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Vector autoregressions (VARs) are a widely used tool for modelling multivariate time-series. It is common to assume a VAR is stationary; this can be enforced by imposing the stationarity condition which restricts the parameter space of the…
Vector autoregressive (VAR) models have become a staple in the analysis of multivariate time series and are formulated in the time domain as difference equations, with an implied covariance structure. In many contexts, it is desirable to…
Real-world time series often exhibit complex interdependencies that cannot be captured in isolation. Global models that model past data from multiple related time series globally while producing series-specific forecasts locally are now…
We present an uncertainty principle for graph signals in the vertex-time domain, unifying the classical time-frequency and graph uncertainty principles within a single framework. By defining vertex-time and spectral-frequency spreads, we…
We propose graph-based predictable feature analysis (GPFA), a new method for unsupervised learning of predictable features from high-dimensional time series, where high predictability is understood very generically as low variance in the…
Accurate multivariate time series forecasting hinges on inter-series correlations, which often evolve in complex ways across different temporal scales. Existing methods are limited in modeling these multi-scale dependencies and struggle to…
Dynamic graph signal processing provides a principled framework for analyzing time-varying data defined on irregular graph domains. However, existing joint time-vertex transforms such as the joint time-vertex fractional Fourier transform…
This work contributes to the development of neural forecasting models with novel randomization-based learning methods. These methods improve the fitting abilities of the neural model, in comparison to the standard method, by generating…
Graph neural networks have emerged as a powerful tool for learning spatiotemporal interactions. However, conventional approaches often rely on predefined graphs, which may obscure the precise relationships being modeled. Additionally,…
In this paper, we aim to improve multivariate anomaly detection (AD) by modeling the \textit{time-varying non-linear spatio-temporal correlations} found in multivariate time series data . In multivariate time series data, an anomaly may be…
Linear time series modelling is dominated by the use of purely autoregressive models even though incorporating moving average components can greatly improve parsimony. We present a convex formulation for vector-ARMA system identification…
In many applications we are interested in making inference on latent time series from indirect measurements, which are often low-dimensional projections resulting from mixing or aggregation. Positron emission tomography, super-resolution,…
Causal inference in multivariate time series is challenging due to the fact that the sampling rate may not be as fast as the timescale of the causal interactions. In this context, we can view our observed series as a subsampled version of…
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.…
Modelling dynamically evolving spatio-temporal signals is a prominent challenge in the Graph Neural Network (GNN) literature. Notably, GNNs assume an existing underlying graph structure. While this underlying structure may not always exist…
Graphs are commonly used to represent objects, such as images and text, for pattern classification. In a dynamic world, an object may continuously evolve over time, and so does the graph extracted from the underlying object. These changes…
Time series prediction is crucial for understanding and forecasting complex dynamics in various domains, ranging from finance and economics to climate and healthcare. Based on Transformer architecture, one approach involves encoding…
High-dimensional networks play a key role in understanding complex relationships. These relationships are often dynamic in nature and can change with multiple external factors (e.g., time and groups). Methods for estimating graphical models…
We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. In a time series graph, each component of the vector series is represented by distinct node,…
Time series of individual subjects have become a common data type in psychological research. These data allow one to estimate models of within-subject dynamics, and thereby avoid the notorious problem of making within-subjects inferences…