English
Related papers

Related papers: Hilbert space methods for approximating multi-outp…

200 papers

Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…

Machine Learning · Statistics 2020-10-23 Jakob Lindinger , David Reeb , Christoph Lippert , Barbara Rakitsch

The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…

Machine Learning · Computer Science 2021-08-02 Armin Lederer , Alejandro Jose Ordonez Conejo , Korbinian Maier , Wenxin Xiao , Jonas Umlauft , Sandra Hirche

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

We introduce a framework to derive quantitative central limit theorems in the context of non-linear approximation of Gaussian random variables taking values in a separable Hilbert space. In particular, our method provides an alternative to…

Probability · Mathematics 2020-11-25 Solesne Bourguin , Simon Campese

Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…

Statistics Theory · Mathematics 2025-12-16 D. Andrew Brown , Peter Kiessler , John Nicholson

In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the…

Numerical Analysis · Mathematics 2014-08-11 Frank J. Pinski , Gideon Simpson , Andrew M. Stuart , Hendrik Weber

A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…

Methodology · Statistics 2019-07-25 Shinichiro Shirota , Andrew O. Finley , Bruce D. Cook , Sudipto Banerjee

Gaussian processes are flexible probabilistic regression models which are widely used in statistics and machine learning. However, a drawback is their limited scalability to large data sets. To alleviate this, full-scale approximations…

Methodology · Statistics 2026-01-13 Tim Gyger , Reinhard Furrer , Fabio Sigrist

Most machine learning methods require careful selection of hyper-parameters in order to train a high performing model with good generalization abilities. Hence, several automatic selection algorithms have been introduced to overcome tedious…

Machine Learning · Computer Science 2020-01-17 Raju Ram , Sabine Müller , Franz-Josef Pfreundt , Nicolas R. Gauger , Janis Keuper

Gaussian process (GP) predictors are an important component of many Bayesian approaches to machine learning. However, even a straightforward implementation of Gaussian process regression (GPR) requires O(n^2) space and O(n^3) time for a…

Machine Learning · Statistics 2012-11-06 Krzysztof Chalupka , Christopher K. I. Williams , Iain Murray

Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…

Computation · Statistics 2016-04-18 Andreas Svensson , Arno Solin , Simo Särkkä , Thomas B. Schön

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

Machine Learning · Computer Science 2014-08-12 Jie Chen , Nannan Cao , Kian Hsiang Low , Ruofei Ouyang , Colin Keng-Yan Tan , Patrick Jaillet

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

Machine Learning · Statistics 2013-05-27 Jie Chen , Nannan Cao , Kian Hsiang Low , Ruofei Ouyang , Colin Keng-Yan Tan , Patrick Jaillet

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

Approximate Bayesian computation (ABC) methods are used to approximate posterior distributions using simulation rather than likelihood calculations. We introduce Gaussian process (GP) accelerated ABC, which we show can significantly reduce…

Computation · Statistics 2014-02-25 Richard D Wilkinson

Gaussian processes are notorious for scaling cubically with the size of the training set, preventing application to very large regression problems. Computation-aware Gaussian processes (CAGPs) tackle this scaling issue by exploiting…

Machine Learning · Statistics 2025-03-24 Disha Hegde , Mohamed Adil , Jon Cockayne

High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear…

Machine Learning · Statistics 2011-07-26 Andreas C. Damianou , Michalis K. Titsias , Neil D. Lawrence

The Gaussian process (GP) model, which has been extensively applied as priors of functions, has demonstrated excellent performance. The specification of a large number of parameters affects the computational efficiency and the feasibility…

Machine Learning · Statistics 2020-02-13 Shisheng Cui , Chia-Jung Chang

Gaussian processes (GPs) are flexible, probabilistic, nonparametric models widely used in fields such as spatial statistics and machine learning. A drawback of Gaussian processes is their computational cost, with $O(N^3)$ time and $O(N^2)$…

Computation · Statistics 2026-05-20 Filippo Rambelli , Fabio Sigrist

Gaussian process priors are a popular choice for Bayesian analysis of regression problems. However, the implementation of these models can be complex, and ensuring that the implementation is correct can be challenging. In this paper we…

Machine Learning · Computer Science 2021-10-29 John Mcleod , Fergus Simpson