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This paper introduces an active learning framework for manifold Gaussian Process (GP) regression, combining manifold learning with strategic data selection to improve accuracy in high-dimensional spaces. Our method jointly optimizes a…

Machine Learning · Statistics 2026-05-12 Yuanxing Cheng , Lulu Kang , Yiwei Wang , Chun Liu

Gaussian process (GP) is a Bayesian model which provides several advantages for regression tasks in machine learning such as reliable quantitation of uncertainty and improved interpretability. Their adoption has been precluded by their…

Machine Learning · Computer Science 2023-06-26 Jonathan Parkinson , Wei Wang

Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper…

Numerical Analysis · Mathematics 2024-10-04 Daniel Sanz-Alonso , Ruiyi Yang

Quantum computing algorithms have been shown to produce performant quantum kernels for machine-learning classification problems. Here, we examine the performance of quantum kernels for regression problems of practical interest. For an…

Quantum Physics · Physics 2024-09-30 Xuyang Guo , Jun Dai , Roman V. Krems

This paper tackles the challenge presented by small-data to the task of Bayesian inference. A novel methodology, based on manifold learning and manifold sampling, is proposed for solving this computational statistics problem under the…

Machine Learning · Statistics 2019-10-29 Christian Soize , Roger Ghanem

This paper investigates the formulation and implementation of Bayesian inverse problems to learn input parameters of partial differential equations (PDEs) defined on manifolds. Specifically, we study the inverse problem of determining the…

Numerical Analysis · Mathematics 2019-10-24 John Harlim , Daniel Sanz-Alonso , Ruiyi Yang

Gaussian processes are typically used for smoothing and interpolation on small datasets. We introduce a new Bayesian nonparametric framework -- GPatt -- enabling automatic pattern extrapolation with Gaussian processes on large…

Machine Learning · Statistics 2014-01-03 Andrew Gordon Wilson , Elad Gilboa , Arye Nehorai , John P. Cunningham

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

Automating statistical modelling is a challenging problem in artificial intelligence. The Automatic Statistician takes a first step in this direction, by employing a kernel search algorithm with Gaussian Processes (GP) to provide…

Machine Learning · Statistics 2018-02-15 Hyunjik Kim , Yee Whye Teh

In a Bayesian learning setting, the posterior distribution of a predictive model arises from a trade-off between its prior distribution and the conditional likelihood of observed data. Such distribution functions usually rely on additional…

Machine Learning · Statistics 2011-11-01 Andrea Schirru , Simone Pampuri , Giuseppe De Nicolao , Sean McLoone

We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…

Computational Physics · Physics 2025-06-09 Christopher DeGrendele , Dongwook Lee

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

Learning the kernel parameters for Gaussian processes is often the computational bottleneck in applications such as online learning, Bayesian optimization, or active learning. Amortizing parameter inference over different datasets is a…

Machine Learning · Computer Science 2023-06-19 Matthias Bitzer , Mona Meister , Christoph Zimmer

This thesis focuses on data that has complex spatio-temporal structure and on probabilistic graphical models that learn the structure in an interpretable and scalable manner. We target two research areas of interest: Gaussian graphical…

Machine Learning · Computer Science 2023-01-18 Yu Wang

Large-scale precision matrix estimation is of fundamental importance yet challenging in many contemporary applications for recovering Gaussian graphical models. In this paper, we suggest a new approach of innovated scalable efficient…

Methodology · Statistics 2016-05-12 Yingying Fan , Jinchi Lv

Multiple kernel learning algorithms are proposed to combine kernels in order to obtain a better similarity measure or to integrate feature representations coming from different data sources. Most of the previous research on such methods is…

Machine Learning · Computer Science 2012-07-03 Mehmet Gonen

We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…

A Gaussian process has been one of the important approaches for emulating computer simulations. However, the stationarity assumption for a Gaussian process and the intractability for large-scale dataset limit its availability in practice.…

Methodology · Statistics 2020-11-06 Chih-Li Sung , Benjamin Haaland , Youngdeok Hwang , Siyuan Lu

Multi-dimensional Hawkes process (MHP) is a class of self and mutually exciting point processes that find wide range of applications -- from prediction of earthquakes to modelling of order books in high frequency trading. This paper makes…

Machine Learning · Statistics 2020-06-05 Sobin Joseph , Lekhapriya Dheeraj Kashyap , Shashi Jain

Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…

Methodology · Statistics 2011-06-29 Anjishnu Banerjee , David Dunson , Surya Tokdar