Related papers: Optimal design for kernel interpolation: applicati…
We propose a computationally efficient method to construct nonparametric, heteroscedastic prediction bands for uncertainty quantification, with or without any user-specified predictive model. Our approach provides an alternative to the…
We propose a new approach to computing global minimizers of singular value functions in two real variables. Specifically, we present new algorithms to compute the Kreiss constant of a matrix and the distance to uncontrollability of a linear…
The radial basis function (RBF) and quasi Monte Carlo (QMC) methods are two very promising schemes to handle high-dimension problems with complex and moving boundary geometry due to the fact that they are independent of dimensionality and…
Random Fourier Features (RFF) is among the most popular and broadly applicable approaches for scaling up kernel methods. In essence, RFF allows the user to avoid costly computations on a large kernel matrix via a fast randomized…
We design quasi-interpolation operators based on piecewise polynomial weight functions of degree less than or equal to $p$ that map into the space of continuous piecewise polynomials of degree less than or equal to $p+1$. We show that the…
We introduce a new structured kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce kernel approximations for fast computations through kernel…
In this paper, we propose a new threshold-kernel jump-detection method for jump-diffusion processes, which iteratively applies thresholding and kernel methods in an approximately optimal way to achieve improved finite-sample performance. We…
We describe a fast method for solving elliptic partial differential equations (PDEs) with uncertain coefficients using kernel interpolation at a lattice point set. By representing the input random field of the system using the model…
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…
The randomly pivoted partial Cholesky algorithm (RPCholesky) computes a factorized rank-k approximation of an N x N positive-semidefinite (psd) matrix. RPCholesky requires only (k + 1) N entry evaluations and O(k^2 N) additional arithmetic…
Recent developments have made it possible to overcome grid-based limitations of finite difference (FD) methods by adopting the kernel-based meshless framework using radial basis functions (RBFs). Such an approach provides a meshless…
The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…
Despite the success of the popular kernelized support vector machines, they have two major limitations: they are restricted to Positive Semi-Definite (PSD) kernels, and their training complexity scales at least quadratically with the size…
Deep neural networks are increasingly being used for the analysis of medical images. However, most works neglect the uncertainty in the model's prediction. We propose an uncertainty-aware deep kernel learning model which permits the…
In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered…
We survey classical kernel methods for providing nonparametric solutions to problems involving measurement error. In particular we outline kernel-based methodology in this setting, and discuss its basic properties. Then we point to close…
Quantum kernel methods leverage a kernel function computed by embedding input information into the Hilbert space of a quantum system. However, large Hilbert spaces can hinder generalization capability, and the scalability of quantum kernels…
We propose a multiple-kernel local-patch descriptor based on efficient match kernels from pixel gradients. It combines two parametrizations of gradient position and direction, each parametrization provides robustness to a different type of…
This paper proposes a new gradient-based optimization approach for designing optimal feedback kernels for parabolic distributed parameter systems with boundary control. Unlike traditional kernel optimization methods for parabolic systems,…
This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting. For a wide class of compact, connected $C^\infty$ Riemannian manifolds, including the important cases of spheres and…