Related papers: Quasi-interpolation on a sparse grid with Gaussian

In his article "Powerlist: A Structure for Parallel Recursion" Jayadev Misra wrote: "Many data parallel algorithms Fast Fourier Transform, Batcher's sorting schemes and prefix sum -exhibit recursive structure. We propose a data structure,…

Representing signals with sparse vectors has a wide range of applications that range from image and video coding to shape representation and health monitoring. In many applications with real-time requirements, or that deal with…

Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings,…

In this paper, we propose a new orthogonal matching pursuit algorithm called quasi-OMP algorithm which greatly enhances the performance of classical orthogonal matching pursuit (OMP) algorithm, at some cost of computational complexity. We…

We propose a sparse algebra for samplet compressed kernel matrices, to enable efficient scattered data analysis. We show the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. It…

The paper aims at proposing an efficient and stable quasi-interpolation based method for numerically computing the Helmholtz-Hodge decomposition of a vector field. To this end, we first explicitly construct a matrix kernel in a general form…

This work presents a new interpolation tool, namely, cubic $q$-spline. Our new analogue generalizes a well known classical cubic spline. This analogue, based on the Jackson $q$-derivative, replaces an interpolating piecewise cubic…

We consider a cross interpolation of high-dimensional arrays in the tensor train format. We prove that the maximum-volume choice of the interpolation sets provides the quasioptimal interpolation accuracy, that differs from the best possible…

We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to…

Multiple kernel learning (MKL) aims to find an optimal, consistent kernel function. In the hierarchical multiple kernel clustering (HMKC) algorithm, sample features are extracted layer by layer from a high-dimensional space to maximize the…

In this paper, we develop a quadrature framework for large-scale kernel machines via a numerical integration representation. Considering that the integration domain and measure of typical kernels, e.g., Gaussian kernels, arc-cosine kernels,…

This paper introduces a novel quantum embedding search algorithm (QES, pronounced as "quest"), enabling search for optimal quantum embedding design for a specific dataset of interest. First, we establish the connection between the…

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…

This paper presents PIQP, a high-performance toolkit for solving generic sparse quadratic programs (QP). Combining an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM), the algorithm can handle…

We provide a new approach for computing integrals over hypersurfaces in the level set framework. The method is based on the discretization (via simple Riemann sums) of the classical formulation used in the level set framework, with the…

Sparse tensor algebra is challenging to efficiently parallelize due to the irregular, data-dependent, and potentially skewed structure of sparse computation. We propose the first partitioning algorithm that provably load balances the…

Recently, enthusiastic studies have devoted to texture synthesis using deep neural networks, because these networks excel at handling complex patterns in images. In these models, second-order statistics, such as Gram matrix, are used to…

Overcoming the influence of noise and imperfections is a major challenge in quantum computing. Here, we present an approach based on applying a desired unitary computation in superposition between the system of interest and some auxiliary…

Gaussian processes (GPs) stand as crucial tools in machine learning and signal processing, with their effectiveness hinging on kernel design and hyper-parameter optimization. This paper presents a novel GP linear multiple kernel (LMK) and a…

In this paper, we first propose a new iterative algorithm, called the K-sets+ algorithm for clustering data points in a semi-metric space, where the distance measure does not necessarily satisfy the triangular inequality. We show that the…