Related papers: Spatial and Spatio-Temporal Log-Gaussian Cox Proce…

In geostatistics, traditional spatial models often rely on the Gaussian Process (GP) to fit stationary covariances to data. It is well known that this approach becomes computationally infeasible when dealing with large data volumes,…

Temporal point process as the stochastic process on continuous domain of time is commonly used to model the asynchronous event sequence featuring with occurrence timestamps. Thanks to the strong expressivity of deep neural networks, they…

Scientific and engineering problems often require the use of artificial intelligence to aid understanding and the search for promising designs. While Gaussian processes (GP) stand out as easy-to-use and interpretable learners, they have…

The Gaussian process is a powerful and flexible technique for interpolating spatiotemporal data, especially with its ability to capture complex trends and uncertainty from the input signal. This chapter describes Gaussian processes as an…

We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…

With the advancement of GPS and remote sensing technologies, large amounts of geospatial and spatiotemporal data are being collected from various domains, driving the need for effective and efficient prediction methods. Given spatial data…

Discrete time spatial time series data arise routinely in meteorological and environmental studies. Inference and prediction associated with them are mostly carried out using any of the several variants of the linear state space model that…

The use of Gaussian processes (GPs) as models for astronomical time series datasets has recently become almost ubiquitous, given their ease of use and flexibility. GPs excel in particular at marginalization over the stellar signal in cases…

We develop a stochastic modeling approach based on spatial point processes of log-Gaussian Cox type for a collection of around 5000 landslide events provoked by a precipitation trigger in Sicily, Italy. Through the embedding into a…

Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…

A critical bottleneck for scientific progress is the costly nature of computer simulations for complex systems. Surrogate models provide an appealing solution: such models are trained on simulator evaluations, then used to emulate and…

We propose a statistical model for narrowing line shapes in spectroscopy that are well approximated as linear combinations of Lorentzian or Voigt functions. We introduce a log-Gaussian Cox process to represent the peak locations thereby…

This paper proposes an online learning method of Gaussian process state-space model (GP-SSM). GP-SSM is a probabilistic representation learning scheme that represents unknown state transition and/or measurement models as Gaussian processes…

A Gaussian Process GP based ground segmentation method is proposed in this paper which is fully developed in a probabilistic framework. The proposed method tends to obtain a continuous realistic model of the ground. The LiDAR…

This paper presents a Bayesian generative model for dependent Cox point processes, alongside an efficient inference scheme which scales as if the point processes were modelled independently. We can handle missing data naturally, infer…

Multi-task regression attempts to exploit the task similarity in order to achieve knowledge transfer across related tasks for performance improvement. The application of Gaussian process (GP) in this scenario yields the non-parametric yet…

Spatio-temporal modelling is an increasingly popular topic in Statistics. Our paper contributes to this line of research by developing the theory, simulation and inference for a spatio-temporal Ornstein-Uhlenbeck process. We conduct…

Latent confounders---unobserved variables that influence both treatment and outcome---can bias estimates of causal effects. In some cases, these confounders are shared across observations, e.g. all students taking a course are influenced by…

Spatio-temporal systems exhibiting multi-scale behaviour are common in applications ranging from cyber-physical systems to systems biology, yet they present formidable challenges for computational modelling and analysis. Here we consider a…

Some scenarios require the computation of a predictive distribution of a new value evaluated on an objective function conditioned on previous observations. We are interested on using a model that makes valid assumptions on the objective…