Related papers: Spectral Eigenfunction Decomposition for Kernel Ad…

Previous analysis of regularized functional linear regression in a reproducing kernel Hilbert space (RKHS) typically requires the target function to be contained in this kernel space. This paper studies the convergence performance of…

We propose a novel framework for solving nonlinear PDEs using sparse radial basis function (RBF) networks. Sparsity-promoting regularization is employed to prevent over-parameterization and reduce redundant features. This work is motivated…

We have developed an extended distance matrix approach to study the molecular geometric configuration through spectral decomposition. It is shown that the positions of all atoms in the eigen-space can be specified precisely by their…

We propose a new data-driven approach for learning the fundamental solutions (Green's functions) of various linear partial differential equations (PDEs) given sample pairs of input-output functions. Building off the theory of functional…

The kernel polynomial method (KPM) is a powerful numerical method for approximating spectral densities. Typical implementations of the KPM require an a prior estimate for an interval containing the support of the target spectral density,…

In this paper, we introduce a new image representation based on a multilayer kernel machine. Unlike traditional kernel methods where data representation is decoupled from the prediction task, we learn how to shape the kernel with…

Kernel-based methods offer a powerful and flexible mathematical framework for addressing histopolation problems. In histopolation, the available input data does not consist of pointwise function samples but of averages taken over intervals…

Kernel methods are powerful tools in statistical learning, but their cubic complexity in the sample size n limits their use on large-scale datasets. In this work, we introduce a scalable framework for kernel regression with O(n log n)…

Random feature approximation is arguably one of the most popular techniques to speed up kernel methods in large scale algorithms and provides a theoretical approach to the analysis of deep neural networks. We analyze generalization…

We propose a novel approach for pixel classification in hyperspectral images, leveraging on both the spatial and spectral information in the data. The introduced method relies on a recently proposed framework for learning on distributions…

The kernel-independent fast multipole method (KIFMM) proposed in [1] is of almost linear complexity. In the original KIFMM the time-consuming M2L translations are accelerated by FFT. However, when more equivalent points are used to achieve…

The aim of this study is to present a good modernistic strategy for solving some well-known classes of Lane-Emden type singular differential equations. The proposed approach is based on the reproducing kernel Hilbert space (RKHS) and…

Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression…

In this paper, an adaptive non-parametric method is proposed to estimate the scalar-valued nonlinear function that appears in uncertain systems governed by ordinary differential equations (ODEs). By employing an infinite-dimensional…

Kernel matrices, as well as weighted graphs represented by them, are ubiquitous objects in machine learning, statistics and other related fields. The main drawback of using kernel methods (learning and inference using kernel matrices) is…

We present a modular, extensible likelihood framework for spectroscopic inference based on synthetic model spectra. The subtraction of an imperfect model from a continuously sampled spectrum introduces covariance between adjacent datapoints…

Kolmogorov-Arnold networks (KANs) represent data features by learning the activation functions and demonstrate superior accuracy with fewer parameters, FLOPs, GPU memory usage (Memory), shorter training time (TraT), and testing time (TesT)…

An infinitely wide model is a weighted integration $\int \varphi(x,v) d \mu(v)$ of feature maps. This model excels at handling an infinite number of features, and thus it has been adopted to the theoretical study of deep learning. Kernel…

Joint image filters are used to transfer structural details from a guidance picture used as a prior to a target image, in tasks such as enhancing spatial resolution and suppressing noise. Previous methods based on convolutional neural…

This paper studies the eigenvalue problem $K \psi = \lambda \psi$ associated with a Fredholm integral operator $K$ defined by a smooth kernel. The focus is on analyzing the convergence behaviour of numerical approximations to eigenvalues…