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When constructing models of the world, we aim for optimal compressions: models that include as few details as possible while remaining as accurate as possible. But which details -- or features measured in data -- should we choose to include…
A graphon is a limiting object used to describe the behaviour of large networks through a function that captures the probability of edge formation between nodes. Although the merits of graphons to describe large and unlabelled networks are…
Bayesian hypothesis testing and minimax hypothesis testing represent extreme instances of detection in which the prior probabilities of the hypotheses are either completely and precisely known, or are completely unknown. Group minimax, also…
The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, information retrieval and many other areas related to the World Wide Web. There exist several algorithms for the problem with…
Community detection is an essential tool for unsupervised data exploration and revealing the organisational structure of networked systems. With a long history in network science, community detection typically relies on objective functions,…
Predicting missing links in complex networks requires algorithms that are able to explore statistical regularities in the existing data. Here we investigate the interplay between algorithm efficiency and network structures through the…
Most existing approaches for community detection require complete information of the graph in a specific scale, which is impractical for many social networks. We propose a novel algorithm that does not embrace the universal approach but…
Many systems can be described using graphs, or networks. Detecting communities in these networks can provide information about the underlying structure and functioning of the original systems. Yet this detection is a complex task and a…
Many real systems can be represented as networks whose analysis can be very informative regarding the original system's organisation. In the past decade community detection received a lot of attention and is now an active field of research.…
We consider several estimation and learning problems that networked agents face when making decisions given their uncertainty about an unknown variable. Our methods are designed to efficiently deal with heterogeneity in both size and…
Local dependence random graph models are a class of block models for network data which allow for dependence among edges under a local dependence assumption defined around the block structure of the network. Since being introduced by…
Clustering bipartite graphs is a fundamental task in network analysis. In the high-dimensional regime where the number of rows $n_1$ and the number of columns $n_2$ of the associated adjacency matrix are of different order, existing methods…
We study low-rank estimation of an unknown sparse graphon from sampled network data under operator-norm loss, motivated by targeted interventions in graphon games. Starting from the observed adjacency matrix, we construct low-rank…
The study of complex networks has significantly advanced our understanding of community structures which serves as a crucial feature of real-world graphs. Detecting communities in graphs is a challenging problem with applications in…
We study the problem of testing for community structure in networks using relations between the observed frequencies of small subgraphs. We propose a simple test for the existence of communities based only on the frequencies of three-node…
Community detection, a fundamental task for network analysis, aims to partition a network into multiple sub-structures to help reveal their latent functions. Community detection has been extensively studied in and broadly applied to many…
Given a network represented by a graph $G=(V,E)$, we consider a dynamical process of influence diffusion in $G$ that evolves as follows: Initially only the nodes of a given $S\subseteq V$ are influenced; subsequently, at each round, the set…
The information-theoretic limits of community detection have been studied extensively for network models with high levels of symmetry or homogeneity. The contribution of this paper is to study a broader class of network models that allow…
We present a simple and flexible method to prove consistency of semidefinite optimization problems on random graphs. The method is based on Grothendieck's inequality. Unlike the previous uses of this inequality that lead to constant…
Given a flow network with variable suppliers and fixed consumers, the minimax flow problem consists in minimizing the maximum flow between nodes, subject to flow conservation and capacity constraints. We solve this problem over acyclic…