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Gaussian processes are machine learning models capable of learning unknown functions in a way that represents uncertainty, thereby facilitating construction of optimal decision-making systems. Motivated by a desire to deploy Gaussian…

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…

Machine Learning · Statistics 2025-06-02 Gabriel V Cardoso , Mike Pereira

This document serves to complement our website which was developed with the aim of exposing the students to Gaussian Processes (GPs). GPs are non-parametric Bayesian regression models that are largely used by statisticians and geospatial…

Machine Learning · Computer Science 2018-09-07 Kshitij Tiwari

Sparse variational Gaussian processes (GPs) construct tractable posterior approximations to GP models. At the core of these methods is the assumption that the true posterior distribution over training function values ${\bf f}$ and inducing…

Machine Learning · Computer Science 2025-06-27 Michalis K. Titsias

Multi-output regression models must exploit dependencies between outputs to maximise predictive performance. The application of Gaussian processes (GPs) to this setting typically yields models that are computationally demanding and have…

Machine Learning · Statistics 2019-02-27 James Requeima , Will Tebbutt , Wessel Bruinsma , Richard E. Turner

Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…

Machine Learning · Computer Science 2016-03-08 Z. Zhang , K. Duraisamy , N. A. Gumerov

Automatic forecasting is the task of receiving a time series and returning a forecast for the next time steps without any human intervention. Gaussian Processes (GPs) are a powerful tool for modeling time series, but so far there are no…

Machine Learning · Statistics 2023-04-27 Giorgio Corani , Alessio Benavoli , Marco Zaffalon

Observations of exoplanet atmospheres in high resolution have the potential to resolve individual planetary absorption lines, despite the issues associated with ground-based observations. The removal of contaminating stellar and telluric…

Earth and Planetary Astrophysics · Physics 2022-03-18 Annabella Meech , Suzanne Aigrain , Matteo Brogi , Jayne Birkby

Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…

Gaussian processes (GPs) are widely used as distributions of random effects in linear mixed models, which are fit using the restricted likelihood or the closely-related Bayesian analysis. This article addresses two problems. First, we…

Methodology · Statistics 2018-05-04 Maitreyee Bose , James S. Hodges , Sudipto Banerjee

Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models.…

Machine Learning · Computer Science 2025-02-04 Oliver Hamelijnck , Arno Solin , Theodoros Damoulas

Deep Gaussian Processes (DGPs) are multi-layer, flexible extensions of Gaussian processes but their training remains challenging. Sparse approximations simplify the training but often require optimization over a large number of inducing…

Machine Learning · Statistics 2021-07-20 Ayush Jain , P. K. Srijith , Mohammad Emtiyaz Khan

In many areas of the observational and experimental sciences data is scarce. Data observation in high-energy astrophysics is disrupted by celestial occlusions and limited telescope time while data derived from laboratory experiments in…

Machine Learning · Statistics 2023-03-28 Ryan-Rhys Griffiths

Gaussian Processes (GPs) are expressive models for capturing signal statistics and expressing prediction uncertainty. As a result, the robotics community has gathered interest in leveraging these methods for inference, planning, and…

Robotics · Computer Science 2023-08-29 Francesco Crocetti , Jeffrey Mao , Alessandro Saviolo , Gabriele Costante , Giuseppe Loianno

Gaussian processes (GPs) are highly flexible function estimators used for geospatial analysis, nonparametric regression, and machine learning, but they are computationally infeasible for large datasets. Vecchia approximations of GPs have…

Methodology · Statistics 2020-12-22 Matthias Katzfuss , Joseph Guinness , Wenlong Gong , Daniel Zilber

Derivatives are a key nonparametric functional in wide-ranging applications where the rate of change of an unknown function is of interest. In the Bayesian paradigm, Gaussian processes (GPs) are routinely used as a flexible prior for…

Statistics Theory · Mathematics 2025-12-30 Zejian Liu , Meng Li

Gaussian Process (GPs) models are a rich distribution over functions with inductive biases controlled by a kernel function. Learning occurs through the optimisation of kernel hyperparameters using the marginal likelihood as the objective.…

Machine Learning · Statistics 2021-11-22 Fergus Simpson , Vidhi Lalchand , Carl Edward Rasmussen

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…

Machine Learning · Computer Science 2026-03-03 Srinath Dama , Prasanth B. Nair

Gaussian processes constitute a very powerful and well-understood method for non-parametric regression and classification. In the classical framework, the training data consists of deterministic vector-valued inputs and the corresponding…

Systems and Control · Computer Science 2018-09-26 Maxim Dolgov , Uwe D. Hanebeck

A multi-output Gaussian process (GP) is introduced as a model for the joint posterior distribution of the local predictive ability of set of models and/or experts, conditional on a vector of covariates, from historical predictions in the…

Methodology · Statistics 2024-10-08 Oscar Oelrich , Mattias Villani