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This monograph studies the relations between two approaches using positive definite kernels: probabilistic methods using Gaussian processes, and non-probabilistic methods using reproducing kernel Hilbert spaces (RKHS). They are widely…

Machine Learning · Statistics 2025-06-24 Motonobu Kanagawa , Philipp Hennig , Dino Sejdinovic , Bharath K. Sriperumbudur

Gaussian Processes (GPs) provide a general and analytically tractable way of modeling complex time-varying, nonparametric functions. The Automatic Bayesian Covariance Discovery (ABCD) system constructs natural-language description of…

Machine Learning · Computer Science 2016-02-15 Yunseong Hwang , Anh Tong , Jaesik Choi

Future gravitational wave (GW) standard siren catalogues will probe the late-time expansion history of the Universe across redshift ranges largely inaccessible to traditional electromagnetic observations. To determine how effectively this…

Cosmology and Nongalactic Astrophysics · Physics 2026-05-27 Gourab Nandi , Anish Ghoshal , David F. Mota

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

Non-parametric reconstruction methods, such as Gaussian process (GP) regression, provide a model-independent way of estimating an underlying function and its uncertainty from noisy data. We demonstrate how GP-reconstruction can be used as a…

Cosmology and Nongalactic Astrophysics · Physics 2017-12-25 Amir Aghamousa , Jan Hamann , Arman Shafieloo

The current knowledge in cosmology deals with open problems whose solutions are still under investigation. The main issue is the so-called Hubble constant ($H_0$) tension, namely, the $4-6 \sigma$ discrepancy between the local value of…

Cosmology and Nongalactic Astrophysics · Physics 2025-01-23 Maria Giovanna Dainotti , Biagio De Simone , Aditya Narendra , Agnieszka Pollo

The Hubble constant ($H_0$) is essential for understanding the universe's evolution. Different methods, such as Affine Invariant Markov chain Monte Carlo Ensemble sampler (EMCEE), Gaussian Process (GP), and Masked Autoregressive Flow (MAF),…

Cosmology and Nongalactic Astrophysics · Physics 2026-04-29 Jing Niu , Jie-Feng Chen , Peng He , Tong-Jie Zhang , Jie Zhang

In nonparametric regression, it is common for the inputs to fall in a restricted subset of Euclidean space. Typical kernel-based methods that do not take into account the intrinsic geometry of the domain across which observations are…

Methodology · Statistics 2021-11-04 David B Dunson , Hau-Tieng Wu , Nan Wu

Blood flow reconstruction in the vasculature is important for many clinical applications. However, in clinical settings, the available data are often quite limited. For instance, Transcranial Doppler ultrasound (TCD) is a noninvasive…

Image and Video Processing · Electrical Eng. & Systems 2024-03-18 Shaghayegh Z. Ashtiani , Mohammad Sarabian , Kaveh Laksari , Hessam Babaee

The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…

Statistics Theory · Mathematics 2022-07-27 Kelly R. Moran , Matthew W. Wheeler

We apply two methods, namely the Gaussian processes and the non-parametric smoothing procedure, to reconstruct the Hubble parameter $H(z)$ as a function of redshift from 15 measurements of the expansion rate obtained from age estimates of…

Cosmology and Nongalactic Astrophysics · Physics 2016-03-02 Zhengxiang Li , J. E. Gonzalez , Hongwei Yu , Zong-Hong Zhu , J. S. Alcaniz

Current methods for stochastic hyperparameter learning in Gaussian Processes (GPs) rely on approximations, such as computing biased stochastic gradients or using inducing points in stochastic variational inference. However, when using such…

Machine Learning · Computer Science 2025-08-29 Neta Shoham , Haim Avron

In decision-making systems, it is important to have classifiers that have calibrated uncertainties, with an optimisation objective that can be used for automated model selection and training. Gaussian processes (GPs) provide uncertainty…

Machine Learning · Statistics 2020-03-05 Vincent Dutordoir , Mark van der Wilk , Artem Artemev , James Hensman

We investigate the ability to reconstruct and derive spatial structure from sparsely sampled 3D piezoresponse force microcopy data, captured using the band-excitation (BE) technique, via Gaussian Process (GP) methods. Even for weakly…

Gaussian Process (GPs) models are a rich distribution over functions with inductive biases controlled by a kernel function. Learning occurs through the optimisation of kernel hyperparameters using the marginal likelihood as the objective.…

Machine Learning · Statistics 2021-11-22 Fergus Simpson , Vidhi Lalchand , Carl Edward Rasmussen

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

Capsule Networks attempt to represent patterns in images in a way that preserves hierarchical spatial relationships. Additionally, research has demonstrated that these techniques may be robust against adversarial perturbations. We present…

Machine Learning · Statistics 2019-06-10 Taylor Killian , Justin Goodwin , Olivia Brown , Sung-Hyun Son

Accurately measuring the Hubble parameter is vital for understanding the expansion history and properties of the universe. In this paper, we propose a new method that supplements the covariance between redshift pairs to improve the…

Cosmology and Nongalactic Astrophysics · Physics 2024-01-23 Jian-Chen Zhang , Yu Hu , Kang Jiao , Hong-Feng Wang , Yuan-Bo Xie , Bo Yu , Li-Li Zhao , Tong-Jie Zhang

Gaussian Processes (GP) are widely used for probabilistic modeling and inference for nonparametric regression. However, their computational complexity scales cubicly with the sample size rendering them unfeasible for large data sets. To…

Statistics Theory · Mathematics 2022-05-11 Amine Hadji , Tammo Hesselink , Botond Szabó