Related papers: Geometric Rates of Convergence for Kernel-based Sa…

Motivated by small bandwidth asymptotics for kernel-based semiparametric estimators in econometrics, this paper establishes Gaussian approximation results for high-dimensional fixed-order $U$-statistics whose kernels depend on the sample…

We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…

This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…

Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…

Constructing a similarity graph from a set $X$ of data points in $\mathbb{R}^d$ is the first step of many modern clustering algorithms. However, typical constructions of a similarity graph have high time complexity, and a quadratic space…

Random feature approximation is arguably one of the most widely used techniques for kernel methods in large-scale learning algorithms. In this work, we analyze the generalization properties of random feature methods, extending previous…

Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when…

This study proposes a data condensation method for multivariate kernel density estimation by genetic algorithm. First, our proposed algorithm generates multiple subsamples of a given size with replacement from the original sample. The…

Kernel regression is a popular non-parametric fitting technique. It aims at learning a function which estimates the targets for test inputs as precise as possible. Generally, the function value for a test input is estimated by a weighted…

We present a Gaussian kernel loss function and training algorithm for convolutional neural networks that can be directly applied to both distance metric learning and image classification problems. Our method treats all training features…

In this paper we analyze a greedy procedure to approximate a linear functional defined in a Reproducing Kernel Hilbert Space by nodal values. This procedure computes a quadrature rule which can be applied to general functionals, including…

This paper presents a comprehensive study on the convergence rates of the stochastic gradient descent (SGD) algorithm when applied to overparameterized two-layer neural networks. Our approach combines the Neural Tangent Kernel (NTK)…

Hyperspectral imaging is a powerful technology that is plagued by large dimensionality. Herein, we explore a way to combat that hindrance via non-contiguous and contiguous (simpler to realize sensor) band grouping for dimensionality…

In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The…

Kernel interpolation is a fundamental technique for approximating functions from scattered data, with a well-understood convergence theory when interpolating elements of a reproducing kernel Hilbert space. Beyond this classical setting,…

With the inspiration of vision transformers, the concept of depth-wise convolution revisits to provide a large Effective Receptive Field (ERF) using Large Kernel (LK) sizes for medical image segmentation. However, the segmentation…

Since the entry of kernel theory in the field of quantum machine learning, quantum kernel methods (QKMs) have gained increasing attention with regard to both probing promising applications and delivering intriguing research insights.…

A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert…

In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…

We show that geometric inference of a point cloud can be calculated by examining its kernel density estimate with a Gaussian kernel. This allows one to consider kernel density estimates, which are robust to spatial noise, subsampling, and…