Related papers: Gaussian kernel expansion with basis functions uni…
Bayesian inference and kernel methods are well established in machine learning. The neural network Gaussian process in particular provides a concept to investigate neural networks in the limit of infinitely wide hidden layers by using…
Image acquisition and segmentation are likely to introduce noise. Further image processing such as image registration and parameterization can introduce additional noise. It is thus imperative to reduce noise measurements and boost signal.…
This paper examines experimental design procedures used to develop surrogates of computational models, exploring the interplay between experimental designs and approximation algorithms. We focus on two widely used approximation approaches,…
Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…
We consider a kernel based harmonic analysis of "boundary," and boundary representations. Our setting is general: certain classes of positive definite kernels. Our theorems extend (and are motivated by) results and notions from classical…
Gaussian process modeling is a standard tool for building emulators for computer experiments, which are usually used to study deterministic functions, for example, a solution to a given system of partial differential equations. This work…
Nonlinear kernels can be approximated using finite-dimensional feature maps for efficient risk minimization. Due to the inherent trade-off between the dimension of the (mapped) feature space and the approximation accuracy, the key problem…
Kernel mean embeddings have recently attracted the attention of the machine learning community. They map measures $\mu$ from some set $M$ to functions in a reproducing kernel Hilbert space (RKHS) with kernel $k$. The RKHS distance of two…
On Euclidean spaces, the Gaussian kernel is one of the most widely used kernels in applications. It has also been used on non-Euclidean spaces, where it is known that there may be (and often are) scale parameters for which it is not…
We show that common choices of kernel functions for a highly accurate and massively scalable nearest-neighbour based GP regression model (GPnn: \cite{GPnn}) exhibit gradual convergence to asymptotic behaviour as dataset-size $n$ increases.…
We obtain upper bounds for the estimation error of Kernel Ridge Regression (KRR) for all non-negative regularization parameters, offering a geometric perspective on various phenomena in KRR. As applications: 1. We address the multiple…
We investigate uncertainties in the estimation of the Hubble constant ($H_0$) arising from Gaussian Process (GP) reconstruction, demonstrating that the choice of kernel introduces systematic variations comparable to those arising from…
The sample complexity of estimating or maximising an unknown function in a reproducing kernel Hilbert space is known to be linked to both the effective dimension and the information gain associated with the kernel. While the information…
Recent cosmological observations have achieved high-precision measurements of the Universe's expansion history, prompting the use of nonparametric methods such as Gaussian processes (GP) regression. We apply GP regression for reconstructing…
This article studies sufficient conditions on families of approximating kernels which provide $N$--term approximation errors from an associated nonlinear approximation space which match the best known orders of $N$--term wavelet expansion.…
Regularization is a well recognized powerful strategy to improve the performance of a learning machine and $l^q$ regularization schemes with $0<q<\infty$ are central in use. It is known that different $q$ leads to different properties of…
A recurrent theme in functional analysis is the interplay between the theory of positive definite functions, and their reproducing kernels, on the one hand, and Gaussian stochastic processes, on the other. This central theme is motivated by…
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…
We consider learning on graphs, guided by kernels that encode similarity between vertices. Our focus is on random walk kernels, the analogues of squared exponential kernels in Euclidean spaces. We show that on large, locally treelike,…
We investigate the capabilities and limitations of Gaussian process models by jointly exploring three complementary directions: (i) scalable and statistically efficient inference; (ii) flexible kernels; and (iii) objective functions for…