Related papers: Optimal Recovery of Block Models with $q$ Communit…
Signed graphs encode similarity and dissimilarity relationships among different entities with positive and negative edges. In this paper, we study the problem of community recovery over signed graphs generated by the signed stochastic block…
Compressed sensing shows that a sparse signal can stably be recovered from incomplete linear measurements. But, in practical applications, some signals have additional structure, where the nonzero elements arise in some blocks. We call such…
Network topology plays a key role in many phenomena, from the spreading of diseases to that of financial crises. Whenever the whole structure of a network is unknown, one must resort to reconstruction methods that identify the least biased…
Community detection in networks is a fundamental problem in machine learning and statistical inference, with applications in social networks, biological systems, and communication networks. The stochastic block model (SBM) serves as a…
In this paper we continue to rigorously establish the predictions in ground breaking work in statistical physics by Decelle, Krzakala, Moore, Zdeborov\'a (2011) regarding the block model, in particular in the case of $q=3$ and $q=4$…
We study the Inexact Restoration framework with random models for minimizing functions whose evaluation is subject to errors. We propose a constrained formulation that includes well-known stochastic problems and an algorithm applicable when…
The community detection problem involves making inferences about node labels in a graph, based on observing the graph edges. This paper studies the effect of additional, non-graphical side information on the phase transition of exact…
We study the problem of community recovery from coarse measurements of a graph. In contrast to the problem of community recovery of a fully observed graph, one often encounters situations when measurements of a graph are made at…
Linear sketching and recovery of sparse vectors with randomly constructed sparse matrices has numerous applications in several areas, including compressive sensing, data stream computing, graph sketching, and combinatorial group testing.…
In this paper, we consider networks consisting of a finite number of non-overlapping communities. To extract these communities, the interaction between pairs of nodes may be sampled from a large available data set, which allows a given node…
In a paper that initiated the modern study of the stochastic block model, Decelle et al., backed by Mossel et al., made the following conjecture: Denote by $k$ the number of balanced communities, $a/n$ the probability of connecting inside…
We propose a Bayesian expectation-maximization (EM) algorithm for reconstructing Markov-tree sparse signals via belief propagation. The measurements follow an underdetermined linear model where the regression-coefficient vector is the sum…
We consider the problem of clustering (or reconstruction) in the stochastic block model, in the regime where the average degree is constant. For the case of two clusters with equal sizes, recent results by Mossel, Neeman and Sly, and by…
We analyze the information-theoretic limits for the recovery of node labels in several network models. This includes the Stochastic Block Model, the Exponential Random Graph Model, the Latent Space Model, the Directed Preferential…
This paper investigates graph clustering in the planted cluster model in the presence of {\em small clusters}. Traditional results dictate that for an algorithm to provably correctly recover the clusters, {\em all} clusters must be…
The stochastic block model (SBM) is an important generative model for random graphs in network science and machine learning, useful for benchmarking community detection (or clustering) algorithms. The symmetric SBM generates a graph with…
We derive sharp thresholds for exact recovery of communities in a weighted stochastic block model, where observations are collected in the form of a weighted adjacency matrix, and the weight of each edge is generated independently from a…
In this paper, we consider sparse networks consisting of a finite number of non-overlapping communities, i.e. disjoint clusters, so that there is higher density within clusters than across clusters. Both the intra- and inter-cluster edge…
The problem of community detection with two equal-sized communities is closely related to the minimum graph bisection problem over certain random graph models. In the stochastic block model distribution over networks with community…
Networks, which represent agents and interactions between them, arise in myriad applications throughout the sciences, engineering, and even the humanities. To understand large-scale structure in a network, a common task is to cluster a…