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We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
The study of random graphs and networks had an explosive development in the last couple of decades. Meanwhile, techniques for the statistical analysis of sequences of networks were less developed. In this paper we focus on networks…
The temporal exponential random graph model (TERGM) and the stochastic actor-oriented model (SAOM, e.g., SIENA) are popular models for longitudinal network analysis. We compare these models theoretically, via simulation, and through a…
Using electrocardiograms as an example, we demonstrate the characteristic problems that arise when modeling one-dimensional signals containing inaccurate repeating pattern by means of standard convolutional networks. We show that these…
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…
Graph Neural Networks (GNN) rely on graph convolutions to learn features from network data. GNNs are stable to different types of perturbations of the underlying graph, a property that they inherit from graph filters. In this paper we…
Recent developments in computers and automated data collection strategies have greatly increased the interest in statistical modeling of dynamic networks. Many of the statistical models employed for inference on large-scale dynamic networks…
Despite the recently exhibited importance of higher-order interactions for various processes, few flexible (null) models are available. In particular, most studies on hypergraphs focus on a small set of theoretical models. Here, we…
The application of network analysis has found great success in a wide variety of disciplines; however, the popularity of these approaches has revealed the difficulty in handling networks whose complexity scales rapidly. One of the main…
Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In…
Deep Learning's recent successes have mostly relied on Convolutional Networks, which exploit fundamental statistical properties of images, sounds and video data: the local stationarity and multi-scale compositional structure, that allows…
The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…
Many popular network models rely on the assumption of (vertex) exchangeability, in which the distribution of the graph is invariant to relabelings of the vertices. However, the Aldous-Hoover theorem guarantees that these graphs are dense or…
Probabilistic Graphical Models are often used to understand dynamics of a system. They can model relationships between features (nodes) and the underlying distribution. Theoretically these models can represent very complex dependency…
The stable matching problem is a prototype model in economics and social sciences where agents act selfishly to optimize their own satisfaction, subject to mutually conflicting constraints. A stable matching is a pairing of adjacent…
Exponential Random Graph Models (ERGMs) are an inferential model for analysing statistical networks. Recent development in ERGMs uses hierarchical Bayesian setup to jointly model a group of networks, which is called a multiple-network…
Over the past few years, research on deep graph learning has shifted from static graphs to temporal graphs in response to real-world complex systems that exhibit dynamic behaviors. In practice, temporal graphs are formalized as an ordered…
Graph neural networks (GNN) have shown great advantages in many graph-based learning tasks but often fail to predict accurately for a task-based on sets of nodes such as link/motif prediction and so on. Many works have recently proposed to…
Are the embeddings of a graph's degenerate core stable? What happens to the embeddings of nodes in the degenerate core as we systematically remove periphery nodes (by repeated peeling off $k$-cores)? We discover three patterns w.r.t.…
Evidence theory is widely used in decision-making and reasoning systems. In previous research, Transferable Belief Model (TBM) is a commonly used evidential decision making model, but TBM is a non-preference model. In order to better fit…