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We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…

Machine Learning · Statistics 2011-10-25 Cedric Archambeau , Francis Bach

Gaussian Process regression is a kernel method successfully adopted in many real-life applications. Recently, there is a growing interest on extending this method to non-Euclidean input spaces, like the one considered in this paper,…

Machine Learning · Computer Science 2022-12-05 Antonio Candelieri , Andrea Ponti , Francesco Archetti

Kernel-based models such as kernel ridge regression and Gaussian processes are ubiquitous in machine learning applications for regression and optimization. It is well known that a major downside for kernel-based models is the high…

Machine Learning · Computer Science 2022-06-22 Sattar Vakili , Jonathan Scarlett , Da-shan Shiu , Alberto Bernacchia

Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various…

Machine Learning · Computer Science 2021-12-16 Yuya Yoshikawa , Tomoharu Iwata

We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…

Computational Physics · Physics 2025-06-09 Christopher DeGrendele , Dongwook Lee

Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient…

Quantum Physics · Physics 2024-02-06 Frederic Rapp , Marco Roth

Gaussian processes are important models in the field of probabilistic numerics. We present a procedure for optimizing Mat\'ern kernel temporal Gaussian processes with respect to the kernel covariance function's hyperparameters. It is based…

Machine Learning · Computer Science 2025-08-14 Wouter M. Kouw

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…

We show that Gaussian process regression (GPR) allows representing multivariate functions with low-dimensional terms via kernel design. When using a kernel built with HDMR (High-dimensional model representation), one obtains a similar type…

Numerical Analysis · Mathematics 2023-01-27 Eita Sasaki , Manabu Ihara , Sergei Manzhos

In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The…

Statistics Theory · Mathematics 2022-07-20 Wenjia Wang , Bing-Yi Jing

In this paper we propose a novel Bayesian solution for nonlinear regression in complex fields. Previous solutions for kernels methods usually assume a complexification approach, where the real-valued kernel is replaced by a complex-valued…

Machine Learning · Computer Science 2018-03-02 Rafael Boloix-Tortosa , Eva Arias-de-Reyna , F. Javier Payan-Somet , Juan J. Murillo-Fuentes

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

Gaussian process regression is a machine learning approach which has been shown its power for estimation of unknown functions. However, Gaussian processes suffer from high computational complexity, as in a basic form they scale cubically…

Machine Learning · Statistics 2018-09-10 Danil Kuzin , Le Yang , Olga Isupova , Lyudmila Mihaylova

We introduce a fast algorithm for Gaussian process regression in low dimensions, applicable to a widely-used family of non-stationary kernels. The non-stationarity of these kernels is induced by arbitrary spatially-varying vertical and…

Numerical Analysis · Mathematics 2025-03-28 P. Michael Kielstra , Michael Lindsey

A fundamental drawback of kernel-based statistical models is their limited scalability to large data sets, which requires resorting to approximations. In this work, we focus on the popular Gaussian kernel and on techniques to linearize…

Machine Learning · Statistics 2022-04-13 Jonas Wacker , Maurizio Filippone

Regularized least-squares (kernel-ridge / Gaussian process) regression is a fundamental algorithm of statistics and machine learning. Because generic algorithms for the exact solution have cubic complexity in the number of datapoints, large…

Machine Learning · Computer Science 2019-11-15 Simon Bartels , Philipp Hennig

Gaussian processes are distributions over functions that are versatile and mathematically convenient priors in Bayesian modelling. However, their use is often impeded for data with large numbers of observations, $N$, due to the cubic (in…

Machine Learning · Statistics 2020-08-04 David R. Burt , Carl Edward Rasmussen , Mark van der Wilk

The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel…

Machine Learning · Computer Science 2019-12-30 Jan Graßhoff , Alexandra Jankowski , Philipp Rostalski

Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…

Methodology · Statistics 2011-06-29 Anjishnu Banerjee , David Dunson , Surya Tokdar

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…

Machine Learning · Statistics 2025-11-26 Jonas Latz , Aretha L. Teckentrup , Simon Urbainczyk