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Gaussian processes~(Kriging) are interpolating data-driven models that are frequently applied in various disciplines. Often, Gaussian processes are trained on datasets and are subsequently embedded as surrogate models in optimization…

Optimization and Control · Mathematics 2024-01-17 Artur M. Schweidtmann , Dominik Bongartz , Daniel Grothe , Tim Kerkenhoff , Xiaopeng Lin , Jaromil Najman , Alexander Mitsos

Exact Kriging and conditional simulation (CS) for uncertainty quantification are computationally infeasible for modern spatial analyses with large numbers of observations and dense prediction grids. We present a rapid approximation to the…

Methodology · Statistics 2026-05-29 Ziyu Li , Gregory Fasshauer , Douglas Nychka

We provide a new kriging procedure of processes on graphs. Based on the construction of Gaussian random processes indexed by graphs, we extend to this framework the usual linear prediction method for spatial random fields, known as kriging.…

Statistics Theory · Mathematics 2014-06-26 Thibault Espinasse , Jean-Michel Loubes

Parameter estimation is crucial for modeling, tracking, and control of complex dynamical systems. However, parameter uncertainties can compromise system performance under a controller relying on nominal parameter values. Typically,…

Robotics · Computer Science 2020-02-20 Mouhyemen Khan , Abhijit Chatterjee

Nonstationary Gaussian process models can capture complex spatially varying dependence structures in spatial datasets. However, the large number of observations in modern datasets makes fitting such models computationally intractable with…

Computation · Statistics 2022-06-13 Paul G. Beckman , Christopher J. Geoga , Michael L. Stein , Mihai Anitescu

Gaussian Processes (GPs) can be used as flexible, non-parametric function priors. Inspired by the growing body of work on Normalizing Flows, we enlarge this class of priors through a parametric invertible transformation that can be made…

Machine Learning · Computer Science 2021-02-26 Juan Maroñas , Oliver Hamelijnck , Jeremias Knoblauch , Theodoros Damoulas

In spatial statistics, a common objective is to predict values of a spatial process at unobserved locations by exploiting spatial dependence. Kriging provides the best linear unbiased predictor using covariance functions and is often…

Machine Learning · Statistics 2022-05-25 Wanfang Chen , Yuxiao Li , Brian J Reich , Ying Sun

Kriging (or Gaussian process regression) is a popular machine learning method for its flexibility and closed-form prediction expressions. However, one of the key challenges in applying kriging to engineering systems is that the available…

Methodology · Statistics 2020-12-23 Jialei Chen , Zhehui Chen , Chuck Zhang , C. F. Jeff Wu

Gaussian processes (GPs) are Bayesian nonparametric models for function approximation with principled predictive uncertainty estimates. Deep Gaussian processes (DGPs) are multilayer generalizations of GPs that can represent complex marginal…

Machine Learning · Statistics 2024-09-20 Qiuxian Meng , Yongyou Zhang

Gaussian Processes (GPs) are Bayesian models that provide uncertainty estimates associated to the predictions made. They are also very flexible due to their non-parametric nature. Nevertheless, GPs suffer from poor scalability as the number…

Machine Learning · Computer Science 2021-07-16 Bahram Jafrasteh , Carlos Villacampa-Calvo , Daniel Hernández-Lobato

Gaussian Processes (\textbf{GPs}) are flexible non-parametric models with strong probabilistic interpretation. While being a standard choice for performing inference on time series, GPs have few techniques to work in a streaming setting.…

Machine Learning · Statistics 2021-07-22 Théo Galy-Fajou , Manfred Opper

In spatial statistics, a common method for prediction over a Gaussian random field (GRF) is maximum likelihood estimation combined with kriging. For massive data sets, kriging is computationally intensive, both in terms of CPU time and…

Methodology · Statistics 2018-09-28 Karl T. Pazdernik , Ranjan Maitra , Douglas Nychka , Stephen Sain

In this paper, we investigate Gaussian process regression models where inputs are subject to measurement error. In spatial statistics, input measurement errors occur when the geographical locations of observed data are not known exactly.…

Methodology · Statistics 2015-06-30 Daniel Cervone , Natesh S. Pillai

Gaussian Process Regression (GPR) is a Bayesian method for inferring profiles based on input data. The technique is increasing in popularity in the fusion community due to its many advantages over traditional fitting techniques including…

Methodology · Statistics 2022-09-07 Jarrod Leddy , Sandeep Madireddy , Eric Howell , Scott Kruger

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

Kriging or Gaussian Process Regression is applied in many fields as a non-linear regression model as well as a surrogate model in the field of evolutionary computation. However, the computational and space complexity of Kriging, that is…

Machine Learning · Computer Science 2017-02-07 Bas van Stein , Hao Wang , Wojtek Kowalczyk , Michael Emmerich , Thomas Bäck

Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model…

Machine Learning · Statistics 2018-03-21 Gonzalo Rios , Felipe Tobar

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.…

Machine Learning · Computer Science 2014-08-12 Jie Chen , Nannan Cao , Kian Hsiang Low , Ruofei Ouyang , Colin Keng-Yan Tan , Patrick Jaillet

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.…

Machine Learning · Statistics 2013-05-27 Jie Chen , Nannan Cao , Kian Hsiang Low , Ruofei Ouyang , Colin Keng-Yan Tan , Patrick Jaillet

Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic…

Numerical Analysis · Mathematics 2020-04-27 Hanno Gottschalk , Karsten Kahl