Related papers: Kernel interpolation in Sobolev spaces of hybrid r…

In this paper we study reproducing kernel Hilbert spaces of arbitrary smoothness on the sphere $\mathbb{S}^d \subset \mathbb{R}^{d+1}$. The reproducing kernel is given by an integral representation using the truncated power function…

Cocompactness is a useful weaker counterpart of compactness in the study of imbeddings between function spaces. In this paper we show that subcritical continuous imbeddings of fractional Sobolev spaces and Besov spaces over \mathbb{R}^{N}…

Prior information can be incorporated in matrix completion to improve estimation accuracy and extrapolate the missing entries. Reproducing kernel Hilbert spaces provide tools to leverage the said prior information, and derive more reliable…

In $\mathbb R^d$, it is well-known that cumulants provide an alternative to moments that can achieve the same goals with numerous benefits such as lower variance estimators. In this paper we extend cumulants to reproducing kernel Hilbert…

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…

Exploiting the variational interpretation of kernel interpolation we exhibit a direct connection between interpolation and regression, where interpolation appears as a limiting case of regression. By applying this framework to point clouds…

This paper extends and analyzes the high-order kernel regularization framework of Beale & Tlupova (arXiv:2510.13639) to all four on-surface boundary integral operators of the Helmholtz Calderon calculus in three dimensions: the…

In complex visual recognition tasks it is typical to adopt multiple descriptors, that describe different aspects of the images, for obtaining an improved recognition performance. Descriptors that have diverse forms can be fused into a…

The field of quantum machine learning is a promising way to lead to a revolution in intelligent data processing methods. In this way, a hybrid learning method based on classic kernel methods is proposed. This proposal also requires the…

We investigate the rate of convergence of linear sampling numbers of the embedding $H^{\alpha,\beta} (\mathbb{T}^d) \hookrightarrow H^\gamma (\mathbb{T}^d)$. Here $\alpha$ governs the mixed smoothness and $\beta$ the isotropic smoothness in…

Hierarchical data pervades diverse machine learning applications, including natural language processing, computer vision, and social network analysis. Hyperbolic space, characterized by its negative curvature, has demonstrated strong…

We present a lower error bound for approximating linear multivariate operators defined over Hilbert spaces in terms of the error bounds for appropriately constructed linear functionals as long as algorithms use function values. Furthermore,…

High-capacity associative memories based on Kernel Logistic Regression (KLR) achieve strong retrieval performance but typically require substantial computational resources. This paper investigates the compressibility of KLR Hopfield…

A kernel method for estimating a probability density function (pdf) from an i.i.d. sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined by a linear…

Let X be a strictly pseudoconcave domain in a closed polarized complex manifold (Y,L) where L is a (semi-)positive line bundle over Y. Any given Hermitian metric on L, together with a volume form, induces by restriction to X a Hilbert space…

In this paper we introduce a generalization of the classical $\Leb_2(\Rd)$-based Sobolev spaces with the help of a vector differential operator $\mathbf{P}$ which consists of finitely or countably many differential operators $P_n$ which…

This work introduces and analyzes B-spline approximation spaces defined on general geometric domains obtained through a mapping from a parameter domain. These spaces are constructed as sparse-grid tensor products of univariate spaces in the…

We propose a new point of view for regularizing deep neural networks by using the norm of a reproducing kernel Hilbert space (RKHS). Even though this norm cannot be computed, it admits upper and lower approximations leading to various…

Supervised dimensionality reduction has emerged as an important theme in the last decade. Despite the plethora of models and formulations, there is a lack of a simple model which aims to project the set of patterns into a space defined by…

We construct a kernel density estimator on symmetric spaces of non-compact type and establish an upper bound for its convergence rate, analogous to the minimax rate for classical kernel density estimators on Euclidean space. Symmetric…