Related papers: Hyperbolic triangulations and discrete random grap…

This paper introduces new methodology to triangulate dynamic Bayesian networks (DBNs) and dynamic graphical models (DGMs). While most methods to triangulate such networks use some form of constrained elimination scheme based on properties…

Network data is ubiquitous in various scientific disciplines, including sociology, economics, and neuroscience. Latent space models are often employed in network data analysis, but the geometric effect of latent space curvature remains a…

Through detailed analysis of scores of publicly available data sets corresponding to a wide range of large-scale networks, from communication and road networks to various forms of social networks, we explore a little-studied geometric…

Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into…

The discovery and analysis of network patterns are central to the scientific enterprise. In the present work, we developed and evaluated a new approach that learns the building blocks of graphs that can be used to understand and generate…

Hyperbolic deep learning leverages the metric properties of hyperbolic spaces to develop efficient and informative embeddings of hierarchical data. Here, we focus on the solvable group structure of hyperbolic spaces, which follows naturally…

Large graphs are present in a variety of domains, including social networks, civil infrastructure, and the physical sciences to name a few. Graph generation is similarly widespread, with applications in drug discovery, network analysis and…

This paper studies real-world road networks from an algorithmic perspective, focusing on empirical studies that yield useful properties of road networks that can be exploited in the design of fast algorithms that deal with geographic data.…

Bayesian networks have been used as a mechanism to represent the joint distribution of multiple random variables in a flexible yet interpretable manner. One major challenge in learning the structure of a Bayesian network is how to model…

We show that a neural network, trained on the entanglement spectra of a nearest neighbor Heisenberg chain in a random transverse magnetic field, can be used to efficiently study the ergodic/many-body localized properties of a number of…

Using machine learning, we explore the utility of various deep neural networks (NN) when applied to high harmonic generation (HHG) scenarios. First, we train the NNs to predict the time-dependent dipole and spectra of HHG emission from…

Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. Recent work at the intersection of formal language theory and graph theory has found that a Hyperedge Replacement Grammar (HRG)…

Networks found in the real-world are numerous and varied. A common type of network is the heterogeneous network, where the nodes (and edges) can be of different types. Accordingly, there have been efforts at learning representations of…

Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…

Graphical models are powerful tools to investigate complex dependency structures in high-throughput datasets. However, most existing graphical models make one of the two canonical assumptions: (i) a homogeneous graph with a common network…

Graph neural networks (GNNs) provide powerful insights for brain neuroimaging technology from the view of graphical networks. However, most existing GNN-based models assume that the neuroimaging-produced brain connectome network is a…

We introduce a new class of identifiable DAG models where the conditional distribution of each node given its parents belongs to a family of generalized hypergeometric distributions (GHD). A family of generalized hypergeometric…

We present a new method for learning Soft Random Geometric Graphs (SRGGs), drawn in probabilistic metric spaces, with the connection function of the graph defined as the marginal posterior probability of an edge random variable, given the…

A rich class of network models associate each node with a low-dimensional latent coordinate that controls the propensity for connections to form. Models of this type are well established in the network analysis literature, where it is…

Hyperbolic neural networks have shown great potential for modeling complex data. However, existing hyperbolic networks are not completely hyperbolic, as they encode features in a hyperbolic space yet formalize most of their operations in…