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Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper…

Numerical Analysis · Mathematics 2024-10-04 Daniel Sanz-Alonso , Ruiyi Yang

Graph-based models require aggregating information in the graph from neighbourhoods of different sizes. In particular, when the data exhibit varying levels of smoothness on the graph, a multi-scale approach is required to capture the…

Machine Learning · Computer Science 2022-02-22 Felix L. Opolka , Yin-Cong Zhi , Pietro Liò , Xiaowen Dong

Bayesian optimization has become a fundamental global optimization algorithm in many problems where sample efficiency is of paramount importance. Recently, there has been proposed a large number of new applications in fields such as…

Artificial Intelligence · Computer Science 2019-02-06 Ruben Martinez-Cantin

This work incorporates the multi-modality of the data distribution into a Gaussian Process regression model. We approach the problem from a discriminative perspective by learning, jointly over the training data, the target space variance in…

Machine Learning · Computer Science 2018-03-20 Silvia L. Pintea , Jan C. van Gemert , Arnold W. M. Smeulders

Gaussian Processes (GPs) can be used as flexible, non-parametric function priors. Inspired by the growing body of work on Normalizing Flows, we enlarge this class of priors through a parametric invertible transformation that can be made…

Machine Learning · Computer Science 2021-02-26 Juan Maroñas , Oliver Hamelijnck , Jeremias Knoblauch , Theodoros Damoulas

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

We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…

This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…

Numerical Analysis · Mathematics 2015-02-20 Qi Ye

Gaussian processes are rich distributions over functions, with generalization properties determined by a kernel function. When used for long-range extrapolation, predictions are particularly sensitive to the choice of kernel parameters. It…

Machine Learning · Statistics 2018-02-05 Phillip A. Jang , Andrew E. Loeb , Matthew B. Davidow , Andrew Gordon Wilson

Gaussian processes (GPs) are an attractive class of machine learning models because of their simplicity and flexibility as building blocks of more complex Bayesian models. Meanwhile, graph neural networks (GNNs) emerged recently as a…

Machine Learning · Computer Science 2023-02-14 Zehao Niu , Mihai Anitescu , Jie Chen

A spectral mixture (SM) kernel is a flexible kernel used to model any stationary covariance function. Although it is useful in modeling data, the learning of the SM kernel is generally difficult because optimizing a large number of…

Machine Learning · Statistics 2020-06-15 Yohan Jung , Kyungwoo Song , Jinkyoo Park

The Gaussian kernel plays a central role in machine learning, uncertainty quantification and scattered data approximation, but has received relatively little attention from a numerical analysis standpoint. The basic problem of finding an…

Numerical Analysis · Mathematics 2021-04-02 Toni Karvonen , Chris J. Oates , Mark Girolami

Kernel based methods have shown effective performance in many remote sensing classification tasks. However their performance significantly depend on its hyper-parameters. The conventional technique to estimate the parameter comes with high…

Machine Learning · Statistics 2018-04-17 Bharath Bhushan Damodaran

Marginalising over families of Gaussian Process kernels produces flexible model classes with well-calibrated uncertainty estimates. Existing approaches require likelihood evaluations of many kernels, rendering them prohibitively expensive…

Machine Learning · Statistics 2023-03-16 Saad Hamid , Sebastian Schulze , Michael A. Osborne , Stephen J. Roberts

Gaussian process regression (GPR) is a popular nonparametric Bayesian method that provides predictive uncertainty estimates and is widely used in safety-critical applications. While prior research has introduced various uncertainty bounds,…

Machine Learning · Computer Science 2025-12-05 Junyi Liu , Stanley Kok

Retinal prostheses restore vision by electrically stimulating surviving neurons, but calibrating perceptual thresholds (i.e., the minimum stimulus intensity required for perception) remains a time-intensive challenge, especially for…

Quantitative Methods · Quantitative Biology 2025-04-30 Roksana Sadeghi , Michael Beyeler

In the univariate setting, using the kernel spectral representation is an appealing approach for generating stationary covariance functions. However, performing the same task for multiple-output Gaussian processes is substantially more…

Machine Learning · Statistics 2021-03-15 Fergus Simpson , Alexis Boukouvalas , Vaclav Cadek , Elvijs Sarkans , Nicolas Durrande

The general perception is that kernel methods are not scalable, and neural nets are the methods of choice for nonlinear learning problems. Or have we simply not tried hard enough for kernel methods? Here we propose an approach that scales…

Machine Learning · Computer Science 2015-09-11 Bo Dai , Bo Xie , Niao He , Yingyu Liang , Anant Raj , Maria-Florina Balcan , Le Song

In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The…

Statistics Theory · Mathematics 2022-07-20 Wenjia Wang , Bing-Yi Jing

There are schemes for realizing different types of kernels by quantum states of light. It is particularly interesting to realize the Gaussian kernel due to its wider applicability. A multimode coherent state can generate the Gaussian kernel…

Quantum Physics · Physics 2024-10-01 Vivek Mehta , Utpal Roy