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We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple…
We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit, given access to the source code that generates the distribution. We consider the basic task of uniformity…
In most domains of network analysis researchers consider networks that arise in nature with weighted edges. Such networks are routinely dichotomized in the interest of using available methods for statistical inference with networks. The…
Network interference amounts to the treatment status of one unit affecting the potential outcome of other units in the population. Testing for spillover effects in this setting makes the null hypothesis non-sharp. An interesting approach to…
The theory of dependency graphs is a powerful toolbox to prove asymptotic normality of sums of random variables. In this article, we introduce a more general notion of weighted dependency graphs and give normality criteria in this context.…
Graph neural networks (GNNs) have achieved remarkable performance on graph-structured data. However, GNNs may inherit prejudice from the training data and make discriminatory predictions based on sensitive attributes, such as gender and…
Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…
Dimensionality effects pose major challenges in high-dimensional and non-Euclidean data analysis. Graph-based two-sample tests and change-point detection are particularly attractive in this context, as they make minimal distributional…
Recent studies on Graph Neural Networks(GNNs) provide both empirical and theoretical evidence supporting their effectiveness in capturing structural patterns on both homophilic and certain heterophilic graphs. Notably, most real-world…
Consider a large social network with possibly severe degree heterogeneity and mixed-memberships. We are interested in testing whether the network has only one community or there are more than one communities. The problem is known to be…
Assume that we have a random sample from an absolutely continuous distribution (univariate, or multivariate) with a known functional form and some unknown parameters. In this paper, we have studied several parametric tests based on…
One-dimensional geometric random graphs are constructed by distributing $n$ nodes uniformly and independently on a unit interval and then assigning an undirected edge between any two nodes that have a distance at most $r_n$. These graphs…
We present a novel framework closely linking the areas of property testing and data streaming algorithms in the setting of general graphs. It has been recently shown (Monemizadeh et al. 2017) that for bounded-degree graphs, any…
Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…
Graph Neural Networks (GNNs) are proposed without considering the agnostic distribution shifts between training and testing graphs, inducing the degeneration of the generalization ability of GNNs on Out-Of-Distribution (OOD) settings. The…
A graph property P is said to be testable if one can check if a graph is close or far from satisfying P using few random local inspections. Property P is said to be non-deterministically testable if one can supply a "certificate" to the…
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…
Network reliability measures the probability that a target node is reachable from a source node in an uncertain graph, i.e., a graph where every edge is associated with a probability of existence. In this paper, we investigate the novel and…
In applications of group testing in networks, e.g. identifying individuals who are infected by a disease spread over a network, exploiting correlation among network nodes provides fundamental opportunities in reducing the number of tests…