Related papers: An efficient and fast sparse grid algorithm for hi…
Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are…
Distributed deep learning has recently been attracting more attention in remote sensing (RS) applications due to the challenges posed by the increased amount of open data that are produced daily by Earth observation programs. However, the…
We consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical…
Matrix Factorization (MF) has been widely applied in machine learning and data mining. A large number of algorithms have been studied to factorize matrices. Among them, stochastic gradient descent (SGD) is a commonly used method.…
Sparse-view synthesis remains a challenging problem due to the difficulty of recovering accurate geometry and appearance from limited observations. While recent advances in 3D Gaussian Splatting (3DGS) have enabled real-time rendering with…
Our main interest in this paper is to study some approximation problems for classes of functions with mixed smoothness. We use technique, based on a combination of results from hyperbolic cross approximation, which were obtained in 1980s --…
Progressive dimensionality reduction algorithms allow for visually investigating intermediate results, especially for large data sets. While different algorithms exist that progressively increase the number of data points, we propose an…
Sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high-performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. The scaling of existing parallel implementations of SpGEMM is…
Tensor decomposition has been widely used in machine learning and high-volume data analysis. However, large-scale tensor factorization often consumes huge memory and computing cost. Meanwhile, modernized computing hardware such as tensor…
Relying on the classical connection between Backward Stochastic Differential Equations (BSDEs) and non-linear parabolic partial differential equations (PDEs), we propose a new probabilistic learning scheme for solving high-dimensional…
Sparse grids based on Lagrange polynomials have become one of the staple methods for approximating functions that are high-dimensional and expensive to evaluate, in the context e.g. of PDE-based parametric design exploration. They are…
Complex object wave recovery from single-shot interference pattern is an important practical problem in interferometry and digital holography. The most popular single-shot interferogram analysis method involves Fourier filtering of…
For low-dimensional data sets with a large amount of data points, standard kernel methods are usually not feasible for regression anymore. Besides simple linear models or involved heuristic deep learning models, grid-based discretizations…
In industrial big data scenarios, high-dimensional sparse matrices (HDI) are widely used to characterize high-order interaction relationships among massive nodes. The stochastic gradient descent-based latent factor analysis (SGD-LFA) method…
The 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 to…
A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V-cycle, using an element-wise block Gauss-Seidel smoother.…
We introduce a computationally efficient method for the automation of inverse design in science and engineering. Based on simple least-square regression, the underlying dynamic mode decomposition algorithm can be used to construct a…
We present a novel algorithm, named the 2D-FFAST, to compute a sparse 2D-Discrete Fourier Transform (2D-DFT) featuring both low sample complexity and low computational complexity. The proposed algorithm is based on mixed concepts from…
Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…
In this paper, a sparse-based method for the estimation of the parameters of multidimensional ($R$-D) modal (harmonic or damped) complex signals in noise is presented. The problem is formulated as $R$ simultaneous sparse approximations of…