Related papers: Dimension-Independent Kernel {\epsilon}-Covers

This paper proves an abstract theorem addressing in a unified manner two important problems in function approximation: avoiding curse of dimensionality and estimating the degree of approximation for out-of-sample extension in manifold…

In this paper we propose a new framework for analyzing the performance of preprocessing algorithms. Our framework builds on the notion of kernelization from parameterized complexity. However, as opposed to the original notion of…

Kernel approximation methods create explicit, low-dimensional kernel feature maps to deal with the high computational and memory complexity of standard techniques. This work studies a supervised kernel learning methodology to optimize such…

Let (M, g) be a compact smooth Riemannian manifold. We obtain new off-diagonal estimates as {\lambda} tend to infinity for the remainder in the pointwise Weyl Law for the kernel of the spectral projector of the Laplacian onto functions with…

This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…

In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel. Recently, other distances…

Universal kernels, whose Reproducing Kernel Hilbert Space is dense in the space of continuous functions are of great practical and theoretical interest. In this paper, we introduce an explicit construction of universal kernels on compact…

We show that common choices of kernel functions for a highly accurate and massively scalable nearest-neighbour based GP regression model (GPnn: \cite{GPnn}) exhibit gradual convergence to asymptotic behaviour as dataset-size $n$ increases.…

In this paper we prove a higher dimensional analogue of Carleson's $\varepsilon^2$ conjecture. Given two arbitrary disjoint open sets $\Omega^+,\Omega^-\subset \mathbb{R}^{n+1}$, and $x\in\mathbb{R}^{n+1}$, $r>0$, we denote…

In batch Kernel Density Estimation (KDE) for a kernel function $f$, we are given as input $2n$ points $x^{(1)}, \cdots, x^{(n)}, y^{(1)}, \cdots, y^{(n)}$ in dimension $m$, as well as a vector $v \in \mathbb{R}^n$. These inputs implicitly…

In this work, we investigate high-dimensional kernel ridge regression (KRR) on i.i.d. Gaussian data with anisotropic power-law covariance. This setting differs fundamentally from the classical source & capacity conditions for KRR, where…

An $\varepsilon$-coreset for a given set $D$ of $n$ points, is usually a small weighted set, such that querying the coreset \emph{provably} yields a $(1+\varepsilon)$-factor approximation to the original (full) dataset, for a given family…

The neural tangent kernel is a kernel function defined over the parameter distribution of an infinite width neural network. Despite the impracticality of this limit, the neural tangent kernel has allowed for a more direct study of neural…

Let $X$ be a set of $n$ points of norm at most $1$ in the Euclidean space $R^k$, and suppose $\varepsilon>0$. An $\varepsilon$-distance sketch for $X$ is a data structure that, given any two points of $X$ enables one to recover the square…

In this paper, we mainly study the random sampling stability for signals in a weighted reproducing kernel subspace of $L_\nu^p(\mathbb{R}^d)$ without the additional requirement that the kernel function has symmetry. The sampling set is…

The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…

We obtain upper bounds for the estimation error of Kernel Ridge Regression (KRR) for all non-negative regularization parameters, offering a geometric perspective on various phenomena in KRR. As applications: 1. We address the multiple…

Given $M \geq 2$ distributions defined on a general measurable space, we introduce a nonparametric (kernel) measure of multi-sample dissimilarity (KMD) -- a parameter that quantifies the difference between the $M$ distributions. The…

We propose and analyze a kernelized version of Q-learning. Although a kernel space is typically infinite-dimensional, extensive study has shown that generalization is only affected by the effective dimension of the data. We incorporate such…

Kernel density estimation is a technique for approximating probability distributions. Here, it is applied to the calculation of mutual information on a metric space. This is motivated by the problem in neuroscience of calculating the mutual…