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Generative models for networks with communities have been studied extensively for being a fertile ground to establish information-theoretic and computational thresholds. In this paper we propose a new toy model for planted generative models…
We analyze the bootstrap percolation process on the stochastic block model (SBM), a natural extension of the Erd\H{o}s--R\'{e}nyi random graph that incorporates the community structure observed in many real systems. In the SBM, nodes are…
In the model-based clustering of networks, blockmodelling may be used to identify roles in the network. We identify a special case of the Stochastic Block Model (SBM) where we constrain the cluster-cluster interactions such that the density…
In community detection on graphs, the semi-supervised learning problem entails inferring the ground-truth membership of each node in a graph, given the connectivity structure and a limited number of revealed node labels. Different subsets…
In the community detection problem, one may have access to additional observations (side information) about the label of each node. This paper studies the effect of the quality and quantity of side information on the phase transition of…
We consider the sparse stochastic block model in the case where the degrees are uninformative. The case where the two communities have approximately the same size has been extensively studied and we concentrate here on the community…
Resolving a conjecture of Abbe, Bandeira and Hall, the authors have recently shown that the semidefinite programming (SDP) relaxation of the maximum likelihood estimator achieves the sharp threshold for exactly recovering the community…
Networks with node covariates offer two advantages to community detection methods, namely, (i) exploit covariates to improve the quality of communities, and more importantly, (ii) explain the discovered communities by identifying the…
We study the problem of $\textit{robust community recovery}$: efficiently recovering communities in sparse stochastic block models in the presence of adversarial corruptions. In the absence of adversarial corruptions, there are efficient…
We study graph matching between two correlated networks in the almost fully seeded regime, where all but a vanishing fraction of vertex correspondences are revealed. Concretely, we consider the correlated stochastic block model and assume…
We study the inference of communities in stochastic block models with a growing number of communities. For block models with $n$ vertices and a fixed number of communities $q$, it was predicted in Decelle et al. (2011) that there are…
We study the problem of community detection in hypergraphs under a stochastic block model. Similarly to how the stochastic block model in graphs suggests studying spiked random matrices, our model motivates investigating statistical and…
We consider spectral clustering algorithms for community detection under a general bipartite stochastic block model (SBM). A modern spectral clustering algorithm consists of three steps: (1) regularization of an appropriate adjacency or…
Variational approximation has been widely used in large-scale Bayesian inference recently, the simplest kind of which involves imposing a mean field assumption to approximate complicated latent structures. Despite the computational…
In this paper, we investigate the problem of recovering hidden communities in the Labeled Stochastic Block Model (LSBM) with a finite number of clusters whose sizes grow linearly with the total number of nodes. We derive the necessary and…
We propose and analyze the problems of \textit{community goodness-of-fit and two-sample testing} for stochastic block models (SBM), where changes arise due to modification in community memberships of nodes. Motivated by practical…
We analyze the bootstrap percolation process on the stochastic block model (SBM), a natural extension of the Erd\"{o}s--R\'{e}nyi random graph that allows representing the "community structure" observed in many real systems. In the SBM,…
There has been a recent interest in understanding the power of local algorithms for optimization and inference problems on sparse graphs. Gamarnik and Sudan (2014) showed that local algorithms are weaker than global algorithms for finding…
Community detection is a fundamental problem in network analysis, with applications in many diverse areas. The stochastic block model is a common tool for model-based community detection, and asymptotic tools for checking consistency of…
Statistical node clustering in discrete time dynamic networks is an emerging field that raises many challenges. Here, we explore statistical properties and frequentist inference in a model that combines a stochastic block model (SBM) for…