Related papers: Spectral Algorithms on Manifolds through Diffusion
We develop novel learning rates for conditional mean embeddings by applying the theory of interpolation for reproducing kernel Hilbert spaces (RKHS). We derive explicit, adaptive convergence rates for the sample estimator under the…
In this paper we combine the theory of reproducing kernel Hilbert spaces with the field of collocation methods to solve boundary value problems with special emphasis on reproducing property of kernels. From the reproducing property of…
This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…
This paper introduces a novel, non-deterministic method for embedding data in low-dimensional Euclidean space based on computing realizations of a Gaussian process depending on the geometry of the data. This type of embedding first appeared…
We demonstrate an equivalence between reproducing kernel Hilbert space (RKHS) embeddings of conditional distributions and vector-valued regressors. This connection introduces a natural regularized loss function which the RKHS embeddings…
We develop a unified geometric framework for nonparametric estimation based on the notion of Twin Kernel Spaces, defined as orbits of a reproducing kernel under a group action. This structure induces a family of transported RKHS geometries…
We address data-driven learning of the infinitesimal generator of stochastic diffusion processes, essential for understanding numerical simulations of natural and physical systems. The unbounded nature of the generator poses significant…
Diffusion maps (DM) constitute a classic dimension reduction technique, for data lying on or close to a (relatively) low-dimensional manifold embedded in a much larger dimensional space. The DM procedure consists in constructing a spectral…
Error estimates for kernel interpolation in Reproducing Kernel Hilbert Spaces (RKHS) usually assume quite restrictive properties on the shape of the domain, especially in the case of infinitely smooth kernels like the popular Gaussian…
We integrate neural operators with diffusion models to address the spectral limitations of neural operators in surrogate modeling of turbulent flows. While neural operators offer computational efficiency, they exhibit deficiencies in…
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…
Practical applications of kernel methods often use variable bandwidth kernels, also known as self-tuning kernels, however much of the current theory of kernel based techniques is only applicable to fixed bandwidth kernels. In this paper, we…
Integral operators play a central role in signal processing, underpinning classical convolution, and filtering on continuous network models such as graphons. While these operators are traditionally analyzed through spectral decompositions,…
Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as to encapsulate the high dimensionality in a reduced set of informative features for subsequent…
Diffusion models (DMs) have emerged as powerful tools for modeling complex data distributions and generating realistic new samples. Over the years, advanced architectures and sampling methods have been developed to make these models…
Recently, there has been much interest in spectral approaches to learning manifolds---so-called kernel eigenmap methods. These methods have had some successes, but their applicability is limited because they are not robust to noise. To…
This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting. For a wide class of compact, connected $C^\infty$ Riemannian manifolds, including the important cases of spheres and…
The aim of this article is to explore in all remaining aspects the spectral theory of locally normal operators. In a previous article we proved the spectral theorem in terms of locally spectral measures. Here we prove the spectral theorem…
In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…
Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…