Related papers: Reproducing kernel Hilbert spaces, polynomials and…

In recent years, transfer learning has garnered significant attention. Its ability to leverage knowledge from related studies to improve generalization performance in a target study has made it highly appealing. This paper focuses on…

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…

Learning kernels in operators from data lies at the intersection of inverse problems and statistical learning, providing a powerful framework for capturing non-local dependencies in function spaces and high-dimensional settings. In contrast…

Indefinite inner product spaces of entire functions and functions analytic inside a disk are considered and their completeness studied. Spaces induced by the rotation invariant reproducing kernels in the form of the generalized…

The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental importance in the theoretical underpinning of kernel methods in…

The role of kernels is central to machine learning. Motivated by the importance of power-law distributions in statistical modeling, in this paper, we propose the notion of power-law kernels to investigate power-laws in learning problem. We…

We establish some new bounds on the log-covering numbers of (anisotropic) Gaussian reproducing kernel Hilbert spaces. Unlike previous results in this direction we focus on small explicit constants and their dependency on crucial parameters…

This paper reviews the functional aspects of statistical learning theory. The main point under consideration is the nature of the hypothesis set when no prior information is available but data. Within this framework we first discuss about…

We describe those reproducing kernel Hilbert spaces of holomorphic functions on domains in ${\Bbb C}^d$ for which an analogue of the Nevanlinna-Pick theorem holds, in other words when the existence of a (possibly matrix-valued) function in…

Fisher's linear discriminant analysis is a classical method for classification, yet it is limited to capturing linear features only. Kernel discriminant analysis as an extension is known to successfully alleviate the limitation through a…

In this work we consider the problem of numerical integration, i.e., approximating integrals with respect to a target probability measure using only pointwise evaluations of the integrand. We focus on the setting in which the target…

We are concerned with nonparametric hypothesis testing of time series functionals. It is known that the popular autoregressive sieve bootstrap is, in general, not valid for statistics whose (asymptotic) distribution depends on moments of…

Kernel mean embeddings, a widely used technique in machine learning, map probability distributions to elements of a reproducing kernel Hilbert space (RKHS). For supervised learning problems, where input-output pairs are observed, the…

We study classes of reproducing kernels $K$ on general domains; these are kernels which arise commonly in machine learning models; models based on certain families of reproducing kernel Hilbert spaces. They are the positive definite kernels…

We consider the roots of uniformly chosen complex and real reciprocal polynomials of degree $N$ whose Mahler measure is bounded by a constant. After a change of variables this reduces to a generalization of Ginibre's complex and real…

Kernel based methods have shown effective performance in many remote sensing classification tasks. However their performance significantly depend on its hyper-parameters. The conventional technique to estimate the parameter comes with high…

Under investigation is the problem of finding the best approximation of a function in a Hilbert space subject to convex constraints and prescribed nonlinear transformations. We show that in many instances these prescriptions can be…

In this work, we develop and study an empirical projection operator scheme for solving nonparametric regression problems. This scheme is based on an approximate projection of the regression function over a suitable reproducing kernel…

This work presents a nonparametric framework for dissipativity learning in reproducing kernel Hilbert spaces, which enables data-driven certification of stability and performance properties for unknown nonlinear systems without requiring an…

Suppose H is a space of functions on X. If H is a Hilbert space with reproducing kernel then that structure of H can be used to build distance functions on X. We describe some of those and their interpretations and interrelations. We also…