Related papers: Gaussian kernel quadrature at scaled Gauss-Hermite…
Ulmer and Kaissl formulas for the deconvolution of one-dimensional Gaussian kernels are generalized to the three-dimensional case. The generalization is based on the use of the scalar version of the Grad's multivariate Hermite polynomials…
It is well-known that polynomial reproduction is not possible when approximating with Gaussian kernels. Quasi-interpolation schemes have been developed which use a finite number of Gaussians at different scales, which then reproduce…
Error estimates for kernel interpolation in Reproducing Kernel Hilbert Spaces (RKHS) usually assume quite restrictive properties on the shape of the domain, especially in the case of infinitely smooth kernels like the popular Gaussian…
In this work we consider the problem of numerical integration, i.e., approximating integrals with respect to a target probability measure using only pointwise evaluations of the integrand. We focus on the setting in which the target…
Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel based methods for additive models. These learning rates compare favourably in particular in high dimensions to…
We develop an exact and scalable algorithm for one-dimensional Gaussian process regression with Mat\'ern correlations whose smoothness parameter $\nu$ is a half-integer. The proposed algorithm only requires $\mathcal{O}(\nu^3 n)$ operations…
Starting with the correspondence between positive definite kernels on the one hand and reproducing kernel Hilbert spaces (RKHSs) on the other, we turn to a detailed analysis of associated measures and Gaussian processes. Point of departure:…
Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…
Gaussian processes offers a convenient way to perform nonparametric reconstructions of observational data assuming only a kernel which describes the covariance between neighbouring points in a data set. We approach the ambiguity in the…
Let L be a holomorphic line bundle over a compact complex projective Hermitian manifold X. Any fixed smooth hermitian metric h on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k th tensor…
Gaussian Process regression is a kernel method successfully adopted in many real-life applications. Recently, there is a growing interest on extending this method to non-Euclidean input spaces, like the one considered in this paper,…
We present an elementary proof for an approximate expression of the Bergman kernel on homogeneous spaces, and products of them. The error term is exponentially small with respect to the inverse semiclassical parameter.
We introduce a kernel approximation strategy that enables computation of the Gaussian process log marginal likelihood and all hyperparameter derivatives in $\mathcal{O}(p)$ time. Our GRIEF kernel consists of $p$ eigenfunctions found using a…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…
In this work, we investigate Gaussian Processes indexed by multidimensional distributions. While directly constructing radial positive definite kernels based on the Wasserstein distance has been proven to be possible in the unidimensional…
Let L be an ample holomorphic line bundle over a compact complex Hermitian manifold X. Any fixed smooth Hermitian metric on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k:th tensor power…
We construct approximate Fekete point sets for kernel-based interpolation by maximising the determinant of a kernel Gram matrix obtained via truncation of an orthonormal expansion of the kernel. Uniform error estimates are proved for kernel…
This work studies the convergence and finite sample approximations of entropic regularized Wasserstein distances in the Hilbert space setting. Our first main result is that for Gaussian measures on an infinite-dimensional Hilbert space,…
We show that geometric inference of a point cloud can be calculated by examining its kernel density estimate with a Gaussian kernel. This allows one to consider kernel density estimates, which are robust to spatial noise, subsampling, and…
Reliable prediction of protein variant effects is crucial for both protein optimization and for advancing biological understanding. For practical use in protein engineering, it is important that we can also provide reliable uncertainty…