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Gaussian Process (GP) regression models typically assume that residuals are Gaussian and have the same variance for all observations. However, applications with input-dependent noise (heteroscedastic residuals) frequently arise in practice,…

Machine Learning · Statistics 2012-12-27 Chunyi Wang , Radford M. Neal

High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear…

Machine Learning · Statistics 2011-07-26 Andreas C. Damianou , Michalis K. Titsias , Neil D. Lawrence

Gaussian process regression is widely applied in computational science and engineering for surrogate modeling owning to its kernel-based and probabilistic nature. In this work, we propose a Bayesian approach that integrates the variability…

Machine Learning · Computer Science 2025-01-03 Dongwei Ye , Weihao Yan , Christoph Brune , Mengwu Guo

Let $X = \{X_{u}\}_{u \in U}$ be a real-valued Gaussian process indexed by a set $U$. It can be thought of as an undirected graphical model with every random variable $X_{u}$ serving as a vertex. We characterize this graph in terms of the…

Statistics Theory · Mathematics 2023-12-13 Kartik G. Waghmare , Victor M. Panaretos

This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…

Machine Learning · Statistics 2019-09-12 Christian Agrell

Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…

Computation · Statistics 2021-03-08 Karla Monterrubio-Gómez , Sara Wade

High-dimensional classification and feature selection tasks are ubiquitous with the recent advancement in data acquisition technology. In several application areas such as biology, genomics and proteomics, the data are often functional in…

Machine Learning · Statistics 2021-09-30 W Yu , S Wade , H D Bondell , L Azizi

Gaussian processes are an effective model class for learning unknown functions, particularly in settings where accurately representing predictive uncertainty is of key importance. Motivated by applications in the physical sciences, the…

Machine Learning · Statistics 2023-04-19 Viacheslav Borovitskiy , Alexander Terenin , Peter Mostowsky , Marc Peter Deisenroth

We address the problem of continual learning in multi-task Gaussian process (GP) models for handling sequential input-output observations. Our approach extends the existing prior-posterior recursion of online Bayesian inference, i.e.\ past…

Machine Learning · Statistics 2019-11-04 Pablo Moreno-Muñoz , Antonio Artés-Rodríguez , Mauricio A. Álvarez

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 (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various…

Machine Learning · Computer Science 2021-12-16 Yuya Yoshikawa , Tomoharu Iwata

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

We present a multivariate Gaussian process regression approach for parameter field reconstruction based on the field's measurements collected at two different scales, the coarse and fine scales. The proposed approach treats the parameter…

Methodology · Statistics 2018-04-19 David A. Barajas-Solano , Alexandre M. Tartakovsky

A new probabilistic post-processing method for wind vectors is presented in a distributional regression framework employing the bivariate Gaussian distribution. In contrast to previous studies all parameters of the distribution are…

Applications · Statistics 2019-07-26 Moritz N. Lang , Georg J. Mayr , Reto Stauffer , Achim Zeileis

A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…

Methodology · Statistics 2023-01-18 Matthias Katzfuss , Florian Schäfer

In this paper we propose a novel Bayesian solution for nonlinear regression in complex fields. Previous solutions for kernels methods usually assume a complexification approach, where the real-valued kernel is replaced by a complex-valued…

Machine Learning · Computer Science 2018-03-02 Rafael Boloix-Tortosa , Eva Arias-de-Reyna , F. Javier Payan-Somet , Juan J. Murillo-Fuentes

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

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

Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…

Methodology · Statistics 2026-03-10 Adam Gorm Hoffmann , Claus Thorn Ekstrøm , Andreas Kryger Jensen

Using the concept of self-decomposable subordinators introduced in Gardini et al. [11], we build a new bivariate Normal Inverse Gaussian process that can capture stochastic delays. In addition, we also develop a novel path simulation scheme…

Computational Finance · Quantitative Finance 2020-11-10 Matteo Gardini , Piergiacomo Sabino , Emanuela Sasso