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Gaussian Processes (GPs) are widely recognized as powerful non-parametric models for regression and classification. Traditional GP frameworks predominantly operate under the assumption that the inputs are either accurately known or subject…

Gaussian processes (GPs) are the most common formalism for defining probability distributions over spaces of functions. While applications of GPs are myriad, a comprehensive understanding of GP sample paths, i.e. the function spaces over…

Gaussian Processes (GPs) are a popular approach to predict the output of a parameterized experiment. They have many applications in the field of Computer Experiments, in particular to perform sensitivity analysis, adaptive design of…

Functional covariates arise in many scientific and engineering applications when model inputs take the form of time-dependent or spatially distributed profiles, such as varying boundary conditions or changing material behaviours. In…

This study utilized the Gaussian Processes (GPs) regression framework to establish stochastic error bounds between the actual and predicted state evolution of nonlinear systems. These systems are embedded in the linear parameter-varying…

Gaussian Process (GP) models are popular tools in uncertainty quantification (UQ) because they purport to furnish functional uncertainty estimates that can be used to represent model uncertainty. It is often difficult to state with…

This paper presents a novel approach for approximate integration over the uncertainty of noise and signal variances in Gaussian process (GP) regression. Our efficient and straightforward approach can also be applied to integration over…

We propose a novel calibration method for computer simulators, dealing with the problem of covariate shift. Covariate shift is the situation where input distributions for training and test are different, and ubiquitous in applications of…

Identifying dynamical system (DS) is a vital task in science and engineering. Traditional methods require numerous calls to the DS solver, rendering likelihood-based or least-squares inference frameworks impractical. For efficient parameter…

Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and…

In nonparametric regression, it is common for the inputs to fall in a restricted subset of Euclidean space. Typical kernel-based methods that do not take into account the intrinsic geometry of the domain across which observations are…

Computer models, also known as simulators, can be computationally expensive to run, and for this reason statistical surrogates, known as emulators, are often used. Any statistical model, including an emulator, should be validated before…

Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but that are rarely used in signal processing. In this tutorial, we present GPs for regression as…

Deep Gaussian Processes (DGPs) compose GP layers to warp inputs, enabling improved emulation of computer models with nonstationary input-output behavior compared with ordinary GPs. In contrast to GPs, the predictive uncertainty for DGP…

Gaussian Process (GP) emulators are widely used to approximate complex computer model behaviour across the input space. Motivated by the problem of coupling computer models, recently progress has been made in the theory of the analysis of…

We present a common framework for Bayesian emulation methodologies for multivariate-output simulators, or computer models, that employ either parametric linear models or nonparametric Gaussian processes. Novel diagnostics suitable for…

Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…

Learning precise surrogate models of complex computer simulations and physical machines often require long-lasting or expensive experiments. Furthermore, the modeled physical dependencies exhibit nonlinear and nonstationary behavior.…

Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…

Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems,…