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Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…

Machine Learning · Statistics 2019-03-04 Philippe Wenk , Alkis Gotovos , Stefan Bauer , Nico Gorbach , Andreas Krause , Joachim M. Buhmann

Identifying dynamical system (DS) is a vital task in science and engineering. Traditional methods require numerous calls to the DS solver, rendering likelihood-based or least-squares inference frameworks impractical. For efficient parameter…

Computation · Statistics 2024-09-19 Ying Zhou , Jinglai Li , Xiang Zhou , Hongqiao Wang

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…

Data Analysis, Statistics and Probability · Physics 2007-05-23 J. C. Lemm

Kernel methods on discrete domains have shown great promise for many challenging data types, for instance, biological sequence data and molecular structure data. Scalable kernel methods like Support Vector Machines may offer good predictive…

Machine Learning · Statistics 2021-05-27 Vincent Fortuin , Gideon Dresdner , Heiko Strathmann , Gunnar Rätsch

Constructing a classical potential suited to simulate a given atomic system is a remarkably difficult task. This chapter presents a framework under which this problem can be tackled, based on the Bayesian construction of nonparametric force…

Computational Physics · Physics 2020-07-01 Aldo Glielmo , Claudio Zeni , Ádám Fekete , Alessandro De Vita

Due to its state-of-the-art estimation performance complemented by rigorous and non-conservative uncertainty bounds, Gaussian process regression is a popular tool for enhancing dynamical system models and coping with their inaccuracies.…

Systems and Control · Electrical Eng. & Systems 2025-02-05 Anna Scampicchio , Elena Arcari , Amon Lahr , Melanie N. Zeilinger

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

Machine Learning · Computer Science 2014-08-12 Jie Chen , Nannan Cao , Kian Hsiang Low , Ruofei Ouyang , Colin Keng-Yan Tan , Patrick Jaillet

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

Machine Learning · Statistics 2013-05-27 Jie Chen , Nannan Cao , Kian Hsiang Low , Ruofei Ouyang , Colin Keng-Yan Tan , Patrick Jaillet

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 machine learning models capable of learning unknown functions in a way that represents uncertainty, thereby facilitating construction of optimal decision-making systems. Motivated by a desire to deploy Gaussian…

Gaussian process regression is used throughout statistics and machine learning for prediction and uncertainty quantification. A Gaussian process is specified by its mean and covariance functions. Many covariance functions, including…

Statistics Theory · Mathematics 2025-10-28 Toni Karvonen , François Bachoc

Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…

Computation · Statistics 2024-02-02 Ahmad Farooq , Cristian A. Galvis-Florez , Simo Särkkä

The focus of this work is the convergence of non-stationary and deep Gaussian process regression. More precisely, we follow a Bayesian approach to regression or interpolation, where the prior placed on the unknown function $f$ is a…

Statistics Theory · Mathematics 2025-03-19 Conor Osborne , Aretha L. Teckentrup

This paper proposes a physically consistent Gaussian Process (GP) enabling the identification of uncertain Lagrangian systems. The function space is tailored according to the energy components of the Lagrangian and the differential equation…

Machine Learning · Computer Science 2023-02-06 Giulio Evangelisti , Sandra Hirche

This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian…

Chemical Physics · Physics 2019-04-04 Andrea Grisafi , David M. Wilkins , Michael J. Willatt , Michele Ceriotti

The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…

Methodology · Statistics 2022-03-29 Ali Rafei , Michael R. Elliott , Carol A. C. Flannagan

In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…

Statistics Theory · Mathematics 2015-03-06 Debdeep Pati , Anirban Bhattacharya , Guang Cheng

Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in…

Machine Learning · Statistics 2016-04-19 Alan D. Saul , James Hensman , Aki Vehtari , Neil D. Lawrence

We discuss the correspondence between Gaussian process regression and Geometric Harmonics, two similar kernel-based methods that are typically used in different contexts. Research communities surrounding the two concepts often pursue…

Machine Learning · Statistics 2021-10-07 Felix Dietrich , Juan M. Bello-Rivas , Ioannis G. Kevrekidis

With the significant advancement in quantum computation in the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used…

Quantum Physics · Physics 2018-03-07 Siddhartha Das , George Siopsis , Christian Weedbrook