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Related papers: New Flexible Compact Covariance Model on a Sphere

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In this paper a local approximation method on the sphere is presented. As interpolation scheme we consider a partition of unity method, such as the modified spherical Shepard's method, which uses zonal basis functions (ZBFs) plus spherical…

Numerical Analysis · Mathematics 2014-04-08 Alessandra De Rossi

We deal with the comparison of space-time covariance kernels having, either, full, spatially dynamical, or space-time compact support. Such a comparison is based on compatibility of these covariance models under fixed domain asymptotics,…

Statistics Theory · Mathematics 2023-06-13 Tarik Faouzi , Reinhard Furrer , Emilio Porcu

We propose a novel approach to parameter estimation for simulator-based statistical models with intractable likelihood. Our proposed method involves recursive application of kernel ABC and kernel herding to the same observed data. We…

Machine Learning · Statistics 2018-06-13 Takafumi Kajihara , Motonobu Kanagawa , Keisuke Yamazaki , Kenji Fukumizu

Spatio-temporal forecasting is challenging attributing to the high nonlinearity in temporal dynamics as well as complex location-characterized patterns in spatial domains, especially in fields like weather forecasting. Graph convolutions…

Machine Learning · Computer Science 2021-12-14 Haitao Lin , Zhangyang Gao , Yongjie Xu , Lirong Wu , Ling Li , Stan. Z. Li

In biomedical studies, we are often interested in the association between different types of covariates and the times to disease events. Because the relationship between the covariates and event times is often complex, standard survival…

Methodology · Statistics 2024-01-19 Hoi Min Ng , Kin Yau Wong

In this paper we introduce a reproducing kernel Hilbert space defined on $\mathbb{R}^{d+1}$ as the tensor product of a reproducing kernel defined on the unit sphere $\mathbb{S}^{d}$ in $\mathbb{R}^{d+1}$ and a reproducing kernel defined on…

Numerical Analysis · Mathematics 2015-12-24 Johann S. Brauchart , Josef Dick , Lou Fang

This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in $\mathbb{R}^3$,…

Statistics Theory · Mathematics 2017-10-05 Alfredo Alegría , Sandra Caro , Moreno Bevilacqua , Emilio Porcu , Jorge Clarke

In this paper, we analyze the spatial information of deep features, and propose two complementary regressions for robust visual tracking. First, we propose a kernelized ridge regression model wherein the kernel value is defined as the…

Computer Vision and Pattern Recognition · Computer Science 2018-04-25 Chong Sun , Dong Wang , Huchuan Lu , Ming-Hsuan Yang

Natural language processing often involves computations with semantic or syntactic graphs to facilitate sophisticated reasoning based on structural relationships. While convolution kernels provide a powerful tool for comparing graph…

Computation and Language · Computer Science 2018-02-13 Sahil Garg , Greg Ver Steeg , Aram Galstyan

Matrix-valued covariance functions are crucial to geostatistical modeling of multivariate spatial data. The classical assumption of symmetry of a multivariate covariance function is overlay restrictive and has been considered as unrealistic…

Statistics Theory · Mathematics 2017-11-28 Alfredo Alegría , Emilio Porcu , Reinhard Furrer

Diffusion magnetic resonance imaging is sensitive to the microstructural properties of brain tissue. However, estimating clinically and scientifically relevant microstructural properties from the measured signals remains a highly…

Image and Video Processing · Electrical Eng. & Systems 2024-02-27 Leevi Kerkelä , Kiran Seunarine , Filip Szczepankiewicz , Chris A. Clark

The method of covariant perturbation theory allowed for the computation of the kernel of the evolution equation on a spin Riemannian manifold. The proposed axiomatic definition of the covariant effective action introduces the universal…

General Relativity and Quantum Cosmology · Physics 2021-03-31 Yuri Vladimirovich Gusev

Needlets have been recognized as state-of-the-art tools to tackle spherical data, due to their excellent localization properties in both spacial and frequency domains. This paper considers developing kernel methods associated with the…

Machine Learning · Computer Science 2015-09-11 Shaobo Lin

Gaussian processes provide a flexible, non-parametric framework for the approximation of functions in high-dimensional spaces. The covariance kernel is the main engine of Gaussian processes, incorporating correlations that underpin the…

Machine Learning · Statistics 2024-03-20 Dionissios T. Hristopulos

This paper presents a method for the approximation of harmonic potentials that combines downward continuation of globally available data on a sphere $\Omega_R$ of radius $R$ (e.g., a satellite's orbit) with locally available data on a…

Numerical Analysis · Mathematics 2015-07-07 Christian Gerhards

Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a…

Machine Learning · Computer Science 2018-07-11 Martin Zaefferer , Thomas Bartz-Beielstein , Günter Rudolph

We derive a new discretisation method for first order PDEs of arbitrary spatial dimension, which is based upon a meshfree spatial approximation. This spatial approximation is similar to the SPH (smoothed particle hydrodynamics) technique…

Numerical Analysis · Mathematics 2016-01-25 Tobias Ramming , Holger Wendland

The method of 'covariant perturbation theory' allowed for the computation of the kernel of the evolution equation on a spin Riemannian manifold. The proposed axiomatic definition of the effective action introduces the universal scale…

General Physics · Physics 2021-02-09 Yuri Vladimirovich Gusev

We present a versatile formulation of the convolution operation that we term a "mapped convolution." The standard convolution operation implicitly samples the pixel grid and computes a weighted sum. Our mapped convolution decouples these…

Computer Vision and Pattern Recognition · Computer Science 2019-06-27 Marc Eder , True Price , Thanh Vu , Akash Bapat , Jan-Michael Frahm

We provide a space domain oriented separation of magnetic fields into parts generated by sources in the exterior and sources in the interior of a given sphere. The separation itself is well-known in geomagnetic modeling, usually in terms of…

Numerical Analysis · Mathematics 2015-06-04 Christian Gerhards