Related papers: Characterising heavy-tailed networks using q-gener…
Not all nodes in a network are created equal. Differences and similarities exist at both individual node and group levels. Disentangling single node from group properties is crucial for network modeling and structural inference. Based on…
Identifying the generating mechanism of a network is challenging as, more often than not, only snapshots are available, but not the full evolution. One candidate for the generating mechanism is preferential attachment which, in its simplest…
We study the asymptotic spectral distribution of the conjugate kernel random matrix $YY^\top$, where $Y= f(WX)$ arises from a two-layer neural network model. We consider the setting where $W$ and $X$ are random rectangular matrices with…
We consider the evolution of scale-free networks according to preferential attachment schemes and show the conditions for which the exponent characterizing the degree distribution is bounded by upper and lower values. Our framework is an…
Two ubiquitous aspects of large-scale data analysis are that the data often have heavy-tailed properties and that diffusion-based or spectral-based methods are often used to identify and extract structure of interest. Perhaps surprisingly,…
Heavy-tailed distributions have been studied in statistics, random matrix theory, physics, and econometrics as models of correlated systems, among other domains. Further, heavy-tail distributed eigenvalues of the covariance matrix of the…
Distributions of the resilience of transport networks are studied numerically, in particular the large-deviation tails. Thus, not only typical quantities like average or variance but the distributions over the (almost) full support can be…
A recent series of theoretical works showed that the dynamics of neural networks with a certain initialisation are well-captured by kernel methods. Concurrent empirical work demonstrated that kernel methods can come close to the performance…
We describe a quantum-assisted machine learning (QAML) method in which multivariate data is encoded into quantum states in a Hilbert space whose dimension is exponentially large in the length of the data vector. Learning in this space…
Bayesian networks (BNs) are a foundational model in machine learning and causal inference. Their graphical structure can handle high-dimensional problems, divide them into a sparse collection of smaller ones, underlies Judea Pearl's…
Network threat detection has been challenging due to the complexities of attack activities and the limitation of historical threat data to learn from. To help enhance the existing practices of using analytics, machine learning, and…
We introduce a novel method for studying systematic trends in nuclear reaction data using generative adversarial networks. Libraries of nuclear cross section evaluations exhibit intricate systematic trends across the nuclear landscape, and…
Empirical studies show that online social networks have not only in- and out-degree distributions with Pareto-like tails but also a high proportion of reciprocal edges. A classical directed preferential attachment (PA) model generates in-…
The analysis in this paper helps to explain the formation of growing networks with degree distributions that follow extended exponential or power-law tails. We present a generic model in which edge dynamics are driven by a continuous…
Latent Euclidean embedding models a given network by representing each node in a Euclidean space, where the probability of two nodes sharing an edge is a function of the distances between the nodes. This implies that for two nodes to share…
We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local tree-like structure), exact equations are derived. These equations are generalized to the…
Network topology is a fundamental aspect of network science that allows us to gather insights into the complicated relational architectures of the world we inhabit. We provide a first specific study of neighbourhood degree sequences in…
Deep connections are known to exist between scale-free networks and non-Gibbsian statistics. For example, typical degree distributions at the thermodynamical limit are of the form $P(k) \propto e_q^{-k/\kappa}$, where the $q$-exponential…
We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…
We study the mixtures of factorizing probability distributions represented as visible marginal distributions in stochastic layered networks. We take the perspective of kernel transitions of distributions, which gives a unified picture of…