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Group testing was conceived during World War II to identify soldiers infected with syphilis using as few tests as possible, and it has attracted renewed interest during the COVID-19 pandemic. A long-standing assumption in the probabilistic…
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…
The stochastic block model is a canonical model of communities in random graphs. It was introduced in the social sciences and statistics as a model of communities, and in theoretical computer science as an average case model for graph…
Motivated by the study of social insects, we introduce a stochastic model based on interacting particle systems in order to understand the effect of communication on the division of labor. Members of the colony are located on the vertex set…
The stochastic block model (SBM) is widely studied as a benchmark for graph clustering aka community detection. In practice, graph data often come with node attributes that bear additional information about the communities. Previous works…
Due to the significant increase of communications between individuals via social media (Facebook, Twitter, Linkedin) or electronic formats (email, web, e-publication) in the past two decades, network analysis has become a unavoidable…
The problem of community detection receives great attention in recent years. Many methods have been proposed to discover communities in networks. In this paper, we propose a Gaussian stochastic blockmodel that uses Gaussian distributions to…
Stochastic blockmodels (SBM) and their variants, $e.g.$, mixed-membership and overlapping stochastic blockmodels, are latent variable based generative models for graphs. They have proven to be successful for various tasks, such as…
We give upper and lower bounds on the information-theoretic threshold for community detection in the stochastic block model. Specifically, let $k$ be the number of groups, $d$ be the average degree, the probability of edges between vertices…
We consider a matrix completion problem that exploits social or item similarity graphs as side information. We develop a universal, parameter-free, and computationally efficient algorithm that starts with hierarchical graph clustering and…
The stochastic block model is a popular tool for detecting community structures in network data. Detecting the difference between two community structures is an important issue for stochastic block models. However, the two-sample test has…
The stochastic block model is widely used to generate graphs with a community structure, but no simple alternative currently exists for hypergraphs, in which more than two nodes can be connected together through a hyperedge. We discuss here…
Hypergraphs, capable of representing high-order interactions via hyperedges, have become a powerful tool for modeling real-world biological and social systems. Inherent relationships within these real-world systems, such as the encoding…
Networks serve as a tool used to examine the large-scale connectivity patterns in complex systems. Modelling their generative mechanism nonparametrically is often based on step-functions, such as the stochastic block models. These models…
This Thesis explores how tools from Statistical Physics and Information Theory can help us describe and understand complex systems. In the first part, we study the interplay between internal interactions, environmental changes, and…
We study community detection in the contextual stochastic block model arXiv:1807.09596 [cs.SI], arXiv:1607.02675 [stat.ME]. In arXiv:1807.09596 [cs.SI], the second author studied this problem in the setting of sparse graphs with…
We study the problem of community detection when there is covariate information about the node labels and one observes multiple correlated networks. We provide an asymptotic upper bound on the per-node mutual information as well as a…
Inference for the stochastic blockmodel is currently of burgeoning interest in the statistical community, as well as in various application domains as diverse as social networks, citation networks, brain connectivity networks…
Networks or graphs can easily represent a diverse set of data sources that are characterized by interacting units or actors. Social networks, representing people who communicate with each other, are one example. Communities or clusters of…
We study stochastic graph optimization problems in a novel distributed setting. As in the standard centralized setting, a random subgraph $G^*$ of a known base graph $G$ is realized by including each edge $e$ independently with a known…