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In this paper we introduce a novel model for Gaussian process (GP) regression in the fully Bayesian setting. Motivated by the ideas of sparsification, localization and Bayesian additive modeling, our model is built around a recursive…

Statistics Theory · Mathematics 2022-06-06 Hengrui Luo , Giovanni Nattino , Matthew T. Pratola

Although machine learning is increasingly applied in control approaches, only few methods guarantee certifiable safety, which is necessary for real world applications. These approaches typically rely on well-understood learning algorithms,…

Machine Learning · Computer Science 2020-06-16 Armin Lederer , Markus Kessler , Sandra Hirche

In this paper we first identify a basic limitation in gradient descent-based optimization methods when used in conjunctions with smooth kernels. An analysis based on the spectral properties of the kernel demonstrates that only a vanishingly…

Machine Learning · Statistics 2017-06-20 Siyuan Ma , Mikhail Belkin

Gaussian process regression generally does not scale to beyond a few thousands data points without applying some sort of kernel approximation method. Most approximations focus on the high eigenvalue part of the spectrum of the kernel…

Machine Learning · Statistics 2018-01-31 Yi Ding , Risi Kondor , Jonathan Eskreis-Winkler

Making predictions and quantifying their uncertainty when the input data is sequential is a fundamental learning challenge, recently attracting increasing attention. We develop SigGPDE, a new scalable sparse variational inference framework…

Machine Learning · Statistics 2021-10-13 Maud Lemercier , Cristopher Salvi , Thomas Cass , Edwin V. Bonilla , Theodoros Damoulas , Terry Lyons

Exact Gaussian Process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure…

Machine Learning · Statistics 2012-09-24 Elad Gilboa , Yunus Saatçi , John P. Cunningham

We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We propose the harmonic kernel decomposition (HKD), which uses Fourier series to…

Machine Learning · Computer Science 2021-06-14 Shengyang Sun , Jiaxin Shi , Andrew Gordon Wilson , Roger Grosse

This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and…

Machine Learning · Statistics 2018-07-10 Motonobu Kanagawa , Philipp Hennig , Dino Sejdinovic , Bharath K Sriperumbudur

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

Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…

Machine Learning · Computer Science 2016-03-08 Z. Zhang , K. Duraisamy , N. A. Gumerov

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…

Machine Learning · Statistics 2018-01-23 Ching-An Cheng , Byron Boots

Gaussian processes are flexible function approximators, with inductive biases controlled by a covariance kernel. Learning the kernel is the key to representation learning and strong predictive performance. In this paper, we develop…

Machine Learning · Computer Science 2019-10-31 Gregory W. Benton , Wesley J. Maddox , Jayson P. Salkey , Julio Albinati , Andrew Gordon Wilson

Kernel methods have revolutionized the fields of pattern recognition and machine learning. Their success, however, critically depends on the choice of kernel parameters. Using Gaussian process (GP) classification as a working example, this…

Methodology · Statistics 2014-05-27 Maurizio Filippone

Gaussian processes~(Kriging) are interpolating data-driven models that are frequently applied in various disciplines. Often, Gaussian processes are trained on datasets and are subsequently embedded as surrogate models in optimization…

Optimization and Control · Mathematics 2024-01-17 Artur M. Schweidtmann , Dominik Bongartz , Daniel Grothe , Tim Kerkenhoff , Xiaopeng Lin , Jaromil Najman , Alexander Mitsos

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

Random binning features, introduced in the seminal paper of Rahimi and Recht (2007), are an efficient method for approximating a kernel matrix using locality sensitive hashing. Random binning features provide a very simple and efficient way…

Machine Learning · Statistics 2020-03-24 Michael Kapralov , Navid Nouri , Ilya Razenshteyn , Ameya Velingker , Amir Zandieh

Kernel methods are versatile tools for function approximation and surrogate modeling. In particular, greedy techniques offer computational efficiency and reliability through inherent sparsity and provable convergence. Inspired by the…

Numerical Analysis · Mathematics 2026-03-09 Marian Klink , Tobias Ehring , Robin Herkert , Robin Lautenschlager , Dominik Göddeke , Bernard Haasdonk

We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of…

Machine Learning · Statistics 2024-02-27 Jiaxin Shi , Michalis K. Titsias , Andriy Mnih

Choosing the most adequate kernel is crucial in many Machine Learning applications. Gaussian Process is a state-of-the-art technique for regression and classification that heavily relies on a kernel function. However, in the Gaussian…

Machine Learning · Computer Science 2019-10-15 Ibai Roman , Roberto Santana , Alexander Mendiburu , Jose A. Lozano

Gaussian processes (GPs) are non-parametric, flexible, models that work well in many tasks. Combining GPs with deep learning methods via deep kernel learning (DKL) is especially compelling due to the strong representational power induced by…

Machine Learning · Computer Science 2021-07-14 Idan Achituve , Aviv Navon , Yochai Yemini , Gal Chechik , Ethan Fetaya