Related papers: Uncertainty quantification and testing in a stocha…
In a sparse stochastic block model with two communities of unequal sizes we derive two posterior concentration inequalities, that imply (1) posterior (almost-)exact recovery of the community structure under sparsity bounds comparable to…
We study the frequentist properties of Bayesian statistical inference for the stochastic block model, with an unknown number of classes of varying sizes. We equip the space of vertex labellings with a prior on the number of classes and,…
Posterior distributions for community structure in sparse planted bi-section models are shown to achieve exact (resp. almost-exact) recovery, with sharp bounds for the sparsity regimes where edge probabilities decrease as $O(\log(n)/n)$…
We introduce a Bayesian estimator of the underlying class structure in the stochastic block model, when the number of classes is known. The estimator is the posterior mode corresponding to a Dirichlet prior on the class proportions, a…
Random graph models with community structure have been studied extensively in the literature. For both the problems of detecting and recovering community structure, an interesting landscape of statistical and computational phase transitions…
Suppose two networks are observed for the same set of nodes, where each network is assumed to be generated from a weighted stochastic block model. This paper considers the problem of testing whether the community memberships of the two…
We study the hierarchy of communities in real-world networks under a generic stochastic block model, in which the connection probabilities are structured in a binary tree. Under such model, a standard recursive bi-partitioning algorithm is…
With the advent of structured data in the form of social networks, genetic circuits and protein interaction networks, statistical analysis of networks has gained popularity over recent years. Stochastic block model constitutes a classical…
The labeled stochastic block model is a random graph model representing networks with community structure and interactions of multiple types. In its simplest form, it consists of two communities of approximately equal size, and the edges…
The planted bisection model is a random graph model in which the nodes are divided into two equal-sized communities and then edges are added randomly in a way that depends on the community membership. We establish necessary and sufficient…
The paper discusses a statistical problem related to testing for differences between two sparse networks with community structures. The community-wise edge probability matrices have entries of order $O(n^{-1}/\log n)$, where $n$ represents…
Community detection is the problem of identifying community structure in graphs. Often the graph is modeled as a sample from the Stochastic Block Model, in which each vertex belongs to a community. The probability that two vertices are…
An imprecise Bayesian nonparametric approach to system reliability with multiple types of components is developed. This allows modelling partial or imperfect prior knowledge on component failure distributions in a flexible way through…
Testing whether a probability distribution is compatible with a given Bayesian network is a fundamental task in the field of causal inference, where Bayesian networks model causal relations. Here we consider the class of causal structures…
We study the fundamental problem of learning an unknown, smooth probability function via pointwise Bernoulli tests. We provide a scalable algorithm for efficiently solving this problem with rigorous guarantees. In particular, we prove the…
Semidefinite programs have recently been developed for the problem of community detection, which may be viewed as a special case of the stochastic blockmodel. Here, we develop a semidefinite program that can be tailored to other instances…
We study the problem of community detection (CD) on Euclidean random geometric graphs where each vertex has two latent variables: a binary community label and a $\mathbb{R}^d$ valued location label which forms the support of a Poisson point…
Bayesian clustering methods have the widely touted advantage of providing a probabilistic characterization of uncertainty in clustering through the posterior distribution. An amazing variety of priors and likelihoods have been proposed for…
Identifying communities in networks is a fundamental and challenging problem of practical importance in many fields of science. Current methods either ignore the heterogeneous distribution of nodal degrees or assume prior knowledge of the…
We study the stochastic block model which is often used to model community structures and study community-detection algorithms. We consider the case of two blocks in regard to its largest connected component and largest biconnected…