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Gaussian processes are a flexible Bayesian nonparametric modelling approach that has been widely applied but poses computational challenges. To address the poor scaling of exact inference methods, approximation methods based on sparse…

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

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…

The Gaussian process (GP) is a popular statistical technique for stochastic function approximation and uncertainty quantification from data. GPs have been adopted into the realm of machine learning in the last two decades because of their…

Many inferential tasks involve fitting models to observed data and predicting outcomes at new covariate values, requiring interpolation or extrapolation. Conventional methods select a single best-fitting model, discarding fits that were…

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) have been widely used in machine learning to model distributions over functions, with applications including multi-modal regression, time-series prediction, and few-shot learning. GPs are particularly useful in the…

The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially…

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…

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,…

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…

Gaussian Processes (GPs) are powerful non-parametric Bayesian models for regression of scalar fields, formulated under the assumption that measurement locations are perfectly known and the corresponding field measurements have Gaussian…

The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…

In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…

Multi-output Gaussian process (MGP) has been attracting increasing attention as a transfer learning method to model multiple outputs. Despite its high flexibility and generality, MGP still faces two critical challenges when applied to…

For many expensive deterministic computer simulators, the outputs do not have replication error and the desired metamodel (or statistical emulator) is an interpolator of the observed data. Realizations of Gaussian spatial processes (GP) are…

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…

Gaussian process (GP) models are widely used to emulate propagation uncertainty in computer experiments. GP emulation sits comfortably within an analytically tractable Bayesian framework. Apart from propagating uncertainty of the input…

Estimating causal effects in quasi-experiments with spatio-temporal panel data often requires adjusting for unmeasured confounding that varies across space and time. Gaussian Processes (GPs) offer a flexible, nonparametric modeling approach…