Related papers: Configuration model for correlation matrices prese…
We describe a way to complete a correlation matrix that is not fully specified. Such matrices often arise in financial applications when the number of stochastic variables becomes large or when several smaller models are combined in a…
We study the structure of loops in networks using the notion of modulus of loop families. We introduce a new measure of network clustering by quantifying the richness of families of (simple) loops. Modulus tries to minimize the expected…
Data similarity is a key concept in many data-driven applications. Many algorithms are sensitive to similarity measures. To tackle this fundamental problem, automatically learning of similarity information from data via self-expression has…
Network science has presented community detection as a valuable tool for revealing functional modules in complex systems rooted in the wiring architectures of complex networks. The varying procedures of community detection can produce,…
Network (or matrix) reconstruction is a general problem which occurs if the margins of a matrix are given and the matrix entries need to be predicted. In this paper we show that the predictions obtained from the iterative proportional…
Community structure is of paramount importance for the understanding of complex networks. Consequently, there is a tremendous effort in order to develop efficient community detection algorithms. Unfortunately, the issue of a fair assessment…
This article investigates emergence and complexity in complex systems that can share information on a network. To this end, we use a theoretical approach from information theory, computability theory, and complex networks. One key studied…
A graph neural network transforms features in each vertex's neighborhood into a vector representation of the vertex. Afterward, each vertex's representation is used independently for predicting its label. This standard pipeline implicitly…
We introduce a novel statistical significance-based approach for clustering hierarchical data using semi-parametric linear mixed-effects models designed for responses with laws in the exponential family (e.g., Poisson and Bernoulli). Within…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
For most networks, the connection between two nodes is the result of their mutual affinity and attachment. In this paper, we propose a mutual selection model to characterize the weighted networks. By introducing a general mechanism of…
A matrix network is a family of matrices, with relatedness modeled by a weighted graph. We consider the task of completing a partially observed matrix network. We assume a novel sampling scheme where a fraction of matrices might be…
Models of networks play a major role in explaining and reproducing empirically observed patterns. Suitable models can be used to randomize an observed network while preserving some of its features, or to generate synthetic graphs whose…
We analyze convergence of decentralized cooperative online estimation algorithms by a network of multiple nodes via information exchanging in an uncertain environment. Each node has a linear observation of an unknown parameter with randomly…
Finite Gaussian mixture models are widely used for model-based clustering of continuous data. Nevertheless, since the number of model parameters scales quadratically with the number of variables, these models can be easily…
Modern data often arises with multiple modalities. For example, covariates and a network are observed on the same subjects, and both contain useful information. Effectively integrating these modalities is important and challenging,…
We apply a method to filter relevant information from the correlation coefficient matrix by extracting a network of relevant interactions. This method succeeds to generate networks with the same hierarchical structure of the Minimum…
We study the time dependence of maximal spanning trees and asset graphs based on correlation matrices of stock returns. In these networks the nodes represent companies and links are related to the correlation coefficients between them.…
An important problem in modeling networks is how to generate a randomly sampled graph with given degrees. A popular model is the configuration model, a network with assigned degrees and random connections. The erased configuration model is…
In the study of networked systems such as biological, technological, and social networks the available data are often uncertain. Rather than knowing the structure of a network exactly, we know the connections between nodes only with a…