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We propose a novel dynamic network model to capture evolving latent communities within temporal networks. To achieve this, we decompose each observed dynamic edge between vertices using a Poisson-gamma edge partition model, assigning each…

We introduce a new approach to prediction in graphical models with latent-shift adaptation, i.e., where source and target environments differ in the distribution of an unobserved confounding latent variable. Previous work has shown that as…

Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…

In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…

Exponential-family random network (ERN) models specify a joint representation of both the dyads of a network and nodal characteristics. This class of models allow the nodal characteristics to be modelled as stochastic processes, expanding…

In this paper we propose to extend the separable temporal exponential random graph model (STERGM) to account for time-varying network- and actor-specific effects. Our application case is the network of international major conventional…

Diffusion models (DMs) are a powerful type of generative models that have achieved state-of-the-art results in various image synthesis tasks and have shown potential in other domains, such as natural language processing and temporal data…

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…

Network theory has often disregarded many-body relationships, solely focusing on pairwise interactions: neglecting them, however, can lead to misleading representations of complex systems. Hypergraphs represent a suitable framework for…

Bayesian brain theory suggests that the brain employs generative models to understand the external world. The sampling-based perspective posits that the brain infers the posterior distribution through samples of stochastic neuronal…

In this document, we present key findings in structured matrix approximation theory, with applications to the regressive representation of dynamic financial processes. Initially, we explore a comprehensive approach involving generic…

We face network data from various sources, such as protein interactions and online social networks. A critical problem is to model network interactions and identify latent groups of network nodes. This problem is challenging due to many…

Empirical temporal networks display strong heterogeneities in their dynamics, which profoundly affect processes taking place on these networks, such as rumor and epidemic spreading. Despite the recent wealth of data on temporal networks,…

Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bl\"asius et al. have proposed a framework for systematic evaluation of the expressivity of random graph models. We extend…

We study tensor network states defined on an underlying graph which is sparsely connected. Generic sparse graphs are expander graphs with a high probability, and one can represent volume law entangled states efficiently with only polynomial…

We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…

We study the limiting behavior of interacting particle systems indexed by large sparse graphs, which evolve either according to a discrete time Markov chain or a diffusion, in which particles interact directly only with their nearest…

Probabilistic graphical modeling (PGM) provides a framework for formulating an interpretable generative process of data and expressing uncertainty about unknowns, but it lacks flexibility. Deep learning (DL) is an alternative framework for…

Exchangeable models for countable vertex-labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distribution observed in many network datasets. Out of this mathematical impossibility emerges the question…

I propose an estimation algorithm for Exponential Random Graph Models (ERGM), a popular statistical network model for estimating the structural parameters of strategic network formation in economics and finance. Existing methods often…