Related papers: Kernel Interpolation with Sparse Grids
We show that a generalised sparse grid combination technique which combines multi-variate extrapolation of finite difference solutions with the standard combination formula lifts a second order accurate scheme on regular meshes to a fourth…
This paper presents GPU performance optimization and scaling results for inference models of the Sparse Deep Neural Network Challenge 2020. Demands for network quality have increased rapidly, pushing the size and thus the memory…
Spherical radial-basis-based kernel interpolation abounds in image sciences including geophysical image reconstruction, climate trends description and image rendering due to its excellent spatial localization property and perfect…
Previous studies have reported that common dense linear algebra operations do not achieve speed up by using multiple geographical sites of a computational grid. Because such operations are the building blocks of most scientific…
The interpolation of high-dimensional potential energy surfaces (PESs) is commonly done with physically-inspired deep-neural network models. In this work, we illustrate that Gaussian Processes (GPs) are also capable of interpolating…
We implement two novel algorithms for sparse-matrix dense-matrix multiplication (SpMM) on the GPU. Our algorithms expect the sparse input in the popular compressed-sparse-row (CSR) format and thus do not require expensive format conversion.…
We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in…
We investigate the connections between sparse approximation methods for making kernel methods and Gaussian processes (GPs) scalable to large-scale data, focusing on the Nystr\"om method and the Sparse Variational Gaussian Processes (SVGP).…
We study polynomial approximation on a $d$-cube, where $d$ is large, and compare interpolation on sparse grids, aka Smolyak's algorithm (SA), with a simple least squares method based on randomly generated points (LS) using standard…
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…
Creating low dimensional representations of a high dimensional data set is an important component in many machine learning applications. How to cluster data using their low dimensional embedded space is still a challenging problem in…
Approximate Bayesian inference methods that scale to very large datasets are crucial in leveraging probabilistic models for real-world time series. Sparse Markovian Gaussian processes combine the use of inducing variables with efficient…
Kernel interpolation is a versatile tool for the approximation of functions from data, and it can be proven to have some optimality properties when used with kernels related to certain Sobolev spaces. In the context of interpolation, the…
The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…
Sparse matrix-matrix multiplication (SpGEMM) is a computational primitive that is widely used in areas ranging from traditional numerical applications to recent big data analysis and machine learning. Although many SpGEMM algorithms have…
Applying Gaussian processes (GPs) to very large datasets remains a challenge due to limited computational scalability. Matrix structures, such as the Kronecker product, can accelerate operations significantly, but their application commonly…
The solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation. We will solve the linear systems using a direct method, in which a…
The geometric multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared…
Nowadays, analyzing and reducing the ever larger astronomical datasets is becoming a crucial challenge, especially for long cumulated observation times. The INTEGRAL/SPI X-gamma-ray spectrometer is an instrument for which it is essential to…
Clustering, a fundamental activity in unsupervised learning, is notoriously difficult when the feature space is high-dimensional. Fortunately, in many realistic scenarios, only a handful of features are relevant in distinguishing clusters.…