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Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but that are rarely used in signal processing. In this tutorial, we present GPs for regression as…

Gaussian processes (GPs) are powerful but computationally expensive machine learning models, requiring an estimate of the kernel covariance matrix for every prediction. In large and complex domains, such as graphs, sets, or images, the…

Machine Learning · Computer Science 2022-04-22 Alessandro Tibo , Thomas Dyhre Nielsen

The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order…

Machine Learning · Statistics 2017-11-16 Jean-Francois Ton , Seth Flaxman , Dino Sejdinovic , Samir Bhatt

Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear…

Machine Learning · Computer Science 2025-02-11 Petar Bevanda , Max Beier , Armin Lederer , Alexandre Capone , Stefan Sosnowski , Sandra Hirche

Gaussian processes (GPs), or distributions over arbitrary functions in a continuous domain, can be generalized to the multi-output case: a linear model of coregionalization (LMC) is one approach. LMCs estimate and exploit correlations…

Machine Learning · Statistics 2017-10-24 Vladimir Feinberg , Li-Fang Cheng , Kai Li , Barbara E Engelhardt

Modern scientific problems are often multi-disciplinary and require integration of computer models from different disciplines, each with distinct functional complexities, programming environments, and computation times. Linked Gaussian…

Machine Learning · Statistics 2023-06-05 Deyu Ming , Daniel Williamson

Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…

Machine Learning · Computer Science 2020-01-01 Ian A. Delbridge , David S. Bindel , Andrew Gordon Wilson

Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…

Machine Learning · Computer Science 2025-07-17 Zachary James , Joseph Guinness

Neural-net-induced Gaussian process (NNGP) regression inherits both the high expressivity of deep neural networks (deep NNs) as well as the uncertainty quantification property of Gaussian processes (GPs). We generalize the current NNGP to…

Machine Learning · Computer Science 2019-03-27 Guofei Pang , Liu Yang , George Em Karniadakis

Gaussian processes provide a compact representation for modeling and estimating an unknown function, that can be updated as new measurements of the function are obtained. This paper extends this powerful framework to the case where the…

Systems and Control · Electrical Eng. & Systems 2023-11-30 Jilles van Hulst , Roy van Zuijlen , Duarte Antunes , W. P. M. H. , Heemels

Continuous input signals like images and time series that are irregularly sampled or have missing values are challenging for existing deep learning methods. Coherently defined feature representations must depend on the values in unobserved…

Machine Learning · Computer Science 2020-10-22 Marc Finzi , Roberto Bondesan , Max Welling

Analysing and computing with Gaussian processes arising from infinitely wide neural networks has recently seen a resurgence in popularity. Despite this, many explicit covariance functions of networks with activation functions used in modern…

Machine Learning · Computer Science 2021-03-02 Russell Tsuchida , Tim Pearce , Chris van der Heide , Fred Roosta , Marcus Gallagher

Learning precise surrogate models of complex computer simulations and physical machines often require long-lasting or expensive experiments. Furthermore, the modeled physical dependencies exhibit nonlinear and nonstationary behavior.…

Machine Learning · Computer Science 2023-03-20 Matthias Bitzer , Mona Meister , Christoph Zimmer

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

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

The behavior of a GP regression depends on the choice of covariance function. Stationary covariance functions are preferred in machine learning applications. However, (non-periodic) stationary covariance functions are always mean reverting…

Machine Learning · Statistics 2024-05-16 Luca Ambrogioni

Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too…

Machine Learning · Statistics 2016-04-12 Roberto Calandra , Jan Peters , Carl Edward Rasmussen , Marc Peter Deisenroth

In recent years, there has been considerable interest in developing machine learning models on graphs to account for topological inductive biases. In particular, recent attention has been given to Gaussian processes on such structures since…

Machine Learning · Computer Science 2024-08-20 Mathieu Alain , So Takao , Brooks Paige , Marc Peter Deisenroth

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 processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…