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A new method is proposed for analyzing complexity and studying the information in random geometric networks using Tsallis entropy tool. Tsallis entropy of the ensemble of random geometric networks is calculated based on the components of…
While deep ensembles are widely considered to be the default method for uncertainty quantification in deep learning, their effectiveness for graph-structured data is often simply assumed based on successes in domains like computer vision.…
Random K-out graphs are used in several applications including modeling by sensor networks secured by the random pairwise key predistribution scheme, and payment channel networks. The random K-out graph with $n$ nodes is constructed as…
The combination of multiple classifiers using ensemble methods is increasingly important for making progress in a variety of difficult prediction problems. We present a comparative analysis of several ensemble methods through two case…
Many networks can be characterised by the presence of communities, which are groups of units that are closely linked. Identifying these communities can be crucial for understanding the system's overall function. Recently, hypergraphs have…
Preferential attachment is an appealing edge generating mechanism for modeling social networks. It provides both an intuitive description of network growth and an explanation for the observed power laws in degree distributions. However,…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…
Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
In the last few years we have witnessed the emergence, primarily in on-line communities, of new types of social networks that require for their representation more complex graph structures than have been employed in the past. One example is…
Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…
We associate all small subgraph counting problems with a systematic graph encoding/representation system which makes a coherent use of graphlet structures. The system can serve as a unified foundation for studying and connecting many…
Deep learning has achieved impressive performance in many domains, such as computer vision and natural language processing, but its advantage over classical shallow methods on tabular datasets remains questionable. It is especially…
We introduce a broad class of random graph models: the generalised hypergeometric ensemble (GHypEG). This class enables to solve some long standing problems in random graph theory. First, GHypEG provides an elegant and compact formulation…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…
The classical Gaussian ensembles of random matrices can be constructed by maximizing Boltzmann-Gibbs-Shannon's entropy, S_{BGS} = - \int d{\bf H} [P({\bf H})] \ln [P({\bf H})], with suitable constraints. Here we construct and analyze…
Ensembles of artificial neural networks show improved generalization capabilities that outperform those of single networks. However, for aggregation to be effective, the individual networks must be as accurate and diverse as possible. An…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
The objective of this paper is to study the characteristics (geometric and otherwise) of very large attribute based undirected networks. Real-world networks are often very large and fast evolving. Their analysis and understanding present a…
In this paper, we derive cumulant bounds for subgraph counts and power-weighted edge length in a class of spatial random networks known as weighted random connection models. This involves dealing with long-range spatial correlations induced…