Related papers: Exact recovery and sharp thresholds of Stochastic …
There is a recent surge of interest in identifying the sharp recovery thresholds for cluster recovery under the stochastic block model. In this paper, we address the more refined question of how many vertices that will be misclassified on…
We introduce the Markov Stochastic Block Model (MSBM): a growth model for community based networks where node attributes are assigned through a Markovian dynamic. We rely on HMMs' literature to design prediction methods that are robust to…
The stochastic block model (SBM) is a popular framework for studying community detection in networks. This model is limited by the assumption that all nodes in the same community are statistically equivalent and have equal expected degrees.…
The group synchronization problem is to estimate unknown group elements at the vertices of a graph when given a set of possibly noisy observations of group differences at the edges. We consider the group synchronization problem on finite…
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…
Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often…
We consider the greedy algorithms for the joint recovery of high-dimensional sparse signals based on the block multiple measurement vector (BMMV) model in compressed sensing (CS). To this end, we first put forth two versions of simultaneous…
Scoring patent documents is very useful for technology management. However, conventional methods are based on static models and, thus, do not reflect the growth potential of the technology cluster of the patent. Because even if the cluster…
We study learning problems on correlated stochastic block models with two balanced communities. Our main result gives the first efficient algorithm for graph matching in this setting. In the most interesting regime where the average degree…
In Gaussian graphical model selection, noise-corrupted samples present significant challenges. It is known that even minimal amounts of noise can obscure the underlying structure, leading to fundamental identifiability issues. A recent line…
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…
Last years have seen a regain of interest for the use of stochastic block modeling (SBM) in recommender systems. These models are seen as a flexible alternative to tensor decomposition techniques that are able to handle labeled data. Recent…
We revisit the problem of efficiently learning the underlying parameters of Ising models from data. Current algorithmic approaches achieve essentially optimal sample complexity when given i.i.d. samples from the stationary measure and the…
Networks are useful representations of many systems with interacting entities, such as social, biological and physical systems. Characterizing the meso-scale organization, i.e. the community structure, is an important problem in network…
We derive rigorous bounds for well-defined community structure in complex networks for a stochastic block model (SBM) benchmark. In particular, we analyze the effect of inter-community "noise" (inter-community edges) on any "community…
Stochastic block models (SBMs) have been playing an important role in modeling clusters or community structures of network data. But, it is incapable of handling several complex features ubiquitously exhibited in real-world networks, one of…
Real-world networks often come with side information that can help to improve the performance of network analysis tasks such as clustering. Despite a large number of empirical and theoretical studies conducted on network clustering methods…
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…
We propose and analyze a generic method for community recovery in stochastic block models and degree corrected block models. This approach can exactly recover the hidden communities with high probability when the expected node degrees are…
We study the optimization landscape of a smooth nonconvex program arising from synchronization over the two-element group $\mathbf{Z}_2$, that is, recovering $z_1, \dots, z_n \in \{\pm 1\}$ from (noisy) relative measurements $R_{ij} \approx…