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Related papers: An Introduction to Gaussian Process Models

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Bayesian methods have become a popular way to incorporate prior knowledge and a notion of uncertainty into machine learning models. At the same time, the complexity of modern machine learning makes it challenging to comprehend a model's…

Machine Learning · Computer Science 2021-09-09 Sarem Seitz

The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…

Machine Learning · Statistics 2022-03-22 Hossein Mohammadi , Peter Challenor , Marc Goodfellow

Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear…

Machine Learning · Computer Science 2025-02-11 Petar Bevanda , Max Beier , Armin Lederer , Alexandre Capone , Stefan Sosnowski , Sandra Hirche

In this work, we employ the Bayesian inference framework to solve the problem of estimating the solution and particularly, its derivatives, which satisfy a known differential equation, from the given noisy and scarce observations of the…

Computation · Statistics 2020-10-09 Hongqiao Wang , Xiang Zhou

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…

Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…

Quantum Physics · Physics 2019-05-29 Zhikuan Zhao , Jack K. Fitzsimons , Joseph F. Fitzsimons

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

We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…

Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant…

Optimization and Control · Mathematics 2025-05-01 Adrian Lepp , Jörn Tebbe , Andreas Besginow

Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in…

Machine Learning · Statistics 2016-04-19 Alan D. Saul , James Hensman , Aki Vehtari , Neil D. Lawrence

Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…

Machine Learning · Statistics 2023-02-10 Tapio Helin , Andrew Stuart , Aretha Teckentrup , Konstantinos Zygalakis

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

Gaussian processes occupy one of the leading places in modern statistics and probability theory due to their importance and a wealth of strong results. The common use of Gaussian processes is in connection with problems related to…

Statistics Theory · Mathematics 2023-02-01 Zexun Chen , Jun Fan , Kuo Wang

In computational physics, machine learning has now emerged as a powerful complementary tool to explore efficiently candidate designs in engineering studies. Outputs in such supervised problems are signals defined on meshes, and a natural…

Machine Learning · Statistics 2025-03-11 Raphaël Carpintero Perez , Sébastien da Veiga , Josselin Garnier , Brian Staber

Gaussian processes are a widely embraced technique for regression and classification due to their good prediction accuracy, analytical tractability and built-in capabilities for uncertainty quantification. However, they suffer from the…

Optimization and Control · Mathematics 2024-02-07 Mickael Binois , Victor Picheny

Yield curve forecasting is an important problem in finance. In this work we explore the use of Gaussian Processes in conjunction with a dynamic modeling strategy, much like the Kalman Filter, to model the yield curve. Gaussian Processes…

Machine Learning · Statistics 2017-03-07 Rajiv Sambasivan , Sourish Das

With the rapid development of modern technology, massive amounts of data with complex pattern are generated. Gaussian process models that can easily fit the non-linearity in data become more and more popular nowadays. It is often the case…

Applications · Statistics 2023-09-11 Zhiyong Hu , Dipak Dey

Biological data objects often have both of the following features: (i) they are functions rather than single numbers or vectors, and (ii) they are correlated due to phylogenetic relationships. In this paper we give a flexible statistical…

Quantitative Methods · Quantitative Biology 2012-12-20 Nick S. Jones , John Moriarty

Reinforcement learning provides a framework for learning to control which actions to take towards completing a task through trial-and-error. In many applications observing interactions is costly, necessitating sample-efficient learning. In…

Machine Learning · Statistics 2020-11-04 Charles Gadd , Markus Heinonen , Harri Lähdesmäki , Samuel Kaski

Gaussian process is one of the most popular non-parametric Bayesian methodologies for modeling the regression problem. It is completely determined by its mean and covariance functions. And its linear property makes it relatively…

Machine Learning · Statistics 2020-06-16 Wenqi Fang , Huiyun Li , Hui Huang , Shaobo Dang , Zhejun Huang , Zheng Wang