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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 introduce a Gaussian process-based model for handling of non-stationarity. The warping is achieved non-parametrically, through imposing a prior on the relative change of distance between subsequent observation inputs. The model allows…

Machine Learning · Statistics 2019-12-06 David Tolpin

Non linear regression models are a standard tool for modeling real phenomena, with several applications in machine learning, ecology, econometry... Estimating the parameters of the model has garnered a lot of attention during many years. We…

Statistics Theory · Mathematics 2020-09-17 Peggy Cénac , Antoine Godichon-Baggioni , Bruno Portier

Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick…

Machine Learning · Statistics 2011-08-15 Ferenc Huszár , Simon Lacoste-Julien

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…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

Machine Learning · Statistics 2026-05-14 Rafael Oliveira

Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for…

Machine Learning · Statistics 2023-12-14 Tomoharu Iwata , Atsutoshi Kumagai

Gaussian Process Regression (GPR) is widely used for inferring functions from noisy data. GPR crucially relies on the choice of a kernel, which might be specified in terms of a collection of hyperparameters that must be chosen or learned.…

Numerical Analysis · Mathematics 2025-06-16 P. Michael Kielstra , Michael Lindsey

We present a novel approach for fully non-stationary Gaussian process regression (GPR), where all three key parameters -- noise variance, signal variance and lengthscale -- can be simultaneously input-dependent. We develop gradient-based…

Machine Learning · Statistics 2015-08-19 Markus Heinonen , Henrik Mannerström , Juho Rousu , Samuel Kaski , Harri Lähdesmäki

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

Gaussian processes constitute a very powerful and well-understood method for non-parametric regression and classification. In the classical framework, the training data consists of deterministic vector-valued inputs and the corresponding…

Systems and Control · Computer Science 2018-09-26 Maxim Dolgov , Uwe D. Hanebeck

Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient…

Quantum Physics · Physics 2024-02-06 Frederic Rapp , Marco Roth

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

Computation · Statistics 2022-08-31 Vahid Keshavarzzadeh , Robert M. Kirby , Akil Narayan

Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…

Machine Learning · Computer Science 2018-09-11 Linfeng Liu , Liping Liu

Structural kernels are a flexible learning paradigm that has been widely used in Natural Language Processing. However, the problem of model selection in kernel-based methods is usually overlooked. Previous approaches mostly rely on setting…

Computation and Language · Computer Science 2015-08-11 Daniel Beck , Trevor Cohn , Christian Hardmeier , Lucia Specia

Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model…

Machine Learning · Statistics 2018-03-21 Gonzalo Rios , Felipe Tobar

In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…

Methodology · Statistics 2020-10-02 Hossein Mohammadi , Peter Challenor , Marc Goodfellow , Daniel Williamson

Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…

Machine Learning · Computer Science 2020-01-01 Ian A. Delbridge , David S. Bindel , Andrew Gordon Wilson

Stationary points embedded in the derivatives are often critical for a model to be interpretable and may be considered as key features of interest in many applications. We propose a semiparametric Bayesian model to efficiently infer the…

Methodology · Statistics 2024-06-11 Cheng-Han Yu , Meng Li , Colin Noe , Simon Fischer-Baum , Marina Vannucci

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…

Statistics Theory · Mathematics 2013-02-19 Michael Vogt