相关论文: A note on sampling recovery of multivariate functi…

We study the $L_{\infty}$-approximation of $d$-variate functions from Hilbert spaces via linear functionals as information. It is a common phenomenon in tractability studies that unweighted problems (with each dimension being equally…

This paper studies the problem of approximating a function $f$ in a Banach space $X$ from measurements $l_j(f)$, $j=1,\dots,m$, where the $l_j$ are linear functionals from $X^*$. Most results study this problem for classical Banach spaces…

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,…

In this paper we extend results taken from compressed sensing to recover Hilbert-space valued vectors. This is an important problem in parametric function approximation in particular when the number of parameters is high. By expanding our…

We construct Monte Carlo methods for the $L^2$-approximation in Hilbert spaces of multivariate functions sampling no more than $n$ function values of the target function. Their errors catch up with the rate of convergence and the…

Let $\mu$ be a positive finite measure on the unit circle. The Dirichlet type space $\mathcal{D}(\mu)$, associated to $\mu$, consists of holomorphic functions on the unit disc whose derivatives are square integrable when weighted against…

Subsampling is an efficient method to deal with massive data. In this paper, we investigate the optimal subsampling for linear quantile regression when the covariates are functions. The asymptotic distribution of the subsampling estimator…

We consider multi-variate signals spanned by the integer shifts of a set of generating functions with distinct frequency profiles and the problem of reconstructing them from samples taken on a random periodic set. We show that such a…

We show that independent and uniformly distributed sampling points are as good as optimal sampling points for the approximation of functions from the Sobolev space $W_p^s(\Omega)$ on bounded convex domains $\Omega\subset \mathbb{R}^d$ in…

The reproducing kernel Hilbert space (RKHS) embedding method is a recently introduced estimation approach that seeks to identify the unknown or uncertain function in the governing equations of a nonlinear set of ordinary differential…

We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…

We consider a problem of approximation of $d$-variate functions defined on $\mathbb{R}^d$ which belong to the Hilbert space with tensor product-type reproducing Gaussian kernel with constant shape parameter. Within worst case setting, we…

We propose the notion of a sample distortion (SD) function for independent and identically distributed (i.i.d) compressive distributions to fundamentally quantify the achievable reconstruction performance of compressed sensing for certain…

Let $Q$ be a relatively compact subset in a Hilbert space $V$. For a given $\e>0$ let $N(\e,Q)$ be the minimal number of linear measurements, sufficient to reconstruct any $x \in Q$ with the accuracy $\e$. We call $N(\e,Q)$ a sampling…

In this article, we give probabilistic versions of Sobolev embeddings on any Riemannian manifold $(M,g)$. More precisely, we prove that for natural probability measures on $L^2(M)$, almost every function belong to all spaces $L^p(M)$,…

We study the numerical integration problem for functions with infinitely many variables. The function spaces of integrands we consider are weighted reproducing kernel Hilbert spaces with norms related to the ANOVA decomposition of the…

We obtain a compact Sobolev embedding for $H$-invariant functions in compact metric-measure spaces, where $H$ is a subgroup of the measure preserving bijections. In Riemannian manifolds, $H$ is a subgroup of the volume preserving…

We study the $L_2$-approximation of functions from a Hilbert space and compare the sampling numbers with the approximation numbers. The sampling number $e_n$ is the minimal worst case error that can be achieved with $n$ function values,…

Learning kernels in operators from data lies at the intersection of inverse problems and statistical learning, providing a powerful framework for capturing non-local dependencies in function spaces and high-dimensional settings. In contrast…

The paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. We use recent general results on sampling discretization to derive a new Marcinkiewicz type discretization theorem for the…