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Gaussian Process Regression is a popular nonparametric regression method based on Bayesian principles that provides uncertainty estimates for its predictions. However, these estimates are of a Bayesian nature, whereas for some important…

Machine Learning · Computer Science 2023-08-09 Christian Fiedler , Carsten W. Scherer , Sebastian Trimpe

Direct quantile regression involves estimating a given quantile of a response variable as a function of input variables. We present a new framework for direct quantile regression where a Gaussian process model is learned, minimising the…

Methodology · Statistics 2012-07-03 Alexis Boukouvalas , Remi Barillec , Dan Cornford

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

A primary goal of computer experiments is to reconstruct the function given by the computer code via scattered evaluations. Traditional isotropic Gaussian process models suffer from the curse of dimensionality, when the input dimension is…

Machine Learning · Statistics 2022-09-01 Gecheng Chen , Rui Tuo

One goal in Bayesian machine learning is to encode prior knowledge into prior distributions, to model data efficiently. We consider prior knowledge from systems of linear partial differential equations together with their boundary…

Machine Learning · Computer Science 2021-02-16 Markus Lange-Hegermann

Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…

Systems and Control · Electrical Eng. & Systems 2021-02-11 Thomas Beckers

Gaussian process regression (GPR) is a popular nonparametric Bayesian method that provides predictive uncertainty estimates and is widely used in safety-critical applications. While prior research has introduced various uncertainty bounds,…

Machine Learning · Computer Science 2025-12-05 Junyi Liu , Stanley Kok

This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…

Numerical Analysis · Mathematics 2020-07-20 Aretha L Teckentrup

We consider the problem of calculating learning curves (i.e., average generalization performance) of Gaussian processes used for regression. On the basis of a simple expression for the generalization error, in terms of the eigenvalue…

Disordered Systems and Neural Networks · Physics 2007-05-23 Peter Sollich , Anason Halees

The performance of Gaussian Process (GP) regression is often hampered by the curse of dimensionality, which inflates computational cost and reduces predictive power in high-dimensional problems. Variable selection is thus crucial for…

Methodology · Statistics 2025-11-24 Minshen Xu , Shiwei Lan , Lulu Kang

The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…

Methodology · Statistics 2024-04-02 Lulu Kang , Yuanxing Cheng , Yiwei Wang , Chun Liu

Gaussian process regression is a powerful method for predicting states based on given data. It has been successfully applied for probabilistic predictions of structural systems to quantify, for example, the crack growth in mechanical…

Machine Learning · Statistics 2022-06-20 Simon Pfingstl , Markus Zimmermann

Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…

Machine Learning · Statistics 2015-11-25 Leo L. Duan , Xia Wang , Rhonda D. Szczesniak

Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…

Machine Learning · Computer Science 2017-08-22 Sourish Das , Sasanka Roy , Rajiv Sambasivan

Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To…

Machine Learning · Statistics 2019-08-27 David Reeb , Andreas Doerr , Sebastian Gerwinn , Barbara Rakitsch

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…

Data Analysis, Statistics and Probability · Physics 2008-02-03 Radford M. Neal

The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…

Methodology · Statistics 2022-03-29 Ali Rafei , Michael R. Elliott , Carol A. C. Flannagan

Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…

Machine Learning · Statistics 2024-02-02 Bernardo Fichera , Viacheslav Borovitskiy , Andreas Krause , Aude Billard

We propose a novel Bayesian nonparametric method for hierarchical modelling on a set of related density functions, where grouped data in the form of samples from each density function are available. Borrowing strength across the groups is a…

Computation · Statistics 2014-10-31 G. S. Rodrigues , David J. Nott , S. A. Sisson

We introduce a novel edge tracing algorithm using Gaussian process regression. Our edge-based segmentation algorithm models an edge of interest using Gaussian process regression and iteratively searches the image for edge pixels in a…

Computer Vision and Pattern Recognition · Computer Science 2021-12-15 Jamie Burke , Stuart King