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Gaussian processes (GPs) are a mature and widely-used component of the ML toolbox. One of their desirable qualities is automatic hyperparameter selection, which allows for training without user intervention. However, in many realistic…

Machine Learning · Computer Science 2024-02-16 Sebastian W. Ober , Artem Artemev , Marcel Wagenländer , Rudolfs Grobins , Mark van der Wilk

We develop an exact and scalable algorithm for one-dimensional Gaussian process regression with Mat\'ern correlations whose smoothness parameter $\nu$ is a half-integer. The proposed algorithm only requires $\mathcal{O}(\nu^3 n)$ operations…

Machine Learning · Statistics 2022-03-11 Haoyuan Chen , Liang Ding , Rui Tuo

Gaussian Processes (GPs) are known to provide accurate predictions and uncertainty estimates even with small amounts of labeled data by capturing similarity between data points through their kernel function. However traditional GP kernels…

Machine Learning · Computer Science 2021-11-16 Ankur Mallick , Chaitanya Dwivedi , Bhavya Kailkhura , Gauri Joshi , T. Yong-Jin Han

Gaussian processes are used in machine learning to learn input-output mappings from observed data. Gaussian process regression is based on imposing a Gaussian process prior on the unknown regressor function and statistically conditioning it…

Machine Learning · Statistics 2019-07-16 Simo Särkkä

In consumer theory, ranking available objects by means of preference relations yields the most common description of individual choices. However, preference-based models assume that individuals: (1) give their preferences only between pairs…

Machine Learning · Computer Science 2023-02-02 Alessio Benavoli , Dario Azzimonti , Dario Piga

Despite the growing availability of sensing and data in general, we remain unable to fully characterise many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture…

Machine Learning · Computer Science 2023-09-20 Elizabeth J Cross , Timothy J Rogers , Daniel J Pitchforth , Samuel J Gibson , Matthew R Jones

Despite the increasing importance of stochastic processes on linear networks and graphs, current literature on multivariate (vector-valued) Gaussian random fields on metric graphs is elusive. This paper challenges several aspects related to…

Statistics Theory · Mathematics 2025-01-20 Tobia Filosi , Emilio Porcu , Xavier Emery , Claudio Agostinelli , Alfredo Alegrìa

Gaussian process models are commonly used as emulators for computer experiments. However, developing a Gaussian process emulator can be computationally prohibitive when the number of experimental samples is even moderately large. Local…

Methodology · Statistics 2018-09-26 Chih-Li Sung , Robert B. Gramacy , Benjamin Haaland

We study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order. The data consist of derivative evaluations at the expansion point and the prior…

Machine Learning · Computer Science 2023-08-29 Toni Karvonen , Jon Cockayne , Filip Tronarp , Simo Särkkä

Gaussian process models -also called Kriging models- are often used as mathematical approximations of expensive experiments. However, the number of observation required for building an emulator becomes unrealistic when using classical…

Machine Learning · Statistics 2012-12-17 Nicolas Durrande , David Ginsbourger , Olivier Roustant , Laurent Carraro

Gaussian process regression has proven very powerful in statistics, machine learning and inverse problems. A crucial aspect of the success of this methodology, in a wide range of applications to complex and real-world problems, is…

Statistics Theory · Mathematics 2021-03-18 Yifan Chen , Houman Owhadi , Andrew M. Stuart

Gaussian Process (GP) models are a class of flexible non-parametric models that have rich representational power. By using a Gaussian process with additive structure, complex responses can be modelled whilst retaining interpretability.…

Machine Learning · Statistics 2022-06-22 Xiaoyu Lu , Alexis Boukouvalas , James Hensman

Feature selection in reinforcement learning (RL), i.e. choosing basis functions such that useful approximations of the unkown value function can be obtained, is one of the main challenges in scaling RL to real-world applications. Here we…

Artificial Intelligence · Computer Science 2012-02-01 Tobias Jung , Peter Stone

Current remote sensing image classification problems have to deal with an unprecedented amount of heterogeneous and complex data sources. Upcoming missions will soon provide large data streams that will make land cover/use classification…

Machine Learning · Computer Science 2017-10-04 Pablo Morales-Alvarez , Adrian Perez-Suay , Rafael Molina , Gustau Camps-Valls

The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The…

Statistics Theory · Mathematics 2025-03-04 David Bolin , Vaibhav Mehandiratta , Alexandre B. Simas

Low-rank approximation is a popular strategy to tackle the "big n problem" associated with large-scale Gaussian process regressions. Basis functions for developing low-rank structures are crucial and should be carefully specified.…

Methodology · Statistics 2024-09-04 Yan Song , Wenlin Dai , Marc G. Genton

This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…

Machine Learning · Statistics 2019-09-12 Christian Agrell

A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. This success is largely attributed to the GP's analytical tractability, robustness, non-parametric…

Machine Learning · Statistics 2022-05-19 Marcus M. Noack , Harinarayan Krishnan , Mark D. Risser , Kristofer G. Reyes

In this article we investigate the effects of conformal transformations on kernel functions used in Support Vector Machines. Our focus lies in the task of text document categorization, which involves assigning each document to a particular…

Machine Learning · Computer Science 2024-06-04 Ioana Rădulescu , Alexandra Băicoianu , Adela Mihai

Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel based methods for additive models. These learning rates compare favourably in particular in high dimensions to…

Machine Learning · Statistics 2014-05-15 Andreas Christmann , Ding-Xuan Zhou