Related papers: A spatio-temporal stochastic pattern generator for…
Generative modeling of spatio-temporal fields is crucial for a variety of applications, including stochastic weather generators and climate-model surrogates. However, many such fields exhibit complex dependence structures that vary across…
Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial…
Gaussian random fields with Mat\'ern covariance functions are popular models in spatial statistics and machine learning. In this work, we develop a spatio-temporal extension of the Gaussian Mat\'ern fields formulated as solutions to a…
We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…
The solutions of Hamiltonian equations are known to describe the underlying phase space of a mechanical system. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations,…
This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies…
We propose a generative model for the spatio-temporal distribution of high dimensional categorical observations. These are commonly produced by robots equipped with an imaging sensor such as a camera, paired with an image classifier,…
Understanding and predicting environmental phenomena often requires the construction of spatio-temporal statistical models, which are typically Gaussian processes. A common assumption made on Gaussian processes is that of covariance…
We present an improved model and theory for time-causal and time-recursive spatio-temporal receptive fields, obtained by a combination of Gaussian receptive fields over the spatial domain and first-order integrators or equivalently…
We develop, simulate and extend an initial proposition by Chaves et al. concerning a random incompressible vector field able to reproduce key ingredients of three-dimensional turbulence in both space and time. In this article, we focus on…
We present an improved model and theory for time-causal and time-recursive spatio-temporal receptive fields, based on a combination of Gaussian receptive fields over the spatial domain and first-order integrators or equivalently truncated…
Fitting Gaussian Processes (GPs) provides interpretable aleatoric uncertainty quantification for estimation of spatio-temporal fields. Spatio-temporal deep learning models, while scalable, typically assume a simplistic independent…
We introduce a scalable Gaussian process (GP) framework with deep product kernels for data-driven learning of parametrized spatio-temporal fields over fixed or parameter-dependent domains. The proposed framework learns a continuous…
Gaussian Schell-model fields are examples of spatially partially coherent fields, which in recent years have found several unique applications. The existing techniques for generating Gaussian Schell-model (GSM) fields are based on…
Discrete automated processes in industrial and cyber-physical systems often exhibit a repetitive structure in which successive repetitions follow a common trajectory while differing in duration, amplitude, and fine-scale dynamics. Such…
A non-stationary spatial Gaussian random field (GRF) is described as the solution of an inhomogeneous stochastic partial differential equation (SPDE), where the covariance structure of the GRF is controlled by the coefficients in the SPDE.…
Gaussian processes provide a flexible, non-parametric framework for the approximation of functions in high-dimensional spaces. The covariance kernel is the main engine of Gaussian processes, incorporating correlations that underpin the…
This work proposes a scalable probabilistic latent variable model based on Gaussian processes (Lawrence, 2004) in the context of multiple observation spaces. We focus on an application in astrophysics where data sets typically contain both…
The Stochastic Backscatter Model involves the generation of a set of random variables characterised by prescribed correlations in space and time. These variables are obtained by smoothing an initially uncorrelated random field, which…
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…