Related papers: Fast generation of isotropic Gaussian random field…

Probability measures on the sphere form an important class of statistical models and are used, for example, in modeling directional data or shapes. Due to their widespread use, but also as an algorithmic building block, efficient sampling…

We introduce a fast algorithm for computing sparse Fourier transforms supported on smooth curves or surfaces. This problem appear naturally in several important problems in wave scattering and reflection seismology. The main observation is…

The 3D Gaussian splatting method has drawn a lot of attention, thanks to its high performance in training and high quality of the rendered image. However, it uses anisotropic Gaussian kernels to represent the scene. Although such…

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…

Statistical and machine-learning algorithms are frequently applied to high-dimensional data. In many of these applications data is scarce, and often much more costly than computation time. We provide the first sample-efficient…

We construct time dependent random fields on the sphere through coordinates change and subordination and we study the associated angular power spectrum. Some of this random fields arise naturally as solutions of partial differential…

We suggest fast algorithm for the matrix generator of pseudorandom numbers based on Kolmogorov-Anosov K systems which has been proposed earlier. This algorithm reduces $N^{2}$ operation of the matrix generator to $NlnN$ and essentially…

In this paper we propose an algorithm for the formation of matrices of isogeometric Galerkin methods. The algorithm is based on three ideas. The first is that we perform the external loop over the rows of the matrix. The second is that we…

A random recursive cell splitting scheme of the $2$-dimensional unit sphere is considered, which is the spherical analogue of the STIT tessellation process from Euclidean stochastic geometry. First-order moments are computed for a large…

Sparse variational approximations are popular methods for scaling up inference and learning in Gaussian processes to larger datasets. For $N$ training points, exact inference has $O(N^3)$ cost; with $M \ll N$ features, state of the art…

Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial…

This paper introduces the Gaussian multi-Graphical Model, a model to construct sparse graph representations of matrix- and tensor-variate data. We generalize prior work in this area by simultaneously learning this representation across…

We describe a uniformly fast algorithm for generating points \vec{x} uniformly in a hypercube with the restriction that the difference between each pair of coordinates is bounded. We discuss the quality of the algorithm in the sense of its…

Random field models are mathematical structures used in the study of stochastic complex systems. In this paper, we compute the shape operator of Gaussian random field manifolds using the first and second fundamental forms (Fisher…

Kernel methods have recently attracted resurgent interest, showing performance competitive with deep neural networks in tasks such as speech recognition. The random Fourier features map is a technique commonly used to scale up kernel…

This paper describes an efficient algorithm for computing steady two-dimensional surface gravity wave in irrotational motion. The algorithm complexity is O(N log N), N being the number of Fourier modes. The algorithm allows the arbitrary…

In this paper, we present a spherical Fast Multipole Method (sFMM) for ray tracing simulation of gravitational lensing (GL) on a curved sky. The sFMM is a non-trivial extension of the Fast Multiple Method (FMM) to sphere $\mathbb S^2$, and…

We introduce the Sphere Encoder, an efficient generative framework capable of producing images in a single forward pass and competing with many-step diffusion models using fewer than five steps. Our approach works by learning an encoder…

This paper presents an algorithm to simulate Gaussian random vectors whose precision matrix can be expressed as a polynomial of a sparse matrix. This situation arises in particular when simulating Gaussian Markov random fields obtained by…

3D Gaussian Splatting (3DGS) enables high-fidelity real-time rendering, a key requirement for immersive applications. However, the extension of 3DGS to dynamic scenes remains limitations on the substantial data volume of dense Gaussians and…