Related papers: Kernel Interpolation with Sparse Grids
A key challenge in scaling Gaussian Process (GP) regression to massive datasets is that exact inference requires computation with a dense n x n kernel matrix, where n is the number of data points. Significant work focuses on approximating…
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…
State-of-the-art methods for scalable Gaussian processes use iterative algorithms, requiring fast matrix vector multiplies (MVMs) with the covariance kernel. The Structured Kernel Interpolation (SKI) framework accelerates these MVMs by…
Recent work shows that inference for Gaussian processes can be performed efficiently using iterative methods that rely only on matrix-vector multiplications (MVMs). Structured Kernel Interpolation (SKI) exploits these techniques by deriving…
Structured Kernel Interpolation (SKI) (Wilson et al. 2015) helps scale Gaussian Processes (GPs) by approximating the kernel matrix via interpolation at inducing points, achieving linear computational complexity. However, it lacks rigorous…
We introduce Soft Kernel Interpolation (SoftKI), a method that combines aspects of Structured Kernel Interpolation (SKI) and variational inducing point methods, to achieve scalable Gaussian Process (GP) regression on high-dimensional…
A fast multilevel algorithm based on directionally scaled tensor-product Gaussian kernels on structured sparse grids is proposed for interpolation of high-dimensional functions and for the numerical integration of high-dimensional…
We present a mapping algorithm to compute large-scale magnetic field maps in indoor environments with approximate Gaussian process (GP) regression. Mapping the spatial variations in the ambient magnetic field can be used for localization…
We consider scattered data approximation on product regions of equal and different dimensionality. On each of these regions, we assume quasi-uniform but unstructured data sites and construct optimal sparse grids for scattered data…
Kernel interpolation, especially in the context of Gaussian process emulation, is a widely used technique in surrogate modelling, where the goal is to cheaply approximate an input-output map using a limited number of function evaluations.…
A multilevel kernel-based interpolation method, suitable for moderately high-dimensional function interpolation problems, is proposed. The method, termed multilevel sparse kernel-based interpolation (MLSKI, for short), uses both level-wise…
Sparse grids are popular tools for high-dimensional function approximation. In this work, we study the use of sparse grids for interpolation using separable Mat\'ern kernels…
The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel…
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…
Gaussian Processes (GPs) are highly expressive, probabilistic models. A major limitation is their computational complexity. Naively, exact GP inference requires $\mathcal{O}(N^3)$ computations with $N$ denoting the number of modeled points.…
Gaussian processes (GPs) provide a principled Bayesian framework for uncertainty estimation, but their computational complexity severely limits scalability to large datasets. We propose SIKA-GP, which accelerates GP inference using sparse…
Motivated by the recent multilevel sparse kernel-based interpolation (MuSIK) algorithm proposed in [Georgoulis, Levesley and Subhan, SIAM J. Sci. Comput., 35(2), pp. A815-A831, 2013], we introduce the new quasi-multilevel sparse…
We propose the use of sparse grids to accelerate particle-in-cell (PIC) schemes. By using the so-called `combination technique' from the sparse grids literature, we are able to dramatically increase the size of the spatial cells in…
Scientific workloads have traditionally exploited high levels of sparsity to accelerate computation and reduce memory requirements. While deep neural networks can be made sparse, achieving practical speedups on GPUs is difficult because…
A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. This success is largely attributed to the GP's analytical tractability, robustness, non-parametric…