Related papers: Edge-indexed network time series with graph Ornste…
Complex Ornstein-Uhlenbeck (OU) processes have various applications in statistical modelling. They play role e.g. in the description of the motion of a charged test particle in a constant magnetic field or in the study of rotating waves in…
Graph processes exhibit a temporal structure determined by the sequence index and and a spatial structure determined by the graph support. To learn from graph processes, an information processing architecture must then be able to exploit…
Graph Neural Networks (GNNs) have been widely used for modeling graph-structured data. With the development of numerous GNN variants, recent years have witnessed groundbreaking results in improving the scalability of GNNs to work on static…
In many domains, including healthcare, biology, and climate science, time series are irregularly sampled with varying time intervals between successive readouts and different subsets of variables (sensors) observed at different time points.…
The linear fractional stable motion generalizes two prominent classes of stochastic processes, namely stable L\'evy processes, and fractional Brownian motion. For this reason it may be regarded as a basic building block for continuous time…
This paper introduces an online approach for identifying time-varying subspaces defined by linear dynamical systems. The approach of representing linear systems by non-parametric subspace models has received significant interest in the…
Existing Graph Neural Network (GNN) methods that learn inductive unsupervised graph representations focus on learning node and edge representations by predicting observed edges in the graph. Although such approaches have shown advances in…
In this work we investigate the long time behavior of the Ornstein-Uhlenbeck process driven by Levy noise with regime-switching. We provide explicit criteria on the transience and recurrence of this process. Contrasted with the…
Optimal power flow (OPF) has been used for real-time grid operations. Prior efforts demonstrated that utilizing flexibility from dynamic topologies will improve grid efficiency. However, this will convert the linear OPF into a mixed-integer…
We propose an automatable data-driven methodology for robust nonlinear reduced-order modelling from time-resolved snapshot data. In the kinematical coarse-graining, the snapshots are clustered into few centroids representable for the whole…
This paper introduces an open-source and reproducible implementation of Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) Networks for time series forecasting. We evaluated LSTM and GRU networks because of their performance…
Modeling neural population dynamics is crucial for foundational neuroscientific research and various clinical applications. Conventional latent variable methods typically model continuous brain dynamics through discretizing time with…
We consider a reflected Ornstein-Uhlenbeck process $X$ driven by a fractional Brownian motion with Hurst parameter $H\in (0, \frac12) \cup (\frac12, 1)$. Our goal is to estimate an unknown drift parameter $\alpha\in (-\infty,\infty)$ on the…
Motivated by the need of observers that are both robust to disturbances and guarantee fast convergence to zero of the estimation error, we propose an observer for linear time-invariant systems with noisy output that consists of the…
In this paper we introduce the well-balanced L\'{e}vy driven Ornstein-Uhlenbeck process as a moving average process of the form $X_t=\int \exp(-\lambda |t-u|)dL_u$. In contrast to L\'{e}vy driven Ornstein-Uhlenbeck processes the…
We analyze the problem of the analytical characterization of the probability distribution of financial returns in the exponential Ornstein-Uhlenbeck model with stochastic volatility. In this model the prices are driven by a Geometric…
We consider the problem of efficient estimation of the drift parameter of an Ornstein-Uhlenbeck type process driven by a L\'{e}vy process when high-frequency observations are given. The estimator is constructed from the time-continuous…
This paper proposes an autoregressive (AR) model for sequences of graphs, which generalises traditional AR models. A first novelty consists in formalising the AR model for a very general family of graphs, characterised by a variable…
Many real-world complex systems, such as epidemic spreading networks and ecosystems, can be modeled as networked dynamical systems that produce multivariate time series. Learning the intrinsic dynamics from observational data is pivotal for…
Score-based Generative Models (SGMs) aim to sample from a target distribution by learning score functions using samples perturbed by Gaussian noise. Existing convergence bounds for SGMs in the W2-distance rely on stringent assumptions about…