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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

The growing demand for accurate, efficient, and scalable solutions in computational mechanics highlights the need for advanced operator learning algorithms that can efficiently handle large datasets while providing reliable uncertainty…

Machine Learning · Statistics 2024-09-18 Sawan Kumar , Rajdip Nayek , Souvik Chakraborty

Data-driven Model Predictive Control (MPC), where the system model is learned from data with machine learning, has recently gained increasing interests in the control community. Gaussian Processes (GP), as a type of statistical models, are…

Systems and Control · Computer Science 2019-10-03 Truong X. Nghiem

We analyse and explain the increased generalisation performance of iterate averaging using a Gaussian process perturbation model between the true and batch risk surface on the high dimensional quadratic. We derive three phenomena…

Machine Learning · Statistics 2021-11-02 Diego Granziol , Xingchen Wan , Samuel Albanie , Stephen Roberts

Gaussian processes (GPs) can provide a principled approach to uncertainty quantification with easy-to-interpret kernel hyperparameters, such as the lengthscale, which controls the correlation distance of function values. However, selecting…

Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator,…

Machine Learning · Statistics 2011-03-22 Nicolas Durrande , David Ginsbourger , Olivier Roustant

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

This paper proposes an efficient general alternating-direction implicit (GADI) framework for solving large sparse linear systems. The convergence property of the GADI framework is discussed. Most of the existing ADI methods can be viewed as…

Numerical Analysis · Mathematics 2022-05-04 Kai Jiang , Xuehong Su , Juan Zhang

Sequential learning with Gaussian processes (GPs) is challenging when access to past data is limited, for example, in continual and active learning. In such cases, errors can accumulate over time due to inaccuracies in the posterior,…

Machine Learning · Computer Science 2023-06-07 Paul E. Chang , Prakhar Verma , S. T. John , Arno Solin , Mohammad Emtiyaz Khan

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

Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…

Machine Learning · Computer Science 2018-09-11 Linfeng Liu , Liping Liu

Gaussian Processes (GPs) are expressive models for capturing signal statistics and expressing prediction uncertainty. As a result, the robotics community has gathered interest in leveraging these methods for inference, planning, and…

Robotics · Computer Science 2023-08-29 Francesco Crocetti , Jeffrey Mao , Alessandro Saviolo , Gabriele Costante , Giuseppe Loianno

Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a…

Numerical Analysis · Mathematics 2024-04-03 Phillip Semler , Martin Weiser

The Gaussian process (GP) regression can be severely biased when the data are contaminated by outliers. This paper presents a new robust GP regression algorithm that iteratively trims the most extreme data points. While the new algorithm…

Machine Learning · Computer Science 2021-06-15 Zhao-Zhou Li , Lu Li , Zhengyi Shao

Gaussian processes (GPs) are widely used in non-parametric Bayesian modeling, and play an important role in various statistical and machine learning applications. In a variety tasks of uncertainty quantification, generating random sample…

Computation · Statistics 2024-08-02 Haoyuan Chen , Rui Tuo

We present a Bayesian approach to identify optimal transformations that map model input points to low dimensional latent variables. The "projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to…

Machine Learning · Statistics 2021-09-22 Panagiotis Tsilifis , Piyush Pandita , Sayan Ghosh , Valeria Andreoli , Thomas Vandeputte , Liping Wang

For applications as varied as Bayesian neural networks, determinantal point processes, elliptical graphical models, and kernel learning for Gaussian processes (GPs), one must compute a log determinant of an $n \times n$ positive definite…

Machine Learning · Statistics 2017-11-10 Kun Dong , David Eriksson , Hannes Nickisch , David Bindel , Andrew Gordon Wilson

A key task in AutoML is to model learning curves of machine learning models jointly as a function of model hyper-parameters and training progression. While Gaussian processes (GPs) are suitable for this task, na\"ive GPs require…

Machine Learning · Computer Science 2024-10-15 Jihao Andreas Lin , Sebastian Ament , Maximilian Balandat , Eytan Bakshy

Operator learning offers a powerful paradigm for solving parametric partial differential equations (PDEs), but scaling probabilistic neural operators such as the recently proposed Gaussian Processes Operators (GPOs) to high-dimensional,…

Machine Learning · Statistics 2025-06-23 Sawan Kumar , Tapas Tripura , Rajdip Nayek , Souvik Chakraborty

Approximations to Gaussian processes based on inducing variables, combined with variational inference techniques, enable state-of-the-art sparse approaches to infer GPs at scale through mini batch-based learning. In this work, we address…

Machine Learning · Statistics 2021-07-21 Gia-Lac Tran , Dimitrios Milios , Pietro Michiardi , Maurizio Filippone