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Complex-valued Gaussian processes are used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an $H_\infty$ function with probability one, then the same model could…

Systems and Control · Electrical Eng. & Systems 2022-11-30 Alex Devonport , Peter Seiler , Murat Arcak

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

Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…

Machine Learning · Statistics 2015-03-23 Yarin Gal , Richard Turner

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

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 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 process hyperparameter optimization requires linear solves with, and log-determinants of, large kernel matrices. Iterative numerical techniques are becoming popular to scale to larger datasets, relying on the conjugate gradient…

Machine Learning · Computer Science 2022-06-22 Jonathan Wenger , Geoff Pleiss , Philipp Hennig , John P. Cunningham , Jacob R. Gardner

Recommender systems are often designed based on a collaborative filtering approach, where user preferences are predicted by modelling interactions between users and items. Many common approaches to solve the collaborative filtering task are…

Machine Learning · Computer Science 2021-10-11 Yinchong Yang , Florian Buettner

Gaussian processes are a powerful class of non-linear models, but have limited applicability for larger datasets due to their high computational complexity. In such cases, approximate methods are required, for example, the recently…

Methodology · Statistics 2026-03-24 Soham Mukherjee , Manfred Claassen , Paul-Christian Bürkner

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

Model calibration or data inversion is one of fundamental tasks in uncertainty quantification. In this work, we study the theoretical properties of the scaled Gaussian stochastic process (S-GaSP), to model the discrepancy between reality…

Statistics Theory · Mathematics 2020-08-04 Mengyang Gu , Fangzheng Xie , Long Wang

We propose a new scalable multi-class Gaussian process classification approach building on a novel modified softmax likelihood function. The new likelihood has two benefits: it leads to well-calibrated uncertainty estimates and allows for…

Machine Learning · Statistics 2019-05-24 Théo Galy-Fajou , Florian Wenzel , Christian Donner , Manfred Opper

A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…

Applications · Statistics 2013-01-14 Shan Ba , V. Roshan Joseph

Computational models providing accurate estimates of their uncertainty are crucial for risk management associated with decision making in healthcare contexts. This is especially true since many state-of-the-art systems are trained using the…

Machine Learning · Computer Science 2022-06-09 Hongshu Liu , Nabeel Seedat , Julia Ive

We address the issue of knots selection for Gaussian predictive process methodology. Predictive process approximation provides an effective solution to the cubic order computational complexity of Gaussian process models. This approximation…

Computation · Statistics 2011-08-03 Surya T Tokdar

Bayesian synthetic likelihood is a widely used approach for conducting Bayesian analysis in complex models where evaluation of the likelihood is infeasible but simulation from the assumed model is tractable. We analyze the behaviour of the…

Statistics Theory · Mathematics 2026-04-17 David T. Frazier , Christopher Drovandi , David J. Nott

This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance,…

Optimization and Control · Mathematics 2024-12-11 Mickael Binois , Arindam Fadikar , Abby Stevens

This paper is concerned with the problem of how to speed up computation for Gaussian process models trained on autocorrelated data. The Gaussian process model is a powerful tool commonly used in nonlinear regression applications. Standard…

Machine Learning · Computer Science 2025-12-03 Ahmadreza Chokhachian , Matthias Katzfuss , Yu Ding

The Gaussian process (GP) is a popular statistical technique for stochastic function approximation and uncertainty quantification from data. GPs have been adopted into the realm of machine learning in the last two decades because of their…

Machine Learning · Statistics 2024-10-02 Marcus M. Noack , Hengrui Luo , Mark D. Risser

Gaussian Process based Bayesian Optimization is a widely applied algorithm to learn and optimize under uncertainty, well-known for its sample efficiency. However, recently -- and more frequently -- research studies have empirically…

Machine Learning · Statistics 2025-05-20 Antonio Candelieri , Andrea Ponti , Francesco Archetti