is a mixture model for heterogeneous network data. Unlike the usual statistical framework, new nodes give additional information about the previous ones in this model. Thereby the…

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 study the optimal estimation of probability matrices of random graph models generated from graphons. This problem has been extensively studied in the case of step-graphons and H\"older smooth graphons. In this work, we characterize the…

We design algorithms for fitting a high-dimensional statistical model to a large, sparse network without revealing sensitive information of individual members. Given a sparse input graph $G$, our algorithms output a…

Performance bounds are given for exploratory co-clustering/ blockmodeling of bipartite graph data, where we assume the rows and columns of the data matrix are samples from an arbitrary population. This is equivalent to assuming that the…

The stochastic block model is a canonical random graph model for clustering and community detection on network-structured data. Decades of extensive study on the problem have established many profound results, among which the phase…

Graph clustering is a fundamental task in unsupervised learning with broad real-world applications. While spectral clustering methods for undirected graphs are well-established and guided by a minimum cut optimization consensus, their…

Networks serve as a tool used to examine the large-scale connectivity patterns in complex systems. Modelling their generative mechanism nonparametrically is often based on step-functions, such as the stochastic block models. These models…

This paper is concerned with nonparametric estimation of the weighted stochastic block model. We first show that the model implies a set of multilinear restrictions on the joint distribution of edge weights of certain subgraphs involving…

Consider the twin problems of estimating the connection probability matrix of an inhomogeneous random graph and the graphon of a W-random graph. We establish the minimax estimation rates with respect to the cut metric for classes of block…