Related papers: Scattered Data Histopolation in Averaging Kernel H…

We study in this paper a smoothness regularization method for functional linear regression and provide a unified treatment for both the prediction and estimation problems. By developing a tool on simultaneous diagonalization of two positive…

We present a novel diffusion scheme for online kernel-based learning over networks. So far, a major drawback of any online learning algorithm, operating in a reproducing kernel Hilbert space (RKHS), is the need for updating a growing number…

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…

Motivated by the need of processing functional-valued data, or more general, operatorvalued data, we introduce the notion of the operator reproducing kernel Hilbert space (ORKHS). This space admits a unique operator reproducing kernel which…

The generalization performance of kernel methods is largely determined by the kernel, but common kernels are stationary thus input-independent and output-independent, that limits their applications on complicated tasks. In this paper, we…

The ability to measure differences in collected data is of fundamental importance for quantitative science and machine learning, motivating the establishment of metrics grounded in physical principles. In this study, we focus on the…

Scattered data interpolation schemes using kriging and radial basis functions (RBFs) have the advantage of being meshless and dimensional independent, however, for the data sets having insufficient observations, RBFs have the advantage over…

The recent developments of basis pursuit and compressed sensing seek to extract information from as few samples as possible. In such applications, since the number of samples is restricted, one should deploy the sampling points wisely. We…

The reproducing kernel Hilbert space (RKHS) embedding of distributions offers a general and flexible framework for testing problems in arbitrary domains and has attracted considerable amount of attention in recent years. To gain insights…

This paper proposes nonparametric kernel-smoothing estimation for panel data to examine the degree of heterogeneity across cross-sectional units. We first estimate the sample mean, autocovariances, and autocorrelations for each unit and…

The main purpose of this paper is providing a systematic study and classification of non-scalar kernels for Reproducing Kernel Hilbert Spaces (RKHS), to be used in the analysis of deformation in shape spaces endowed with metrics induced by…

We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…

Reproducing kernel Hilbert spaces (RKHSs) are very important function spaces, playing an important role in machine learning, statistics, numerical analysis and pure mathematics. Since Lipschitz and H\"older continuity are important…

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…

Anisotropic patchy particles have become an archetypical statistical model system for associating fluids. Here we formulate an approach to the Kern-Frenkel model via classical density functional theory to describe the positionally and…

Compositional data, such as human gut microbiomes, consist of non-negative variables whose only the relative values to other variables are available. Analyzing compositional data such as human gut microbiomes needs a careful treatment of…

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…

This article is concerned with solving the time fractional Vakhnenko Parkes equation using the reproducing kernels. Reproducing kernel theory, the normal basis, some important Hilbert spaces, homogenization of constraints, and the…

Motivated by applications to the study of stochastic processes, we introduce a new analysis of positive definite kernels $K$, their reproducing kernel Hilbert spaces (RKHS), and an associated family of feature spaces that may be chosen in…

Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…