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Gaussian processes scale prohibitively with the size of the dataset. In response, many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited…

Machine Learning · Computer Science 2023-10-11 Jonathan Wenger , Geoff Pleiss , Marvin Pförtner , Philipp Hennig , John P. Cunningham

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 (GPs) are widely used as surrogate models for complicated functions in scientific and engineering applications. In many cases, prior knowledge about the function to be approximated, such as monotonicity, is available and…

Machine Learning · Statistics 2025-07-10 Chao Zhang , Jasper M. Everink , Jakob Sauer Jørgensen

Gaussian processes (GPs) provide a framework for Bayesian inference that can offer principled uncertainty estimates for a large range of problems. For example, if we consider regression problems with Gaussian likelihoods, a GP model enjoys…

Machine Learning · Computer Science 2022-12-21 Felix Leibfried , Vincent Dutordoir , ST John , Nicolas Durrande

Gaussian Process (GPs) models are a rich distribution over functions with inductive biases controlled by a kernel function. Learning occurs through the optimisation of kernel hyperparameters using the marginal likelihood as the objective.…

Machine Learning · Statistics 2021-11-22 Fergus Simpson , Vidhi Lalchand , Carl Edward Rasmussen

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

Gaussian processes (GPs) are widely used for regression and optimization tasks such as Bayesian optimization (BO) due to their expressiveness and principled uncertainty estimates. However, in settings with large datasets corrupted by…

Machine Learning · Computer Science 2026-01-13 Marshal Arijona Sinaga , Julien Martinelli , Samuel Kaski

Gaussian processes (GPs) are a class of Kernel methods that have shown to be very useful in geoscience and remote sensing applications for parameter retrieval, model inversion, and emulation. They are widely used because they are simple,…

Machine Learning · Computer Science 2020-05-21 J. Emmanuel Johnson , Valero Laparra , Gustau Camps-Valls

Gaussian processes (GP) provide a prior over functions and allow finding complex regularities in data. Gaussian processes are successfully used for classification/regression problems and dimensionality reduction. In this work we consider…

Machine Learning · Computer Science 2016-11-21 Pavel Izmailov , Dmitry Kropotov

We apply Gaussian process (GP) regression, which provides a powerful non-parametric probabilistic method of relating inputs to outputs, to survival data consisting of time-to-event and covariate measurements. In this context, the covariates…

Statistics Theory · Mathematics 2014-09-08 James E. Barrett , Anthony C. C. Coolen

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 (GPs) defined through intrinsic random fields provide a flexible framework for modeling spatial phenomena, and have been advocated in a variety of applications over the past several decades. Nevertheless, their adoption…

Numerical Analysis · Mathematics 2026-05-19 Christopher Beattie , David Higdon , Leanna House , Colby Stakun-Pickering , Jared Clark

We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement…

Methodology · Statistics 2019-04-25 Filip Tronarp , Hans Kersting , Simo Särkkä , Philipp Hennig

A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. This success is largely attributed to the GP's analytical tractability, robustness, non-parametric…

Machine Learning · Statistics 2022-05-19 Marcus M. Noack , Harinarayan Krishnan , Mark D. Risser , Kristofer G. Reyes

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

Gaussian processes provide probabilistic surrogates for various applications including classification, uncertainty quantification, and optimization. Using a gradient-enhanced covariance matrix can be beneficial since it provides a more…

Optimization and Control · Mathematics 2023-07-13 André L. Marchildon , David W. Zingg

A method to perform unfolding with Gaussian processes (GPs) is presented. Using Bayesian regression, we define an estimator for the underlying truth distribution as the mode of the posterior. We show that in the case where the bin contents…

Data Analysis, Statistics and Probability · Physics 2018-11-07 Adam Bozson , Glen Cowan , Francesco Spanò

Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy…

Machine Learning · Computer Science 2020-04-10 Andrew Pensoneault , Xiu Yang , Xueyu Zhu

We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…

Machine Learning · Computer Science 2020-06-09 Ang Yang , Cheng Li , Santu Rana , Sunil Gupta , Svetha Venkatesh

Gaussian processes (GPs) based methods for solving partial differential equations (PDEs) demonstrate great promise by bridging the gap between the theoretical rigor of traditional numerical algorithms and the flexible design of machine…

Numerical Analysis · Mathematics 2024-02-02 Xianjin Yang , Houman Owhadi