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Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…

Data Analysis, Statistics and Probability · Physics 2008-02-03 Radford M. Neal

We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of…

Machine Learning · Statistics 2024-02-27 Jiaxin Shi , Michalis K. Titsias , Andriy Mnih

We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…

Machine Learning · Statistics 2011-10-25 Cedric Archambeau , Francis Bach

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

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…

Machine Learning · Statistics 2019-11-19 Leen Alawieh , Jonathan Goodman , John B. Bell

This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical…

Machine Learning · Computer Science 2024-07-18 Hwanwoo Kim , Daniel Sanz-Alonso

Non-stationary time series with non-linear trends are frequently encountered in applications. We consider here the feasibility of accurately forecasting the signals of multiple such time series considering jointly when the number of…

Methodology · Statistics 2016-08-05 Kerry Fendick

Locally weighted regression was created as a nonparametric learning method that is computationally efficient, can learn from very large amounts of data and add data incrementally. An interesting feature of locally weighted regression is…

Machine Learning · Computer Science 2014-02-05 Franziska Meier , Philipp Hennig , Stefan Schaal

Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To…

Machine Learning · Statistics 2019-08-27 David Reeb , Andreas Doerr , Sebastian Gerwinn , Barbara Rakitsch

Inverse problems are prevalent in both scientific research and engineering applications. In the context of Bayesian inverse problems, sampling from the posterior distribution can be particularly challenging when the forward models are…

Computation · Statistics 2026-02-17 Zhihang Xu , Xiaoyu Zhu , Daoji Li , Qifeng Liao

Non-Gaussian likelihoods are essential for modelling complex real-world observations but pose significant computational challenges in learning and inference. Even with Gaussian priors, non-Gaussian likelihoods often lead to analytically…

Machine Learning · Statistics 2024-10-29 Thang D. Bui

Through sequential construction of posteriors on observing data online, Bayes' theorem provides a natural framework for continual learning. We develop Variational Auto-Regressive Gaussian Processes (VAR-GPs), a principled posterior updating…

Machine Learning · Statistics 2021-06-15 Sanyam Kapoor , Theofanis Karaletsos , Thang D. Bui

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

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

A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as…

Machine Learning · Computer Science 2023-01-24 Arthur Leroy , Pierre Latouche , Benjamin Guedj , Servane Gey

In complex and unknown processes, global models are initially generated over the entire experimental space but often fail to provide accurate predictions in local areas. A common approach is to use local models, which requires partitioning…

Machine Learning · Computer Science 2025-05-29 Dominik Polke , Tim Kösters , Elmar Ahle , Dirk Söffker

This research proposes a flexible Bayesian extension of the composite Gaussian process (CGP) model of Ba and Joseph (2012) for predicting (stationary or) non-stationary $y(\mathbf{x})$. The CGP generalizes the regression plus stationary…

Methodology · Statistics 2019-06-27 Casey B. Davis , Christopher M. Hans , Thomas J. Santner

We propose a new method for simplification of Gaussian process (GP) models by projecting the information contained in the full encompassing model and selecting a reduced number of variables based on their predictive relevance. Our results…

Methodology · Statistics 2017-12-18 Juho Piironen , Aki Vehtari

We study the use of Gaussian process emulators to approximate the parameter-to-observation map or the negative log-likelihood in Bayesian inverse problems. We prove error bounds on the Hellinger distance between the true posterior…

Numerical Analysis · Mathematics 2024-10-01 Andrew M. Stuart , Aretha L. Teckentrup

This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…

Machine Learning · Computer Science 2020-08-26 Chiwoo Park , David J. Borth , Nicholas S. Wilson , Chad N. Hunter