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We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their…
Learning graphs from sets of nodal observations represents a prominent problem formally known as graph topology inference. However, current approaches are limited by typically focusing on inferring single networks, and they assume that…
Staged trees are a relatively recent class of probabilistic graphical models that extend Bayesian networks to formally and graphically account for non-symmetric patterns of dependence. Machine learning algorithms to learn them from data…
Unlike in the traditional statistical modeling for which a user typically hand-specify a prior, Neural Processes (NPs) implicitly define a broad class of stochastic processes with neural networks. Given a data stream, NP learns a stochastic…
We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information…
We introduce a time-varying network model accounting for burstiness and tie reinforcement observed in social networks. The analytical solution indicates a non-trivial phase diagram determined by the competition of the leading terms of the…
Graph embedding is a popular algorithmic approach for creating vector representations for individual vertices in networks. Training these algorithms at scale is important for creating embeddings that can be used for classification, ranking,…
Bipartite networks provide a major insight into the organisation of many real-world systems. One of the most relevant issues encountered when modelling a bipartite network is that of facing the information shortage concerning intra-layer…
Random graphs are an important tool for modelling and analyzing the underlying properties of complex real-world networks. In this paper, we study a class of random graphs known as the inhomogeneous random K-out graphs which were recently…
Nonlinear data visualization using t-distributed stochastic neighbor embedding (t-SNE) enables the representation of complex single-cell transcriptomic landscapes in two or three dimensions to depict biological populations accurately.…
Random geometric graphs are widely used in modeling geometry and dependence structure in networks. In a random geometric graph, nodes are independently generated from some probability distribution $F$ over a metric space, and edges link…
We propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process, and naturally generalizes existing probabilistic models with…
Many real world networks are very large and constantly change over time. These dynamic networks exist in various domains such as social networks, traffic networks and biological interactions. To handle large dynamic networks in downstream…
Networks represent relationships between entities in many complex systems, spanning from online social interactions to biological cell development and brain connectivity. In many cases, relationships between entities are unambiguously…
The degrees are a classical and relevant way to study the topology of a network. They can be used to assess the goodness-of-fit for a given random graph model. In this paper we introduce goodness-of-fit tests for two classes of models.…
Recently, graph neural networks have been widely used for network embedding because of their prominent performance in pairwise relationship learning. In the real world, a more natural and common situation is the coexistence of pairwise…
The problem of unsupervised learning node embeddings in graphs is one of the important directions in modern network science. In this work we propose a novel framework, which is aimed to find embeddings by \textit{discriminating…
In this paper, we consider the problem of testing the equality of two multivariate distributions based on geometric graphs constructed using the interpoint distances between the observations. These include the tests based on the minimum…
Heterogeneous graphs (HGs) also known as heterogeneous information networks have become ubiquitous in real-world scenarios; therefore, HG embedding, which aims to learn representations in a lower-dimension space while preserving the…
Networks are one of the most powerful structures for modeling problems in the real world. Downstream machine learning tasks defined on networks have the potential to solve a variety of problems. With link prediction, for instance, one can…