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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…
We introduce a framework for the reconstruction and representation of functions in a setting where these objects cannot be directly observed, but only indirect and noisy measurements are available, namely an inverse problem setting. The…
There has been a recent surge of interest in time series modeling using the Transformer architecture. However, forecasting multivariate time series with Transformer presents a unique challenge as it requires modeling both temporal…
Multivariate time series are ubiquitous objects in signal processing. Measuring a distance or similarity between two such objects is of prime interest in a variety of applications, including machine learning, but can be very difficult as…
Spatial-temporal data modeling aims to mine the underlying spatial relationships and temporal dependencies of objects in a system. However, most existing methods focus on the modeling of spatial-temporal data in a single mode, lacking the…
Modelling multivariate circular time series is considered. The cross-sectional and serial dependence is described by circulas, which are analogs of copulas for circular distributions. In order to obtain a simple expression of the dependence…
Accurate stochastic simulations of hourly precipitation are needed for impact studies at local spatial scales. Statistically, hourly precipitation data represent a difficult challenge. They are non-negative, skewed, heavy tailed, contain a…
One approach to understanding complex data is to study its shape through the lens of algebraic topology. While the early development of topological data analysis focused primarily on static data, in recent years, theoretical and applied…
We develop multiple Deep Learning (DL) models that advance the state-of-the-art predictions of the global auroral particle precipitation. We use observations from low Earth orbiting spacecraft of the electron energy flux to develop a model…
Time series sequence prediction and modelling has proven to be a challenging endeavor in real world datasets. Two key issues are the multi-dimensionality of data and the interaction of independent dimensions forming a latent output signal,…
Spatio-temporal covariances are important for describing the spatio-temporal variability of underlying random processes in geostatistical data. For second-order stationary processes, there exist subclasses of covariance functions that…
High-dimensional vector autoregressive (VAR) models provide a flexible framework for characterizing dynamic dependence in multivariate spatio-temporal systems, but their unrestricted estimation becomes infeasible when multiple variables are…
Traditional methods for covariate adjustment of treatment means in designed experiments are inherently conditional on the observed covariate values. In order to develop a coherent general methodology for analysis of covariance, we propose a…
We introduce a method for decomposition of trend, cycle and seasonal components in spatio-temporal models and apply it to investigate the existence of climate changes in temperature and rainfall series. The method incorporates critical…
The exact 1+3 covariant dynamical fluid equations for a multi-component plasma, together with Maxwell's equations are presented in such a way as to make them suitable for a gauge-invariant analysis of linear density and velocity…
We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. We envision this method being generally applicable…
Covariates provide valuable information on external factors that influence time series and are critical in many real-world time series forecasting tasks. For example, in retail, covariates may indicate promotions or peak dates such as…
This paper develops forecasting methodology and application of new classes of dynamic models for time series of non-negative counts. Novel univariate models synthesise dynamic generalized linear models for binary and conditionally Poisson…
Solar radio flux along with geomagnetic indices are important indicators of solar activity and its effects. Extreme solar events such as flares and geomagnetic storms can negatively affect the space environment including satellites in…
In geostatistics, it is common to model spatially distributed phenomena through an underlying stationary and isotropic spatial process. However, these assumptions are often untenable in practice because of the influence of local effects in…