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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.…

The standard linear and logistic regression models assume that the response variables are independent, but share the same linear relationship to their corresponding vectors of covariates. The assumption that the response variables are…

Spatially embedded networks are shaped by a combination of purely topological (space-independent) and space-dependent formation rules. While it is quite easy to artificially generate networks where the relative importance of these two…

Many complex systems--from social and communication networks to biological networks and the Internet--are thought to exhibit scale-free structure. However, prevailing explanations rely on the constant addition of new nodes, an assumption…

While the vast majority of the literature on models for temporal networks focuses on binary graphs, often one can associate a weight to each link. In such cases the data are better described by a weighted, or valued, network. An important…

Network structures underlie the dynamics of many complex phenomena, from gene regulation and foodwebs to power grids and social media. Yet, as they often cannot be observed directly, their connectivities must be inferred from observations…

For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the…

The study of complex networks has pursued an understanding of macroscopic behavior by focusing on power-laws in microscopic observables. Here, we uncover two universal fundamental physical principles that are at the basis of complex…

This paper introduces a new concept of stochastic dependence among many random variables which we call conditional neighborhood dependence (CND). Suppose that there are a set of random variables and a set of sigma algebras where both sets…

We propose a novel Bayesian methodology which uses random walks for rapid inference of statistical properties of undirected networks with weighted or unweighted edges. Our formalism yields high-accuracy estimates of the probability…

It is becoming increasingly common to see large collections of network data objects -- that is, data sets in which a network is viewed as a fundamental unit of observation. As a result, there is a pressing need to develop network-based…

We study two-layer belief networks of binary random variables in which the conditional probabilities Pr[childlparents] depend monotonically on weighted sums of the parents. In large networks where exact probabilistic inference is…

Weak convergence of maxima of dependent sequences of identically distributed continuous random variables is studied under normalizing sequences arising as subsequences of the normalizing sequences from an associated iid sequence. This…

Networks of disparate phenomena-- be it the global ecology, human social institutions, within the human brain, or in micro-scale protein interactions-- exhibit broadly consistent architectural features. To explain this, we propose a new…

The paper investigates isotropic random fields for which the spectral density is unbounded at some frequencies. Limit theorems for weighted functionals of these random fields are established. It is shown that for a wide class of…

In this paper, we introduce a conceptual framework that model human social networks as an undirected dot-product graph of independent individuals. Their relationships are only determined by a cost-benefit analysis, i.e. by maximizing an…

Samples of dynamic or time-varying networks and other random object data such as time-varying probability distributions are increasingly encountered in modern data analysis. Common methods for time-varying data such as functional data…

We will consider multivariate stochastic processes indexed either by vertices or pairs of vertices of a dynamic network. Under a dynamic network we understand a network with a fixed vertex set and an edge set which changes randomly over…

This paper considers deep neural networks for learning weakly dependent processes in a general framework that includes, for instance, regression estimation, time series prediction, time series classification. The $\psi$-weak dependence…

This paper introduces the notion of pseudo-independence on the sublinear expectation space $(\Omega,\mathcal{F},\mathcal{P})$ via the classical conditional expectation, and the relations between pseudo-independence and Peng's independence…