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Testing for independence between graphs is a problem that arises naturally in social network analysis and neuroscience. In this paper, we address independence testing for inhomogeneous Erd\H{o}s-R\'{e}nyi random graphs on the same vertex…
Copulas are mathematical objects that fully capture the dependence structure among random variables and hence, offer a great flexibility in building multivariate stochastic models. In statistics, a copula is used as a general way of…
Statisticians and quantitative neuroscientists have actively promoted the use of independence relationships for investigating brain networks, genomic networks, and other measurement technologies. Estimation of these graphs depends on two…
We propose a variation of the self organizing map algorithm by considering the random placement of neurons on a two-dimensional manifold, following a blue noise distribution from which various topologies can be derived. These topologies…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
Joint distributions over many variables are frequently modeled by decomposing them into products of simpler, lower-dimensional conditional distributions, such as in sparsely connected Bayesian networks. However, automatically learning such…
The final step of most large-scale structure analyses involves the comparison of power spectra or correlation functions to theoretical models. It is clear that the theoretical models have parameter dependence, but frequently the…
For various purposes and, in particular, in the context of data compression, a graph can be examined at three levels. Its structure can be described as the unlabeled version of the graph; then the labeling of its structure can be added; and…
The McNemar test evaluates the hypothesis that two correlated proportion is common in $2 \times 2$ contingency tables with the same categories. This study discusses a test for symmetry in $2 \times 2$ contingency tables with nonignorable…
We propose a novel structure, the data-sharing graph, for characterizing sharing patterns in large-scale data distribution systems. We analyze this structure in two such systems and uncover small-world patterns for data-sharing…
Bipartite networks provide an effective resource for representing, characterizing, and modeling several abstract and real-world systems and structures involving binary relations, which include food webs, social interactions, and…
We investigate the structure of graphs of twin-width at most $1$, and obtain the following results: - Graphs of twin-width at most $1$ are permutation graphs. In particular they have an intersection model and a linear structure. - There is…
We show and interpret three examples of nontrivial results obtained in numerical simulations of many-body systems: exponential convergence of low-lying energy eigenvalues in the process of progressive truncation of huge shell-model…
Decomposable graphs are known for their tedious and complicated Markov update steps. Instead of modelling them directly, this work introduces a class of tree-dependent bipartite graphs that span the projective space of decomposable graphs.…
Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the…
Clustering is one of the most common unsupervised learning tasks in machine learning and data mining. Clustering algorithms have been used in a plethora of applications across several scientific fields. However, there has been limited…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely…
Our interest is in the scaled joint distribution associated with $k$-increasing subsequences for random involutions with a prescribed number of fixed points. We proceed by specifying in terms of correlation functions the same distribution…
Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective…