Related papers: Vector-Valued Native Space Embedding for Adaptive …

In a general context of positive definite kernels $k$, we develop tools and algorithms for sampling in reproducing kernel Hilbert space $\mathscr{H}$ (RKHS). With reference to these RKHSs, our results allow inference from samples; more…

In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this…

Recently, there has been growing interest in characterizing the function spaces underlying neural networks. While shallow and deep scalar-valued neural networks have been linked to scalar-valued reproducing kernel Banach spaces (RKBS),…

The robust distributed state estimation for a class of continuous-time linear time-invariant systems is achieved by a novel kernel-based distributed observer, which, for the first time, ensures fixed-time convergence properties. The…

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…

Proximities are at the heart of almost all machine learning methods. If the input data are given as numerical vectors of equal lengths, euclidean distance, or a Hilbertian inner product is frequently used in modeling algorithms. In a more…

This paper addresses the problem of filtering with a state-space model. Standard approaches for filtering assume that a probabilistic model for observations (i.e. the observation model) is given explicitly or at least parametrically. We…

Learning in the reproducing kernel Hilbert space (RKHS) such as the support vector machine has been recognized as a promising technique. It continues to be highly effective and competitive in numerous prediction tasks, particularly in…

We develop a new framework for estimating joint probability distributions using tensor product reproducing kernel Hilbert spaces (RKHS). Our framework accommodates a low-dimensional, normalized and positive model of a Radon--Nikodym…

Consider the problem: given the data pair $(\mathbf{x}, \mathbf{y})$ drawn from a population with $f_*(x) = \mathbf{E}[\mathbf{y} | \mathbf{x} = x]$, specify a neural network model and run gradient flow on the weights over time until…

We investigate the unsupervised learning of non-invertible observation functions in nonlinear state-space models. Assuming abundant data of the observation process along with the distribution of the state process, we introduce a…

The support vector machine (SVM) is a popular machine learning classification method which produces a nonlinear decision boundary in a feature space by constructing linear boundaries in a transformed Hilbert space. It is well known that…

Quantum coherence and entanglement are fundamental resources in quantum technologies, yet their efficient estimation for unknown states by employing minimal resources in experimental settings remains challenging, particularly in…

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…

A new adaptive observer is proposed for a certain class of nonlinear systems with bounded unknown input and parametric uncertainty. Unlike most existing solutions, the proposed approach ensures asymptotic convergence of the unknown…

Constructing latent vector representation for nodes in a network through embedding models has shown its practicality in many graph analysis applications, such as node classification, clustering, and link prediction. However, despite the…

Generative models, such as large language models or text-to-image diffusion models, can generate relevant responses to user-given queries. Response-based vector embeddings of generative models facilitate statistical analysis and inference…

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 method for learning Hamiltonian dynamics from a limited and noisy dataset is proposed. The method learns a Hamiltonian vector field on a reproducing kernel Hilbert space (RKHS) of inherently Hamiltonian vector fields, and in particular,…

This paper studies convergence rates for some value function approximations that arise in a collection of reproducing kernel Hilbert spaces (RKHS) $H(\Omega)$. By casting an optimal control problem in a specific class of native spaces,…