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Related papers: Remarks on multivariate Gaussian Process

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In this paper we address the statistical problem of testing if a stationary process is Gaussian. The observation consists in a finite sample path of the process. Using a random projection technique introduced and studied in Cuesta-Albertos…

Methodology · Statistics 2009-11-19 Juan . A. Cuesta-Albertos , Fabrice Gamboa Alicia Nieto-Reyes

The process $(G_t)_{t\in[0,T]}$ is referred to as a fractional Gaussian process if the first-order partial derivative of the difference between its covariance function and that of the fractional Brownian motion $(B^H_t)_{t\in[0,T ]}$ is a…

Probability · Mathematics 2023-09-20 Yong Chen , Ying Li

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

Stochastic integration \textit{wrt} Gaussian processes has raised strong interest in recent years, motivated in particular by its applications in Internet traffic modeling, biomedicine and finance. The aim of this work is to define and…

Probability · Mathematics 2018-02-15 Joachim Lebovits

Recently there has been an increasing interest in methods that deal with multiple outputs. This has been motivated partly by frameworks like multitask learning, multisensor networks or structured output data. From a Gaussian processes…

Machine Learning · Statistics 2009-11-30 Mauricio A. Álvarez , Neil D. Lawrence

Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…

Computation · Statistics 2016-04-18 Andreas Svensson , Arno Solin , Simo Särkkä , Thomas B. Schön

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

We study nonparametric Bayesian inference for the intensity function of a covariate-driven point process. We extend recent results from the literature, showing that a wide class of Gaussian priors, combined with flexible link functions,…

Statistics Theory · Mathematics 2025-05-27 Patric Dolmeta , Matteo Giordano

Gaussian processes are one of the dominant approaches in Bayesian learning. Although the approach has been applied to numerous problems with great success, it has a few fundamental limitations. Multiple methods in literature have addressed…

Machine Learning · Computer Science 2021-06-24 Kalvik Jakkala

Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…

This tutorial aims to provide an intuitive introduction to Gaussian process regression (GPR). GPR models have been widely used in machine learning applications due to their representation flexibility and inherent capability to quantify…

Machine Learning · Statistics 2024-01-30 Jie Wang

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…

This paper develops a generalization of Brownian motion with stationary, autocorrelated increments as a tractable model for problems in business and finance. We show that any real continuous Gaussian Markov process with stationary…

Probability · Mathematics 2012-12-03 Kerry Fendick

A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…

Data Analysis, Statistics and Probability · Physics 2019-09-10 Christopher G. Albert

A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…

Applications · Statistics 2013-01-14 Shan Ba , V. Roshan Joseph

Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic…

Machine Learning · Computer Science 2022-02-24 Krista Longi , Jakob Lindinger , Olaf Duennbier , Melih Kandemir , Arto Klami , Barbara Rakitsch

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 processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the…

Gaussian processes (GPs) are widely-used tools in spatial statistics and machine learning and the formulae for the mean function and covariance kernel of a GP $T u$ that is the image of another GP $u$ under a linear transformation $T$…

Probability · Mathematics 2024-10-08 Tadashi Matsumoto , T. J. Sullivan

Multivariate categorical data occur in many applications of machine learning. One of the main difficulties with these vectors of categorical variables is sparsity. The number of possible observations grows exponentially with vector length,…

Machine Learning · Statistics 2015-03-10 Yarin Gal , Yutian Chen , Zoubin Ghahramani