Related papers: Edge-indexed network time series with graph Ornste…
The Ornstein-Uhlenbeck (OU) process describes the dynamics of Brownian particles in a confining harmonic potential, thereby constituting the paradigmatic model of overdamped, mean-reverting Langevin dynamics. Despite its widespread…
In today's world, modern infrastructures are being equipped with information and communication technologies to create large IoT networks. It is essential to monitor these networks to ensure smooth operations by detecting and correcting link…
In this paper, we consider the statistical inference of the drift parameter $\theta$ of non-ergodic Ornstein-Uhlenbeck~(O-U) process driven by a general Gaussian process $(G_t)_{t\ge 0}$. When $H \in (0, \frac 12) \cup (\frac 12,1) $ the…
We establish a diffusion approximation for a class of multi-agent controlled queueing systems, demonstrating their convergence to a system of interacting reflected Ornstein--Uhlenbeck (OU) processes. The limiting process captures essential…
We propose a non-Gaussian operator-valued extension of the Barndorff-Nielsen and Shephard stochastic volatility dynamics, defined as the square-root of an operator-valued Ornstein-Uhlenbeck process with Levy noise and bounded drift. We…
Forecasting univariate time series in the financial market is a challenging endeavor. While numerous statistical and machine learning models have been introduced to address this challenge, they typically concentrate solely on analyzing…
Power grid frequency stability is fundamental to the secure operation of modern energy systems, yet the growing penetration of renewables and the associated reduction of system inertia have made frequency fluctuations increasingly…
We consider a time varying analogue of the Erd{\H o}s-R{\' e}nyi graph and study the topological variations of its associated clique complex. The dynamics of the graph are stationary and are determined by the edges, which evolve…
In this paper we consider the problem of learning undirected graphical models from data generated according to the Glauber dynamics. The Glauber dynamics is a Markov chain that sequentially updates individual nodes (variables) in a…
In this paper, we consider an inference problem for an Ornstein-Uhlenbeck process driven by a general one-dimensional centered Gaussian process $(G_t)_{t\ge 0}$. The second order mixed partial derivative of the covariance function $ R(t,\,…
The so-called "supOU" processes, namely the superpositions of Ornstein-Uhlenbeck type processes are stationary processes for which one can specify separately the marginal distribution and the dependence structure. They can have finite or…
We propose an extension of the Contextual Graph Markov Model, a deep and probabilistic machine learning model for graphs, to model the distribution of edge features. Our approach is architectural, as we introduce an additional Bayesian…
Despite the recent success of graph neural networks (GNN), common architectures often exhibit significant limitations, including sensitivity to oversmoothing, long-range dependencies, and spurious edges, e.g., as can occur as a result of…
In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting…
The aim of this short note is to show that Denoising Diffusion Probabilistic Model DDPM, a non-homogeneous discrete-time Markov process, can be represented by a time-homogeneous continuous-time Markov process observed at non-uniformly…
Energy and data-efficient online time series prediction for predicting evolving dynamical systems are critical in several fields, especially edge AI applications that need to update continuously based on streaming data. However, current…
Multivariate time series is prevalent in many scientific and industrial domains. Modeling multivariate signals is challenging due to their long-range temporal dependencies and intricate interactions--both direct and indirect. To confront…
We give the first polynomial-time, differentially node-private, and robust algorithm for estimating the edge density of Erd\H{o}s-R\'enyi random graphs and their generalization, inhomogeneous random graphs. We further prove…
We present a theory-guided generalized Bayesian methodology for spatio-temporal raster data, which we use to train an ensemble of stochastic feed-forward neural networks with Gaussian-distributed weights. The methodology incorporates the…
Pedestrian trajectory prediction is an active research area with recent works undertaken to embed accurate models of pedestrians social interactions and their contextual compliance into dynamic spatial graphs. However, existing works rely…