Related papers: Modeling heterogeneity in random graphs through la…
Machine learning has made important headway in helping to improve the treatment of quantum many-body systems. A domain of particular relevance are correlated inhomogeneous systems. What has been missing so far is a general, scalable…
Inferring temporal interaction graphs and higher-order structure from neural signals is a key problem in building generative models for systems neuroscience. Foundation models for large-scale neural data represent shared latent structures…
Generative models that can model and predict sequences of future events can, in principle, learn to capture complex real-world phenomena, such as physical interactions. However, a central challenge in video prediction is that the future is…
In this paper we study the component structure of random graphs with independence between the edges. Under mild assumptions, we determine whether there is a giant component, and find its asymptotic size when it exists. We assume that the…
We study a recent class of models which uses graph neural networks (GNNs) to improve forecasting in multivariate time series. The core assumption behind these models is that there is a latent graph between the time series (nodes) that…
In many applications of finance, biology and sociology, complex systems involve entities interacting with each other. These processes have the peculiarity of evolving over time and of comprising latent factors, which influence the system…
We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications.
We present a comprehensive extension of the latent position network model known as the random dot product graph to accommodate multiple graphs -- both undirected and directed -- which share a common subset of nodes, and propose a method for…
Generative network models are extremely useful for understanding the mechanisms that operate in network formation and are widely used across several areas of knowledge. However, when it comes to bipartite networks -- a class of network…
With ever-increasing available data, predicting individuals' preferences and helping them locate the most relevant information has become a pressing need. Understanding and predicting preferences is also important from a fundamental point…
The heterogeneity of breast cancer presents considerable challenges for its early detection, prognosis, and treatment selection. Convolutional neural networks often neglect the spatial relationships within histopathological images, which…
In this paper a computationally efficient approach is suggested for the stochastic modeling of an inhomogeneous reluctivity of magnetic materials. These materials can be part of electrical machines, such as a single phase transformer (a…
Stochastic embedding transitions introduce a probabilistic mechanism for adjusting token representations dynamically during inference, mitigating the constraints imposed through static or deterministic embeddings. A transition framework was…
Sampling algorithms, hypergraph degree sequences, and polytopes play a crucial role in statistical analysis of network data. This article offers a brief overview of open problems in this area of discrete mathematics from the point of view…
For statistical analysis of multiway contingency tables we propose modeling interaction terms in each maximal compact component of a hierarchical model. By this approach we can search for parsimonious models with smaller degrees of freedom…
The study of random graphs has become very popular for real-life network modeling such as social networks or financial networks. Inhomogeneous long-range percolation (or scale-free percolation) on the lattice $\mathbb Z^d$, $d\ge1$, is a…
Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model.…
We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…
We explore the usage of meta-learning to derive the causal direction between variables by optimizing over a measure of distribution simplicity. We incorporate a stochastic graph representation which includes latent variables and allows for…
We introduce a rigorous framework for stochastic cell transmission models for general traffic networks. The performance of traffic systems is evaluated based on preference functionals and acceptable designs. The numerical implementation…