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Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…

Machine Learning · Statistics 2018-02-02 Xiuming Liu , Dave Zachariah , Edith C. H. Ngai

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) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…

Machine Learning · Computer Science 2010-02-23 Yuan Qi , Ahmed H. Abdel-Gawad , Thomas P. Minka

Variable selection in Gaussian processes (GPs) is typically undertaken by thresholding the inverse lengthscales of automatic relevance determination kernels, but in high-dimensional datasets this approach can be unreliable. A more…

Machine Learning · Statistics 2022-02-25 Hugh Dance , Brooks Paige

Belonging to the family of Bayesian nonparametrics, Gaussian process (GP) based approaches have well-documented merits not only in learning over a rich class of nonlinear functions, but also in quantifying the associated uncertainty.…

Machine Learning · Statistics 2021-10-14 Qin Lu , Georgios V. Karanikolas , Georgios B. Giannakis

We propose a principled way to define Gaussian process priors on various sets of unweighted graphs: directed or undirected, with or without loops. We endow each of these sets with a geometric structure, inducing the notions of closeness and…

Machine Learning · Statistics 2023-02-28 Viacheslav Borovitskiy , Mohammad Reza Karimi , Vignesh Ram Somnath , Andreas Krause

Gaussian process (GP) regression is a fundamental tool in Bayesian statistics. It is also known as kriging and is the Bayesian counterpart to the frequentist kernel ridge regression. Most of the theoretical work on GP regression has focused…

Statistics Theory · Mathematics 2023-10-27 Simon Barthelmé , Pierre-Olivier Amblard , Nicolas Tremblay , Konstantin Usevich

Gaussian processes (GPs) provide a gold standard for performance in online settings, such as sample-efficient control and black box optimization, where we need to update a posterior distribution as we acquire data in a sequential fashion.…

Machine Learning · Statistics 2021-03-03 Samuel Stanton , Wesley J. Maddox , Ian Delbridge , Andrew Gordon Wilson

Although machine learning is increasingly applied in control approaches, only few methods guarantee certifiable safety, which is necessary for real world applications. These approaches typically rely on well-understood learning algorithms,…

Machine Learning · Computer Science 2020-06-16 Armin Lederer , Markus Kessler , Sandra Hirche

Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost for big data. In this paper, we propose a new Bayesian approach, EigenGP, that learns both…

Machine Learning · Computer Science 2015-07-14 Hao Peng , Yuan Qi

Amidst the growing interest in nonparametric regression, we address a significant challenge in Gaussian processes(GP) applied to manifold-based predictors. Existing methods primarily focus on low dimensional constrained domains for heat…

Optimization and Control · Mathematics 2024-02-01 Ke Ye , Mu Niu , Pokman Cheung , Zhenwen Dai , Yuan Liu

We propose two methods for exact Gaussian process (GP) inference and learning on massive image, video, spatial-temporal, or multi-output datasets with missing values (or "gaps") in the observed responses. The first method ignores the gaps…

Machine Learning · Statistics 2018-08-13 Trefor W. Evans , Prasanth B. Nair

To speed up Gaussian process inference, a number of fast kernel matrix-vector multiplication (MVM) approximation algorithms have been proposed over the years. In this paper, we establish an exact fast kernel MVM algorithm based on exact…

Machine Learning · Statistics 2025-08-05 Nicolas Langrené , Xavier Warin , Pierre Gruet

Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are nonparametric probabilistic models…

Mechanistic simulation models are inverted against observations in order to gain inference on modeled processes. However, with the increasing ability to collect high resolution observations, these observations represent more patterns of…

Computation · Statistics 2018-12-20 Thomas Wutzler

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

Machine Learning · Statistics 2022-04-29 Alexander Terenin

In decision-making systems, it is important to have classifiers that have calibrated uncertainties, with an optimisation objective that can be used for automated model selection and training. Gaussian processes (GPs) provide uncertainty…

Machine Learning · Statistics 2020-03-05 Vincent Dutordoir , Mark van der Wilk , Artem Artemev , James Hensman

We propose a representation of Gaussian processes (GPs) based on powers of the integral operator defined by a kernel function, we call these stochastic processes integral Gaussian processes (IGPs). Sample paths from IGPs are functions…

Machine Learning · Statistics 2019-03-08 Zilong Tan , Sayan Mukherjee

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

Machine Learning · Statistics 2014-10-01 Yarin Gal , Mark van der Wilk , Carl E. Rasmussen

Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…

Machine Learning · Computer Science 2025-07-10 Jihao Andreas Lin