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Statistical properties of ensembles of random density matrices are investigated. We compute traces and von Neumann entropies averaged over ensembles of random density matrices distributed according to the Bures measure. The eigenvalues of…
Anomaly detection aims to identify data instances that deviate significantly from majority of data, which has been widely used in fraud detection, network security, and industrial quality control. Existing methods struggle with datasets…
We propose and investigate new complementary methodologies for estimating predictive variance networks in regression neural networks. We derive a locally aware mini-batching scheme that result in sparse robust gradients, and show how to…
In this paper, we explore how network centrality and network entropy can be used to identify a bifurcation network event. A bifurcation often occurs when a network undergoes a qualitative change in its structure as a response to internal…
Neural networks have seen limited use in prediction for high-dimensional data with small sample sizes, because they tend to overfit and require tuning many more hyperparameters than existing off-the-shelf machine learning methods. With…
We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all…
Motivation :Reconstructing the topology of a gene regulatory network is one of the key tasks in systems biology. Despite of the wide variety of proposed methods, very little work has been dedicated to the assessment of their stability…
Comparing weighted networks in neuroscience is hard, because the topological properties of a given network are necessarily dependent on the number of edges of that network. This problem arises in the analysis of both weighted and unweighted…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
We establish an exact analytic relation between random spanning forests and the heat-kernel partition function. This identity enables estimation of partition functions, energies, and the Von Neumann entropy by Wilson sampling of forests,…
Network modeling based on ensemble averages tacitly assumes that the networks meant to be modeled are typical in the ensemble. Previous research on network eigenvalues, which govern a range of dynamical phenomena, has shown that this is…
We introduce a new procedure for training of artificial neural networks by using the approximation of an objective function by arithmetic mean of an ensemble of selected randomly generated neural networks, and apply this procedure to the…
In-depth studies of sociotechnical systems are largely limited to single instances. Network surveys are expensive, and platforms vary in important ways, from interface design, to social norms, to historical contingencies. With single…
By collecting and expanding several numerical recipes developed in previous work, we implement an object-oriented Python code, based on the networkX library, for the realization of the configuration model and Newman rewiring. The software…
The power grid is going through significant changes with the introduction of renewable energy sources and incorporation of smart grid technologies. These rapid advancements necessitate new models and analyses to keep up with the various…
In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…
We introduce Inner Ensemble Networks (IENs) which reduce the variance within the neural network itself without an increase in the model complexity. IENs utilize ensemble parameters during the training phase to reduce the network variance.…
The von Neumann graph entropy is a measure of graph complexity based on the Laplacian spectrum. It has recently found applications in various learning tasks driven by networked data. However, it is computational demanding and hard to…
This chapter provides a comprehensive and self-contained discussion of the most recent developments of information theory of networks. Maximum entropy models of networks are the least biased ensembles enforcing a set of constraints and are…
Consider observing an undirected network that is `noisy' in the sense that there are Type I and Type II errors in the observation of edges. Such errors can arise, for example, in the context of inferring gene regulatory networks in genomics…