Related papers: Stochastic Block Models and Reconstruction
Structured sparsity is an important part of the modern statistical toolkit. We say a set of model parameters has block diagonal sparsity up to permutations if its elements can be viewed as the edges of a graph that has multiple connected…
This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is…
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…
We show that model-based Bayesian clustering, the probabilistically most systematic approach to the partitioning of data, can be mapped into a statistical physics problem for a gas of particles, and as a result becomes amenable to a…
Complex systems in nature and in society are often represented as networks, describing the rich set of interactions between objects of interest. Many deterministic and probabilistic clustering methods have been developed to analyze such…
Modeling relations between individuals is a classical question in social sciences, ecology, etc. In order to uncover a latent structure in the data, a popular approach consists in clustering individuals according to the observed patterns of…
The initial purpose of this work is to provide a probabilistic explanation of a recent result on a version of Smoluchowski's coagulation equations in which the number of aggregations is limited. The latter models the deterministic evolution…
Attributed graphs model real networks by enriching their nodes with attributes accounting for properties. Several techniques have been proposed for partitioning these graphs into clusters that are homogeneous with respect to both semantic…
The paper proposes the combination of stochastic blockmodels with smooth graphon models. The first allow for partitioning the set of individuals in a network into blocks which represent groups of nodes that presumably connect stochastically…
In the planted bisection model a random graph $G(n,p_+,p_- )$ with $n$ vertices is created by partitioning the vertices randomly into two classes of equal size (up to $\pm1$). Any two vertices that belong to the same class are linked by an…
The stochastic block model is a powerful tool for inferring community structure from network topology. However, it predicts a Poisson degree distribution within each community, while most real-world networks have a heavy-tailed degree…
Mixture models are probabilistic models aimed at uncovering and representing latent subgroups within a population. In the realm of network data analysis, the latent subgroups of nodes are typically identified by their connectivity…
High-dimensional planted problems, such as finding a hidden dense subgraph within a random graph, often exhibit a gap between statistical and computational feasibility. While recovering the hidden structure may be statistically possible, it…
We consider the problem of reconstructing sparse symmetric block models with two blocks and connection probabilities $a/n$ and $b/n$ for inter- and intra-block edge probabilities, respectively. It was recently shown that one can do better…
A central problem in analyzing networks is partitioning them into modules or communities. One of the best tools for this is the stochastic block model, which clusters vertices into blocks with statistically homogeneous pattern of links.…
We study a planted clique model introduced by Feige where a complete graph of size $c\cdot n$ is planted uniformly at random in an arbitrary $n$-vertex graph. We give a simple deterministic algorithm that, in almost linear time, recovers a…
In the standard stochastic block model for networks, the probability of a connection between two nodes, often referred to as the edge probability, depends on the unobserved communities each of these nodes belongs to. We consider a flexible…
In this paper, we investigate the use of probabilistic graphical models, specifically stochastic blockmodels, for the purpose of hierarchical entity clustering on knowledge graphs. These models, seldom used in the Semantic Web community,…
Clustering is a crucial task in various domains of knowledge, including medicine, epidemiology, genomics, environmental science, economics, and visual sciences, among others. Methodologies for inferring the number of clusters have often…
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…