Related papers: Robust Nonlinear System Identification in Reproduc…
Reproducing kernel Hilbert spaces (RKHSs) are key elements of many non-parametric tools successfully used in signal processing, statistics, and machine learning. In this work, we aim to address three issues of the classical RKHS based…
We consider the problem of optimising functions in the reproducing kernel Hilbert space (RKHS) of a Mat\'ern kernel with smoothness parameter $\nu$ over the domain $[0,1]^d$ under noisy bandit feedback. Our contribution, the $\pi$-GP-UCB…
Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…
In this paper, we present a fast and accurate numerical scheme for the solution of fifth-order boundary-value problems. We apply the reproducing kernel Hilbert space method (RKHSM) for solving this problem. The analytic results of the…
This work constructs a hypothesis test for detecting whether an data-generating function $h: R^p \rightarrow R$ belongs to a specific reproducing kernel Hilbert space $\mathcal{H}_0$ , where the structure of $\mathcal{H}_0$ is only…
We propose a generic spatiotemporal event forecasting method, which we developed for the National Institute of Justice's (NIJ) Real-Time Crime Forecasting Challenge. Our method is a spatiotemporal forecasting model combining scalable…
We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system…
Recently, some works have suggested methods to combine variational probabilistic inference with Monte Carlo sampling. One promising approach is via local optimal transport. In this approach, a gradient steepest descent method based on local…
Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…
We develop a comprehensive framework for spatio-temporal prediction of time-varying vector fields using operator-valued reproducing kernel Hilbert spaces (OV RKHS). By integrating Sobolev regularity with Koopman operator theory, we…
This paper addresses the problem of approximating an unknown function from point evaluations. When obtaining these point evaluations is costly, minimising the required sample size becomes crucial, and it is unreasonable to reserve a…
Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks as the curse of dimensionality (CoD) cannot be evaded when trying to approximate even a single ReLU neuron…
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…
In this article, the reproducing kernel Hilbert space [0, 1] is employed for solving a class of third-order periodic boundary value problem by using fitted reproducing kernel algorithm. The reproducing kernel function is built to get fast…
Building highly non-linear and non-parametric models is central to several state-of-the-art machine learning systems. Kernel methods form an important class of techniques that induce a reproducing kernel Hilbert space (RKHS) for inferring…
Kernel methods have been among the most popular techniques in machine learning, where learning tasks are solved using the property of reproducing kernel Hilbert space (RKHS). In this paper, we propose a novel data analysis framework with…
A mathematical model for variable selection in functional regression models with scalar response is proposed. By "variable selection" we mean a procedure to replace the whole trajectories of the functional explanatory variables with their…
This paper studies convergence of empirical risks in reproducing kernel Hilbert spaces (RKHS). A conventional assumption in the existing research is that empirical training data do not contain any noise but this may not be satisfied in some…
In this article, we consider convergence rates in functional linear regression with functional responses, where the linear coefficient lies in a reproducing kernel Hilbert space (RKHS). Without assuming that the reproducing kernel and the…
These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…