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This paper studies the fundamental problem of multi-layer generator models in learning hierarchical representations. The multi-layer generator model that consists of multiple layers of latent variables organized in a top-down architecture…

Potential energy landscapes can be represented as a network of minima linked by transition states. The community structure of such networks has been obtained for a series of small Lennard-Jones clusters. This community structure is compared…

Spatial ecological networks are widely used to model interactions between georeferenced biological entities (e.g., populations or communities). The analysis of such data often leads to a two-step approach where groups containing similar…

Detecting the dimensionality of graphs is a central topic in machine learning. While the problem has been tackled empirically as well as theoretically, existing methods have several drawbacks. On the one hand, empirical tools are…

Repeated small dynamic networks are integral to studies in evolutionary game theory, where networked public goods games offer novel insights into human behaviors. Building on these findings, it is necessary to develop a statistical model…

We propose a robust, scalable, integrated methodology for community detection and community comparison in graphs. In our procedure, we first embed a graph into an appropriate Euclidean space to obtain a low-dimensional representation, and…

We present a novel hierarchical graph clustering algorithm inspired by modularity-based clustering techniques. The algorithm is agglomerative and based on a simple distance between clusters induced by the probability of sampling node pairs.…

We develop approximate estimation methods for exponential random graph models (ERGMs), whose likelihood is proportional to an intractable normalizing constant. The usual approach approximates this constant with Monte Carlo simulations,…

An important question in statistical network analysis is how to estimate models of discrete and dependent network data with intractable likelihood functions, without sacrificing computational scalability and statistical guarantees. We…

Probabilistic graphical models (PGMs) are widely used to discover latent structure in data, but their success hinges on selecting an appropriate model design. In practice, model specification is difficult and often requires iterative…

Large language models (LLMs) have presented significant opportunities to enhance various machine learning applications, including graph neural networks (GNNs). By leveraging the vast open-world knowledge within LLMs, we can more effectively…

Latent space models (LSM) for network data were introduced by Hoff et al. (2002) under the basic assumption that each node of the network has an unknown position in a D-dimensional Euclidean latent space: generally the smaller the distance…

We propose an autoregressive framework for modelling dynamic networks with dependent edges. It encompasses models that accommodate, for example, transitivity, degree heterogenenity, and other stylized features often observed in real network…

Individual personalities significantly influence our perceptions, decisions, and social interactions, which is particularly crucial for gaining insights into human behavior patterns in online social network analysis. Many psychological…

Applications of structural equation models (SEMs) are often restricted to linear associations between variables. Maximum likelihood (ML) estimation in non-linear models may be complex and require numerical integration. Furthermore, ML…

The exponential random graph model (ERGM) is a central object in the study of clustering properties in social networks as well as canonical ensembles in statistical physics. Despite some breakthrough works in the mathematical understanding…

All networks can be analyzed at multiple scales. A higher scale of a network is made up of macro-nodes: subgraphs that have been grouped into individual nodes. Recasting a network at higher scales can have useful effects, such as decreasing…

We propose a Multi-Layer Network based on the Bayesian framework of the Factor Graphs in Reduced Normal Form (FGrn) applied to a two-dimensional lattice. The Latent Variable Model (LVM) is the basic building block of a quadtree hierarchy…

Analysis of the topology of a graph, regular or bipartite one, can be done by clustering for regular ones or co-clustering for bipartite ones. The Stochastic Block Model and the Latent Block Model are two models, which are very similar for…

Synthetic power grids enable secure, real-world energy system simulations and are crucial for algorithm testing, resilience assessment, and policy formulation. We propose a novel method for the generation of synthetic transmission power…