Related papers: Stationary time-vertex signal processing

Modeling inter-dependencies between time-series is the key to achieve high performance in anomaly detection for multivariate time-series data. The de-facto solution to model the dependencies is to feed the data into a recurrent neural…

Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and…

Multivariate time series data that capture the temporal evolution of interconnected systems are ubiquitous in diverse areas. Understanding the complex relationships and potential dependencies among co-observed variables is crucial for the…

This work introduces a novel, simple, and flexible method to quantify irreversibility in generic high-dimensional time series based on the well-known mapping to a binary classification problem. Our approach utilizes gradient boosting for…

Learning the dynamics of complex systems features a large number of applications in data science. Graph-based modeling and inference underpins the most prominent family of approaches to learn complex dynamics due to their ability to capture…

Time-dependent data often exhibit characteristics, such as non-stationarity and heavy-tailed errors, that would be inappropriate to model with the typical assumptions used in popular models. Thus, more flexible approaches are required to be…

High dimensional piecewise stationary graphical models represent a versatile class for modelling time varying networks arising in diverse application areas, including biology, economics, and social sciences. There has been recent work in…

High-dimensional multivariate time series are challenging due to the dependent and high-dimensional nature of the data, but in many applications there is additional structure that can be exploited to reduce computing time along with…

Our understanding of a variety of phenomena in physics, biology and economics crucially depends on the analysis of multivariate time series. While a wide range of tools and techniques for time series analysis already exist, the increasing…

The analysis of nonstationary time series is of great importance in many scientific fields such as physics and neuroscience. In recent years, Gaussian process regression has attracted substantial attention as a robust and powerful method…

State-space models effectively model multivariate time series by updating over time a representation of the system state from which predictions are made. The state representation is usually a vector without any explicit structure.…

Graph representations offer powerful and intuitive ways to describe data in a multitude of application domains. Here, we consider stochastic processes generating graphs and propose a methodology for detecting changes in stationarity of such…

Time series analysis has gained significant attention due to its critical applications in diverse fields such as healthcare, finance, and sensor networks. The complexity and non-stationarity of time series make it challenging to capture the…

We study the problem of graph structure identification, i.e., of recovering the graph of dependencies among time series. We model these time series data as components of the state of linear stochastic networked dynamical systems. We assume…

We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix…

We develop a timescale synthesis-based probabilistic approach for the modeling of locally stationary signals. Inspired by our previous work, the model involves zero-mean, complex Gaussian wavelet coefficients, whose distribution varies as a…

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…

Graphical interaction models have become an important tool for analysing multivariate time series. In these models, the interrelationships among the components of a time series are described by undirected graphs in which the vertices depict…

During the last two decades, locally stationary processes have been widely studied in the time series literature. In this paper we consider the locally-stationary vector-auto-regression model of order one, or LS-VAR(1), and estimate its…

Recent studies have shown great promise in applying graph neural networks for multivariate time series forecasting, where the interactions of time series are described as a graph structure and the variables are represented as the graph…