Related papers: The Graph-Embedded Hazard Model (GEHM): Stochastic…

We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph…

This work introduces NetDiff, an expressive graph denoising diffusion probabilistic architecture that generates wireless ad hoc network link topologies. Such networks, with directional antennas, can achieve unmatched performance when the…

We provide a well-posedness theory for a class of nonlocal continuity equations on co-evolving graphs. We describe the connection among vertices through an edge weight function and we let it evolve in time, coupling its dynamics with the…

Financial returns are known to exhibit heavy tails, volatility clustering and abrupt jumps that are poorly captured by classical diffusion models. Advances in machine learning have enabled highly flexible functional forms for conditional…

Graph neural networks are increasingly becoming the go-to approach in various fields such as computer vision, computational biology and chemistry, where data are naturally explained by graphs. However, unlike traditional convolutional…

The coordinated dispatch of power and gas in the electricity-gas integrated energy system (EG-IES) is fundamental for ensuring operational security. However, the gas dynamics in the natural gas system (NGS) are governed by the nonlinear…

We introduce a novel paradigm for learning non-parametric drift and diffusion functions for stochastic differential equation (SDE). The proposed model learns to simulate path distributions that match observations with non-uniform time…

We propose a covariate-dependent discrete graphical model for capturing dynamic networks among discrete random variables, allowing the dependence structure among vertices to vary with covariates. This discrete dynamic network encompasses…

We introduce the Graph Sylvester Embedding (GSE), an unsupervised graph representation of local similarity, connectivity, and global structure. GSE uses the solution of the Sylvester equation to capture both network structure and…

Social networks have become an inseparable part of human life and processing them in an efficient manner is a top priority in the study of networks. These networks are highly dynamic and they are growing incessantly. Inspired by the concept…

In this paper we propose a distributed algorithm for the estimation and control of the connectivity of ad-hoc networks in the presence of a random topology. First, given a generic random graph, we introduce a novel stochastic power…

Graphical models provide a powerful methodology for learning the conditional independence structure in multivariate data. Inference is often focused on estimating individual edges in the latent graph. Nonetheless, there is increasing…

Neural networks with a large number of parameters admit a mean-field description, which has recently served as a theoretical explanation for the favorable training properties of "overparameterized" models. In this regime, gradient descent…

We propose a heterogeneous simultaneous graphical dynamic linear model (H-SGDLM), which extends the standard SGDLM framework to incorporate a heterogeneous autoregressive realised volatility (HAR-RV) model. This novel approach creates a…

Understanding the behavior of stochastic gradient methods is a central problem in modern machine learning. Recent work has highlighted diagonal linear networks as a simplified yet expressive setting for analyzing the optimization and…

We propose a novel class of graph neural networks based on the discretised Beltrami flow, a non-Euclidean diffusion PDE. In our model, node features are supplemented with positional encodings derived from the graph topology and jointly…

Estimating conditional independence graphs from high-dimensional Gaussian data is challenging because methods must detect relevant edges while rigorously controlling statistical errors. We propose a Bayesian framework based on a prior…

Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…

We analyze the dynamics of streaming stochastic gradient descent (SGD) in the high-dimensional limit when applied to generalized linear models and multi-index models (e.g. logistic regression, phase retrieval) with general data-covariance.…

We introduce a fast simulation technique for modeling epidemics on adaptive networks. Our rejection-based algorithm efficiently simulates the co-evolution of the network structure and the epidemic dynamics. We extend the classical SIS model…