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The Gaussian process (GP) is a Bayesian nonparametric paradigm that is widely adopted for uncertainty quantification (UQ) in a number of safety-critical applications, including robotics, healthcare, as well as surveillance. The consistency…

Machine Learning · Computer Science 2024-10-10 Jinwen Xu , Qin Lu , Georgios B. Giannakis

Safety is an essential aspect in the facilitation of automated vehicle deployment. Current testing practices are not enough, and going beyond them leads to infeasible testing requirements, such as needing to drive billions of kilometres on…

Machine Learning · Computer Science 2019-07-12 Felix Batsch , Alireza Daneshkhah , Madeline Cheah , Stratis Kanarachos , Anthony Baxendale

The deployment of autonomous systems that operate in unstructured environments necessitates algorithms to verify their safety. This can be challenging due to, e.g., black-box components in the control software, or undermodelled dynamics…

Systems and Control · Electrical Eng. & Systems 2020-06-17 John Jackson , Luca Laurenti , Eric Frew , Morteza Lahijanian

Gaussian processes are ubiquitous in machine learning, statistics, and applied mathematics. They provide a flexible modelling framework for approximating functions, whilst simultaneously quantifying uncertainty. However, this is only true…

Statistics Theory · Mathematics 2021-05-19 George Wynne , François-Xavier Briol , Mark Girolami

We consider a sequential decision making task, where the goal is to optimize an unknown function without evaluating parameters that violate an a~priori unknown (safety) constraint. A common approach is to place a Gaussian process prior on…

Machine Learning · Computer Science 2024-05-13 Alessandro G. Bottero , Carlos E. Luis , Julia Vinogradska , Felix Berkenkamp , Jan Peters

Bayesian inference and Gaussian processes are widely used in applications ranging from robotics and control to biological systems. Many of these applications are safety-critical and require a characterization of the uncertainty associated…

Machine Learning · Computer Science 2018-10-26 Luca Cardelli , Marta Kwiatkowska , Luca Laurenti , Andrea Patane

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

Machine Learning · Statistics 2022-04-29 Alexander Terenin

Complex-valued Gaussian processes are commonly used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an $H_\infty$ function with probability one, then the same…

Systems and Control · Electrical Eng. & Systems 2023-12-19 Alex Devonport , Peter Seiler , Murat Arcak

Non-conservative uncertainty bounds are essential for making reliable predictions about latent functions from noisy data, and thus, a key enabler for safe learning-based control. In this domain, kernel methods such as Gaussian process…

Machine Learning · Computer Science 2026-05-26 Amon Lahr , Anna Scampicchio , Johannes Köhler , Melanie N. Zeilinger

Gaussian Process Regression (GPR) is widely used in statistics and machine learning for prediction tasks requiring uncertainty measures. Its efficacy depends on the appropriate specification of the mean function, covariance kernel function,…

Machine Learning · Computer Science 2024-09-20 Shifan Zhao , Jiaying Lu , Ji Yang , Edmond Chow , Yuanzhe Xi

Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. Such scenarios demand that GP decisions are not only accurate, but also robust to perturbations. In this…

Machine Learning · Computer Science 2021-04-08 Andrea Patane , Arno Blaas , Luca Laurenti , Luca Cardelli , Stephen Roberts , Marta Kwiatkowska

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

In this work, we present a new class of models, called uncertain-input models, that allows us to treat system-identification problems in which a linear system is subject to a partially unknown input signal. To encode prior information about…

Systems and Control · Computer Science 2017-09-12 Riccardo Sven Risuleo , Giulio Bottegal , Håkan Hjalmarsson

Many functions have approximately-known upper and/or lower bounds, potentially aiding the modeling of such functions. In this paper, we introduce Gaussian process models for functions where such bounds are (approximately) known. More…

Machine Learning · Computer Science 2022-10-20 Vu Nguyen , Marc Peter Deisenroth , Michael A. Osborne

We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian…

Machine Learning · Statistics 2017-07-20 Tomoharu Iwata , Zoubin Ghahramani

The high efficiency of a recently proposed method for computing with Gaussian processes relies on expanding a (translationally invariant) covariance kernel into complex exponentials, with frequencies lying on a Cartesian equispaced grid.…

Numerical Analysis · Mathematics 2023-05-19 Alex Barnett , Philip Greengard , Manas Rachh

Safety-critical technical systems operating in unknown environments require the ability to quickly adapt their behavior, which can be achieved in control by inferring a model online from the data stream generated during operation. Gaussian…

Systems and Control · Electrical Eng. & Systems 2022-02-24 Armin Lederer , Mingmin Zhang , Samuel Tesfazgi , Sandra Hirche

This paper considers the quantification of the prediction performance in Gaussian process regression. The standard approach is to base the prediction error bars on the theoretical predictive variance, which is a lower bound on the mean…

Machine Learning · Statistics 2017-03-16 Johan Wågberg , Dave Zachariah , Thomas B. Schön , Petre Stoica

Active learning of physical systems must commonly respect practical safety constraints, which restricts the exploration of the design space. Gaussian Processes (GPs) and their calibrated uncertainty estimations are widely used for this…

Machine Learning · Computer Science 2024-04-16 Jörn Tebbe , Christoph Zimmer , Ansgar Steland , Markus Lange-Hegermann , Fabian Mies

Gaussian processes scale prohibitively with the size of the dataset. In response, many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited…

Machine Learning · Computer Science 2023-10-11 Jonathan Wenger , Geoff Pleiss , Marvin Pförtner , Philipp Hennig , John P. Cunningham