Related papers: Learning Temporal Evolution of Spatial Dependence …

This work presents a non-parametric spatio-temporal model for mapping human activity by mobile autonomous robots in a long-term context. Based on Variational Gaussian Process Regression, the model incorporates prior information of spatial…

In the study "Spatio-temporal Gaussian process models for extended and group object tracking with irregular shapes" (IEEE Trans. Veh. Tech., vol. 68, no. 3, pp. 2137-2151, Mar. 2019), the extended object tracking problem was tackled by an…

Deep learning methods achieve remarkable predictive performance in modeling complex, large-scale data. However, assessing the quality of derived models has become increasingly challenging, as more classical statistical assumptions may no…

We develop a Bayesian approach to learning from sequential data by using Gaussian processes (GPs) with so-called signature kernels as covariance functions. This allows to make sequences of different length comparable and to rely on strong…

Very large spatio-temporal lattice data are becoming increasingly common across a variety of disciplines. However, estimating interdependence across space and time in large areal datasets remains challenging, as existing approaches are…

We introduce a nonstationary spatio-temporal statistical model for gridded data on the sphere. The model specifies a computationally convenient covariance structure that depends on heterogeneous geography. Widely used statistical models on…

2D Gaussian Splatting (2DGS) has recently become a promising paradigm for high-quality video representation. However, existing methods employ content-agnostic or spatio-temporal feature overlapping embeddings to predict canonical Gaussian…

Data derived from remote sensing or numerical simulations often have a regular gridded structure and are large in volume, making it challenging to find accurate spatial models that can fill in missing grid cells or simulate the process…

Spatio-temporal processes often exhibit highly heterogeneous and non-intuitive responses to localized disruptions, limiting the effectiveness of conventional message passing approaches in modeling local heterogeneity. We reformulate…

We present a theory-guided generalized Bayesian methodology for spatio-temporal raster data, which we use to train an ensemble of stochastic feed-forward neural networks with Gaussian-distributed weights. The methodology incorporates the…

Stochastic Gradient Langevin Dynamics (SGLD) is a popular variant of Stochastic Gradient Descent, where properly scaled isotropic Gaussian noise is added to an unbiased estimate of the gradient at each iteration. This modest change allows…

Effective multivariate time series forecasting often benefits from accurately modeling complex inter-variable dependencies. However, existing attention- or graph-based methods face three key issues: (a) strong temporal self-dependencies are…

State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…

Bayesian models based on Gaussian processes (GPs) offer a flexible framework to predict spatially distributed variables with uncertainty. But the use of nonstationary priors, often necessary for capturing complex spatial patterns, makes…

We introduce a Gaussian process-based model for handling of non-stationarity. The warping is achieved non-parametrically, through imposing a prior on the relative change of distance between subsequent observation inputs. The model allows…

Among various region embedding methods, graph-based region relation learning models stand out, owing to their strong structure representation ability for encoding spatial correlations with graph neural networks. Despite their effectiveness,…

Multi-task Gaussian process (MTGP) is a well-known non-parametric Bayesian model for learning correlated tasks effectively by transferring knowledge across tasks. But current MTGPs are usually limited to the multi-task scenario defined in…

Deep Gaussian process models typically employ discrete hierarchies, but recent advancements in differential Gaussian processes (DiffGPs) have extended these models to infinite depths. However, existing DiffGP approaches often overlook the…

We construct flexible spatio-temporal models through stochastic partial differential equations (SPDEs) where both diffusion and advection can be spatially varying. Computations are done through a Gaussian Markov random field approximation…

Spatiotemporal graph neural networks (STGNNs) have shown promising results in many domains, from forecasting to epidemiology. However, understanding the dynamics learned by these models and explaining their behaviour is significantly more…