Related papers: $\mathcal{H}^2$-matrices for translation-invariant…

The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…

This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…

We present a method for updating certain hierarchical factorizations for solving linear integral equations with elliptic kernels. In particular, given a factorization corresponding to some initial geometry or material parameters, we can…

We present in this work a new methodology to design kernels on data which is structured with smaller components, such as text, images or sequences. This methodology is a template procedure which can be applied on most kernels on measures…

In the context of structure-to-structure transformation tasks, learning sequences of discrete symbolic operations poses significant challenges due to their non-differentiability. To facilitate the learning of these symbolic sequences, we…

Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…

The paper presents a variational quantum algorithm to solve initial-boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum hardware that is well suited for quantum…

With lowrank approximation the storage requirements for dense data are reduced down to linear complexity and with the addition of hierarchy this also works for data without global lowrank properties. However, the lowrank factors itself are…

In this work, we propose a simple but effective method to interpret black-box machine learning models globally. That is, we use a compact binary tree, the interpretation tree, to explicitly represent the most important decision rules that…

This paper presents reproducing kernel Hilbert spaces method to obtain the numerical solution for partial differential equation constrained optimization problem.

This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…

Matrix-vector multiplication forms the basis of many iterative solution algorithms and as such is an important algorithm also for hierarchical matrices which are used to represent dense data in an optimized form by applying low-rank…

We consider a fast, data-sparse directional method to realize matrix-vector products related to point evaluations of the Helmholtz kernel. The method is based on a hierarchical partitioning of the point sets and the matrix. The considered…

We present memory-efficient and scalable algorithms for kernel methods used in machine learning. Using hierarchical matrix approximations for the kernel matrix the memory requirements, the number of floating point operations, and the…

The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix…

We study kernel functions, and associated reproducing kernel Hilbert spaces $\mathscr{H}$ over infinite, discrete and countable sets $V$. Numerical analysis builds discrete models (e.g., finite element) for the purpose of finding…

A generalization of the Wasserstein metric, the integrated transportation distance, establishes a novel distance between probability kernels of Markov systems. This metric serves as the foundation for an efficient approximation technique,…

We present an application-oriented approach to Urysohn and Hammerstein integral operators acting between spaces of H"older continuous functions over compact metric spaces. These nonlinear mappings are formulated by means of an abstract…

In column-oriented query processing, a materialization strategy determines when lightweight positions (row IDs) are translated into tuples. It is an important part of column-store architecture, since it defines the class of supported query…

This paper investigates the eigenvalue problem of integral operators whose kernels can be expressed as a finite sum of pairwise products of single-variable functions, making them separable. By consdiering the matrix form of the separable…