Related papers: Fast simulation of Gaussian random fields
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
Convolutional networks are one of the most widely employed architectures in computer vision and machine learning. In order to leverage their ability to learn complex functions, large amounts of data are required for training. Training a…
We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error…
We introduce a fast algorithm for generating long self-affine profiles. The algorithm, which is based on the fast wavelet transform, is faster than the conventional Fourier filtering algorithm. In addition to increased performance for large…
Transforms using random matrices have been found to have many applications. We are concerned with the projection of a signal onto Gaussian-distributed random orthogonal bases. We also would like to easily invert the process through…
We consider the relations between well-known Fourier transform algorithms.
We introduce a fast algorithm for Gaussian process regression in low dimensions, applicable to a widely-used family of non-stationary kernels. The non-stationarity of these kernels is induced by arbitrary spatially-varying vertical and…
Fast Fourier transform (FFT) based methods have turned out to be an effective computational approach for numerical homogenisation. In particular, Fourier-Galerkin methods are computational methods for partial differential equations that are…
Recently, the numerical schemes of the Fokker-Planck equations describing anomalous diffusion with two internal states have been proposed in [Nie, Sun and Deng, arXiv: 1811.04723], which use convolution quadrature to approximate the…
This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian…
We present a simple and fast algorithm for the computation of the coefficients of the expansion of a function f(cos u) in ultraspherical (Gegenbauer) polynomials. We prove that these coefficients coincide with the Fourier coefficients of an…
It was demonstrated in earlier work that, by approximating its range kernel using shiftable functions, the non-linear bilateral filter can be computed using a series of fast convolutions. Previous approaches based on shiftable approximation…
Motivated by the modeling of the spatial structure of the velocity field of three-dimensional turbulent flows, and the phenomenology of cascade phenomena, a linear dynamics has been recently proposed able to generate high velocity gradients…
Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations…
This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…
Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they…
Monte Carlo simulations are one of the major tools in statistical physics, complex system science, and other fields, and an increasing number of these simulations is run on distributed systems like clusters or grids. This raises the issue…
Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically self-similar processes instead of traditional Poisson processes [LTWW94,PF95]. One difficulty in dealing with…