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Time series of matrix-valued data are increasingly available in various areas including economics, finance, social science, among others. These data may shed light on the inter-dynamical relationships between two sets of attributes, for…
Modelling the extremal dependence structure of spatial data is considerably easier if that structure is stationary. However, for data observed over large or complicated domains, non-stationarity will often prevail. Current methods for…
Understanding the dynamical response of quantum materials is central to revealing their microscopic properties, yet access to long-time and large-scale dynamics remains severely limited by rapidly growing computational costs and…
To obtain a probabilistic model for a dependent variable based on some set of explanatory variables, a distributional approach is often adopted where the parameters of the distribution are linked to regressors. In many classical models this…
A Vector Auto-Regressive (VAR) model is commonly used to model multivariate time series, and there are many penalized methods to handle high dimensionality. However in terms of spatio-temporal data, most methods do not take the spatial and…
Spatial processes observed in various fields, such as climate and environmental science, often occur on a large scale and demonstrate spatial nonstationarity. Fitting a Gaussian process with a nonstationary Mat\'ern covariance is…
Autoregressive models have recently shown great promise in visual generation by leveraging discrete token sequences akin to language modeling. However, existing approaches often suffer from inefficiency, either due to token-by-token…
We address the problem of prediction for extreme observations by proposing an extremal linear prediction method. We construct an inner product space of nonnegative random variables derived from transformed-linear combinations of independent…
We develop a class of nearest-neighbor mixture models that provide direct, computationally efficient, probabilistic modeling for non-Gaussian geospatial data. The class is defined over a directed acyclic graph, which implies conditional…
Quantifying the impacts of anthropogenic global warming requires accurate Earth system model (ESM) simulations. Statistical bias correction and downscaling can be applied to reduce errors and increase the resolution of ESMs. However,…
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,…
Traffic forecasting is a challenging task due to the complex spatio-temporal correlations among traffic series. In this paper, we identify an underexplored problem in multivariate traffic series prediction: extreme events. Road congestion…
Spatial maps of extreme precipitation are crucial in flood protection. With the aim of producing maps of precipitation return levels, we propose a novel approach to model a collection of spatially distributed time series where the…
Understanding the spatial distribution of animals, during all their life phases, as well as how the distributions are influenced by environmental covariates, is a fundamental requirement for the effective management of animal populations.…
Convolutional neural networks have been widely applied to hyperspectral image classification. However, traditional convolutions can not effectively extract features for objects with irregular distributions. Recent methods attempt to address…
Diffusion models have emerged as powerful generative frameworks with widespread applications across machine learning and artificial intelligence systems. While current research has predominantly focused on linear diffusions, these…
Heavy-tailed distributions have been studied in statistics, random matrix theory, physics, and econometrics as models of correlated systems, among other domains. Further, heavy-tail distributed eigenvalues of the covariance matrix of the…
The conditional autoregressive model is a routinely used statistical model for areal data that arise from, for instances, epidemiological, socio-economic or ecological studies. Various multivariate conditional autoregressive models have…
Inference in extreme value theory relies on a limited number of extreme observations, making estimation challenging. To address this limitation, we propose a non-parametric simulation scheme, the multivariate extreme events spectral…
In time-series analyses, particularly for finance, generalized autoregressive conditional heteroscedasticity (GARCH) models are widely applied statistical tools for modelling volatility clusters (i.e., periods of increased or decreased…