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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 provide a powerful probabilistic kernel learning framework, which allows learning high quality nonparametric regression models via methods such as Gaussian process regression. Nevertheless, the learning phase of Gaussian…

Numerical Analysis · Mathematics 2021-01-06 Paz Fink Shustin , Haim Avron

Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but that are rarely used in signal processing. In this tutorial, we present GPs for regression as…

We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in…

Machine Learning · Statistics 2019-01-04 Pablo Moreno-Muñoz , Antonio Artés-Rodríguez , Mauricio A. Álvarez

Gaussian process regression is a powerful method for predicting states based on given data. It has been successfully applied for probabilistic predictions of structural systems to quantify, for example, the crack growth in mechanical…

Machine Learning · Statistics 2022-06-20 Simon Pfingstl , Markus Zimmermann

We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a…

Machine Learning · Statistics 2017-09-19 Erik Bodin , Neill D. F. Campbell , Carl Henrik Ek

Gaussian Process Regression (GPR) is widely used in statistics and machine learning for prediction tasks requiring uncertainty measures. Its efficacy depends on the appropriate specification of the mean function, covariance kernel function,…

Machine Learning · Computer Science 2024-09-20 Shifan Zhao , Jiaying Lu , Ji Yang , Edmond Chow , Yuanzhe Xi

In application areas where data generation is expensive, Gaussian processes are a preferred supervised learning model due to their high data-efficiency. Particularly in model-based control, Gaussian processes allow the derivation of…

Machine Learning · Computer Science 2021-01-15 Armin Lederer , Jonas Umlauft , Sandra Hirche

In this paper, we present a comprehensive analysis of the posterior covariance field in Gaussian processes, with applications to the posterior covariance matrix. The analysis is based on the Gaussian prior covariance but the approach also…

Machine Learning · Statistics 2025-04-03 Difeng Cai , Edmond Chow , Yuanzhe Xi

This paper presents a unified treatment of Gaussian process models that extends to data from the exponential dispersion family and to survival data. Our specific interest is in the analysis of data sets with predictors that have an a priori…

Methodology · Statistics 2011-06-17 Terrance Savitsky , Marina Vannucci , Naijun Sha

Calibration is a highly challenging task, in particular in multiple yield curve markets. This paper is a first attempt to study the chances and challenges of the application of machine learning techniques for this. We employ Gaussian…

Pricing of Securities · Quantitative Finance 2020-04-20 Sandrine Gümbel , Thorsten Schmidt

Let $P$ be a linear differential operator over $\mathcal{D} \subset \mathbb{R}^d$ and $U = (U_x)_{x \in \mathcal{D}}$ a second order stochastic process. In the first part of this article, we prove a new necessary and sufficient condition…

Statistics Theory · Mathematics 2022-02-11 Iain Henderson , Pascal Noble , Olivier Roustant

Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the…

Machine Learning · Statistics 2013-10-18 Amir F. Atiya , Hatem A. Fayed , Ahmed H. Abdel-Gawad

We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…

Machine Learning · Computer Science 2021-11-03 Oliver Hamelijnck , William J. Wilkinson , Niki A. Loppi , Arno Solin , Theodoros Damoulas

Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns…

Machine Learning · Statistics 2014-01-03 Andrew Gordon Wilson , Ryan Prescott Adams

This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…

Methodology · Statistics 2019-02-14 Pallavi Ray , Debdeep Pati , Anirban Bhattacharya

Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…

Machine Learning · Statistics 2015-03-23 Yarin Gal , Richard Turner

Despite the widespread utilization of Gaussian process models for versatile nonparametric modeling, they exhibit limitations in effectively capturing abrupt changes in function smoothness and accommodating relationships with heteroscedastic…

Machine Learning · Statistics 2023-09-01 Taehee Lee , Jun S. Liu

Gaussian processes (GPs) are powerful and widely used probabilistic regression models, but their effectiveness in practice is often limited by the choice of kernel function. This kernel function is typically handcrafted from a small set of…

Machine Learning · Computer Science 2026-02-13 Jihao Andreas Lin , Sebastian Ament , Louis C. Tiao , David Eriksson , Maximilian Balandat , Eytan Bakshy

Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial…

Machine Learning · Computer Science 2019-08-05 Mamikon Gulian , Maziar Raissi , Paris Perdikaris , George Karniadakis