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Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…

Machine Learning · Statistics 2022-10-12 Marcus M. Noack , James A. Sethian

Gaussian Process (GP) models are a class of flexible non-parametric models that have rich representational power. By using a Gaussian process with additive structure, complex responses can be modelled whilst retaining interpretability.…

Machine Learning · Statistics 2022-06-22 Xiaoyu Lu , Alexis Boukouvalas , James Hensman

Gaussian process (GP) emulators have become essential tools for approximating complex simulators, significantly reducing computational demands in optimization, sensitivity analysis, and model calibration. While traditional GP emulators…

Computation · Statistics 2026-03-26 Deyu Ming , Daniel Williamson

Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns…

Machine Learning · Statistics 2014-01-03 Andrew Gordon Wilson , Ryan Prescott Adams

In simulation-based engineering design with time-consuming simulators, Gaussian process (GP) models are widely used as fast emulators to speed up the design optimization process. In its most commonly used form, the input of GP is a simple…

Machine Learning · Computer Science 2024-07-24 Xi Chen , Yashika Sharma , Hao Helen Zhang , Xin Hao , Qiang Zhou

Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…

Machine Learning · Computer Science 2020-08-25 Vladimir Joukov , Dana Kulić

Gaussian Processes face two primary challenges: constructing models for large datasets and selecting the optimal model. This master's thesis tackles these challenges in the low-dimensional case. We examine recent convergence results to…

Machine Learning · Statistics 2024-11-13 Marcel Neugebauer

The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The…

Statistics Theory · Mathematics 2025-03-04 David Bolin , Vaibhav Mehandiratta , Alexandre B. Simas

The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…

Machine Learning · Statistics 2022-03-22 Hossein Mohammadi , Peter Challenor , Marc Goodfellow

Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…

Machine Learning · Statistics 2018-02-02 Xiuming Liu , Dave Zachariah , Edith C. H. Ngai

Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The…

Machine Learning · Statistics 2016-10-05 Benjamin Fischer , Nico Gorbach , Stefan Bauer , Yatao Bian , Joachim M. Buhmann

Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…

Machine Learning · Computer Science 2020-06-09 Jarred Barber

Computer experiments with both quantitative and qualitative (QQ) inputs are commonly used in science and engineering applications. Constructing desirable emulators for such computer experiments remains a challenging problem. In this…

Methodology · Statistics 2022-03-22 Qian Xiao , Abhyuday Mandal , C. Devon Lin , Xinwei Deng

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

In this paper we investigate a link between state- space models and Gaussian Processes (GP) for time series modeling and forecasting. In particular, several widely used state- space models are transformed into continuous time form and…

Machine Learning · Statistics 2016-10-27 Alexander Grigorievskiy , Juha Karhunen

Many fields of science and engineering rely on running simulations with complex and computationally expensive models to understand the involved processes in the system of interest. Nevertheless, the high cost involved hamper reliable and…

Machine Learning · Computer Science 2019-12-16 Daniel Heestermans Svendsen , Luca Martino , Gustau Camps-Valls

Surrogate models have become ubiquitous in science and engineering for their capability of emulating expensive computer codes, necessary to model and investigate complex phenomena. Bayesian emulators based on Gaussian processes adequately…

Computation · Statistics 2017-08-02 A. Garbuno-Inigo , F. A. DiazDelaO , K. M. Zuev

We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix…

Machine Learning · Statistics 2026-05-12 Anthony Stephenson

Fitting a theoretical model to experimental data in a Bayesian manner using Markov chain Monte Carlo typically requires one to evaluate the model thousands (or millions) of times. When the model is a slow-to-compute physics simulation,…

Machine Learning · Statistics 2022-08-25 Steven Stetzler , Michael Grosskopf , Earl Lawrence

Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…

Machine Learning · Computer Science 2025-07-10 Jihao Andreas Lin