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Gaussian process regression is a popular method for non-parametric probabilistic modeling of functions. The Gaussian process prior is characterized by so-called hyperparameters, which often have a large influence on the posterior model and…

Machine Learning · Statistics 2016-11-18 Andreas Svensson , Johan Dahlin , Thomas B. Schön

The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…

Methodology · Statistics 2024-04-02 Lulu Kang , Yuanxing Cheng , Yiwei Wang , Chun Liu

Quantum computing algorithms have been shown to produce performant quantum kernels for machine-learning classification problems. Here, we examine the performance of quantum kernels for regression problems of practical interest. For an…

Quantum Physics · Physics 2024-09-30 Xuyang Guo , Jun Dai , Roman V. Krems

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 are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

A powerful tool for the analysis of nonrandomized observational studies has been the potential outcomes model. Utilization of this framework allows analysts to estimate average treatment effects. This article considers the situation in…

Statistics Theory · Mathematics 2019-05-31 Debashis Ghosh , Efrén Cruz-Cortés

We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to…

Machine Learning · Computer Science 2013-09-27 James Hensman , Nicolo Fusi , Neil D. Lawrence

In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…

Machine Learning · Statistics 2025-03-19 Minoru Kusaba , Megumi Iwayama , Ryo Yoshida

This work presents a novel method for extracting potential barrier distributions from experimental fusion cross sections. We utilize a simple Gaussian process regression (GPR) framework to model the observed cross sections as a function of…

Nuclear Theory · Physics 2024-06-10 Kyle Godbey

Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems,…

Machine Learning · Statistics 2020-12-10 Juan Emmanuel Johnson , Valero Laparra , Gustau Camps-Valls

Gaussian processes (GPs) are an important tool in machine learning and statistics with applications ranging from social and natural science through engineering. They constitute a powerful kernelized non-parametric method with…

Machine Learning · Statistics 2021-12-20 Manuel Schürch , Dario Azzimonti , Alessio Benavoli , Marco Zaffalon

Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a…

Graph models are relevant in many fields, such as distributed computing, intelligent tutoring systems or social network analysis. In many cases, such models need to take changes in the graph structure into account, i.e. a varying number of…

Artificial Intelligence · Computer Science 2018-10-09 Benjamin Paaßen , Christina Göpfert , Barbara Hammer

Gaussian processes have become a promising tool for various safety-critical settings, since the posterior variance can be used to directly estimate the model error and quantify risk. However, state-of-the-art techniques for safety-critical…

Machine Learning · Computer Science 2022-07-22 Alexandre Capone , Armin Lederer , Sandra Hirche

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

The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an…

Machine Learning · Statistics 2022-11-07 Vidhi Lalchand , Wessel P. Bruinsma , David R. Burt , Carl E. Rasmussen

One goal in Bayesian machine learning is to encode prior knowledge into prior distributions, to model data efficiently. We consider prior knowledge from systems of linear partial differential equations together with their boundary…

Machine Learning · Computer Science 2021-02-16 Markus Lange-Hegermann

This paper presents a Gaussian process (GP) model for estimating piecewise continuous regression functions. In scientific and engineering applications of regression analysis, the underlying regression functions are piecewise continuous in…

Methodology · Statistics 2021-04-15 Chiwoo Park

We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes of the graph. The model is designed to capture various graph signal structures through a highly adaptive kernel that incorporates a flexible…

Machine Learning · Computer Science 2020-10-29 Yin-Cong Zhi , Yin Cheng Ng , Xiaowen Dong

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