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We propose a Standing Wave Decomposition (SWD) approximation to Gaussian Process regression (GP). GP involves a costly matrix inversion operation, which limits applicability to large data analysis. For an input space that can be…

Machine Learning · Statistics 2018-09-19 Chi-Ken Lu , Scott Cheng-Hsin Yang , Patrick Shafto

Gaussian Processes (GPs) are widely recognized as powerful non-parametric models for regression and classification. Traditional GP frameworks predominantly operate under the assumption that the inputs are either accurately known or subject…

Systems and Control · Electrical Eng. & Systems 2025-10-14 Muzaffar Qureshi , Tochukwu Elijah Ogri , Zachary I. Bell , Wanjiku A. Makumi , Rushikesh Kamalapurkar

Gaussian processes (GP) for machine learning have been studied systematically over the past two decades and they are by now widely used in a number of diverse applications. However, GP kernel design and the associated hyper-parameter…

Machine Learning · Computer Science 2020-10-28 Feng Yin , Lishuo Pan , Xinwei He , Tianshi Chen , Sergios Theodoridis , Zhi-Quan , Luo

Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…

Gaussian process (GP) regression is a non-parametric, Bayesian framework to approximate complex models. Standard GP regression can lead to an unbounded model in which some points can take infeasible values. We introduce a new GP method that…

Machine Learning · Statistics 2024-04-04 Didem Kochan , Xiu Yang

Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…

Methodology · Statistics 2011-06-29 Anjishnu Banerjee , David Dunson , Surya Tokdar

We explore the link between deep ensembles and Gaussian processes (GPs) through the lens of the Neural Tangent Kernel (NTK): a recent development in understanding the training dynamics of wide neural networks (NNs). Previous work has shown…

Machine Learning · Statistics 2020-10-27 Bobby He , Balaji Lakshminarayanan , Yee Whye Teh

Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick…

Machine Learning · Statistics 2011-08-15 Ferenc Huszár , Simon Lacoste-Julien

In this paper, we study the inverse scattering problem for a class of signals that have a compactly supported reflection coefficient. The problem boils down to the solution of the Gelfand-Levitan-Marchenko (GLM) integral equations with a…

Computational Physics · Physics 2019-02-12 Vishal Vaibhav

Gaussian Process (GPs) models are a rich distribution over functions with inductive biases controlled by a kernel function. Learning occurs through the optimisation of kernel hyperparameters using the marginal likelihood as the objective.…

Machine Learning · Statistics 2021-11-22 Fergus Simpson , Vidhi Lalchand , Carl Edward Rasmussen

A single-index model (SIM) provides for parsimonious multi-dimensional nonlinear regression by combining parametric (linear) projection with univariate nonparametric (non-linear) regression models. We show that a particular Gaussian process…

Methodology · Statistics 2011-08-18 Robert B. Gramacy , Heng Lian

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 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

Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…

Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…

Machine Learning · Statistics 2022-10-12 Marcus M. Noack , James A. Sethian

Gaussian processes (GPs) are the most common formalism for defining probability distributions over spaces of functions. While applications of GPs are myriad, a comprehensive understanding of GP sample paths, i.e. the function spaces over…

Machine Learning · Computer Science 2026-01-06 Nathaël Da Costa , Marvin Pförtner , Lancelot Da Costa , Philipp Hennig

Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains…

Machine Learning · Computer Science 2026-01-14 Md Shafiqul Islam , Shakti Prasad Padhy , Douglas Allaire , Raymundo Arróyave

This work presents a family of parsimonious Gaussian process models which allow to build, from a finite sample, a model-based classifier in an infinite dimensional space. The proposed parsimonious models are obtained by constraining the…

Methodology · Statistics 2012-06-18 Charles Bouveyron , Stéphane Girard , Mathieu Fauvel

Gaussian processes (GPs) produce good probabilistic models of functions, but most GP kernels require $O((n+m)n^2)$ time, where $n$ is the number of data points and $m$ the number of predictive locations. We present a new kernel that allows…

Machine Learning · Computer Science 2023-04-03 Michael K. Cohen , Samuel Daulton , Michael A. Osborne

Many datasets are in the form of tables of binned data. Performing regression on these data usually involves either reading off bin heights, ignoring data from neighbouring bins or interpolating between bins thus over or underestimating the…

Machine Learning · Statistics 2019-05-21 Michael Thomas Smith , Mauricio A Alvarez , Neil D Lawrence