Related papers: Spectral Inference Methods on Sparse Graphs: Theor…
Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank…
The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function…
This paper revisits the classical concept of network modularity and its spectral relaxations used throughout graph data analysis. We formulate and study several modularity statistic variants for which we establish asymptotic distributional…
Network science provides valuable insights across numerous disciplines including sociology, biology, neuroscience and engineering. A task of major practical importance in these application domains is inferring the network structure from…
Spectral graph theory is a captivating area of graph theory that employs the eigenvalues and eigenvectors of matrices associated with graphs to study them. In this paper, we present a collection of $20$ topics in spectral graph theory,…
Graphical network inference is used in many fields such as genomics or ecology to infer the conditional independence structure between variables, from measurements of gene expression or species abundances for instance. In many practical…
Spectral sparsification is a technique that is used to reduce the number of non-zero entries in a positive semidefinite matrix with little changes to its spectrum. In particular, the main application of spectral sparsification is to…
Signal modeling lies at the core of numerous signal and image processing applications. A recent approach that has drawn considerable attention is sparse representation modeling, in which the signal is assumed to be generated as a…
Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to…
Inferring a binary connectivity graph from resting-state fMRI data for a single subject requires making several methodological choices and assumptions that can significantly affect the results. In this study, we investigate the robustness…
Structured sparse optimization is an important and challenging problem for analyzing high-dimensional data in a variety of applications such as bioinformatics, medical imaging, social networks, and astronomy. Although a number of structured…
Statistical field theory methods have been very successful with a number of random graph and random matrix problems, but it is challenging to apply these methods to graphs with prescribed degree sequences due to the extensive number of…
Graphs play a central role in modeling complex relationships in data, yet most graph learning methods falter when faced with cold-start nodes--new nodes lacking initial connections--due to their reliance on adjacency information. To tackle…
Recently, graph neural networks (GNNs) have been widely used for document classification. However, most existing methods are based on static word co-occurrence graphs without sentence-level information, which poses three challenges:(1) word…
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
Generative graph models struggle to scale due to the need to predict the existence or type of edges between all node pairs. To address the resulting quadratic complexity, existing scalable models often impose restrictive assumptions such as…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
To learn (statistical) dependencies among random variables requires exponentially large sample size in the number of observed random variables if any arbitrary joint probability distribution can occur. We consider the case that sparse data…
Graphs and networks provide a canonical representation of relational data, with massive network data sets becoming increasingly prevalent across a variety of scientific fields. Although tools from mathematics and computer science have been…