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Among generalized additive models, additive Mat\'ern Gaussian Processes (GPs) are one of the most popular for scalable high-dimensional problems. Thanks to their additive structure and stochastic differential equation representation,…

Machine Learning · Statistics 2023-05-02 Lu Zou , Haoyuan Chen , Liang Ding

We investigate the frequentist guarantees of the variational sparse Gaussian process regression model. In the theoretical analysis, we focus on the variational approach with spectral features as inducing variables. We derive guarantees and…

Statistics Theory · Mathematics 2023-09-29 Dennis Nieman , Botond Szabo , Harry van Zanten

As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…

Multi-task learning models using Gaussian processes (GP) have been developed and successfully applied in various applications. The main difficulty with this approach is the computational cost of inference using the union of examples from…

Machine Learning · Computer Science 2012-11-29 Yuyang Wang , Roni Khardon

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

We develop a scalable deep non-parametric generative model by augmenting deep Gaussian processes with a recognition model. Inference is performed in a novel scalable variational framework where the variational posterior distributions are…

Machine Learning · Computer Science 2016-03-02 Zhenwen Dai , Andreas Damianou , Javier González , Neil Lawrence

Gaussian processes (GPs) are the main surrogate functions used for sequential modelling such as Bayesian Optimization and Active Learning. Their drawbacks are poor scaling with data and the need to run an optimization loop when using a…

Machine Learning · Computer Science 2022-11-03 Paul E. Chang , Prakhar Verma , ST John , Victor Picheny , Henry Moss , Arno Solin

We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…

Computation · Statistics 2019-04-23 Linda S. L. Tan , David J. Nott

Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian…

Machine Learning · Computer Science 2015-11-03 David A. Moore , Stuart J. Russell

Gaussian process ($GP$) regression is a widely used non-parametric modeling tool, but its cubic complexity in the training size limits its use on massive data sets. A practical remedy is to predict using only the nearest neighbours of each…

Machine Learning · Statistics 2026-04-09 Robert Allison , Tomasz Maciazek , Anthony Stephenson

The use of Gaussian process models is typically limited to datasets with a few tens of thousands of observations due to their complexity and memory footprint. The two most commonly used methods to overcome this limitation are 1) the…

Machine Learning · Statistics 2020-01-16 Vincent Adam , Stefanos Eleftheriadis , Nicolas Durrande , Artem Artemev , James Hensman

A generalized Gaussian process model (GGPM) is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of the…

Machine Learning · Statistics 2013-11-28 Lifeng Shang , Antoni B. Chan

The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…

Methodology · Statistics 2014-02-14 Yue Wu , Jose Miguel Hernandez Lobato , Zoubin Ghahramani

Thompson Sampling (TS) from Gaussian Process (GP) models is a powerful tool for the optimization of black-box functions. Although TS enjoys strong theoretical guarantees and convincing empirical performance, it incurs a large computational…

Machine Learning · Statistics 2021-11-08 Sattar Vakili , Henry Moss , Artem Artemev , Vincent Dutordoir , Victor Picheny

Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…

Machine Learning · Computer Science 2021-01-07 Laura Swiler , Mamikon Gulian , Ari Frankel , Cosmin Safta , John Jakeman

Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach…

Machine Learning · Statistics 2020-04-07 Vidhi Lalchand , Carl Edward Rasmussen

Gaussian processes (GPs) are widely used metamodels for approximating expensive computer simulations, particularly in engineering design and spatial prediction. However, their performance can deteriorate significantly when covariance…

Computation · Statistics 2025-11-17 Ayumi Mutoh , Junoh Heo

In this paper, we investigate a class of approximate Gaussian processes (GP) obtained by taking a linear combination of compactly supported basis functions with the basis coefficients endowed with a dependent Gaussian prior distribution.…

Statistics Theory · Mathematics 2025-06-02 Jaehoan Kim , Anirban Bhattacharya , Debdeep Pati

Derivatives are a key nonparametric functional in wide-ranging applications where the rate of change of an unknown function is of interest. In the Bayesian paradigm, Gaussian processes (GPs) are routinely used as a flexible prior for…

Statistics Theory · Mathematics 2025-12-30 Zejian Liu , Meng Li

Choosing a proper set of kernel functions is an important problem in learning Gaussian Process (GP) models since each kernel structure has different model complexity and data fitness. Recently, automatic kernel composition methods provide…

Machine Learning · Computer Science 2021-02-25 Anh Tong , Toan Tran , Hung Bui , Jaesik Choi