Related papers: Analysis via Orthonormal Systems in Reproducing Ke…

We illustrate relationships between classical kernel-based dimensionality reduction techniques and eigendecompositions of empirical estimates of reproducing kernel Hilbert space (RKHS) operators associated with dynamical systems. In…

We study distributed learning with the least squares regularization scheme in a reproducing kernel Hilbert space (RKHS). By a divide-and-conquer approach, the algorithm partitions a data set into disjoint data subsets, applies the least…

In this paper, we study the problem of learning dynamical properties of ensemble systems from their collective behaviors using statistical approaches in reproducing kernel Hilbert space (RKHS). Specifically, we provide a framework to…

We propose new reproducing kernel-based tests for model checking in conditional moment restriction models. By regressing estimated residuals on kernel functions via kernel ridge regression (KRR), we obtain a coefficient function in a…

We propose a novel test procedure for comparing mean functions across two groups within the reproducing kernel Hilbert space (RKHS) framework. Our proposed method is adept at handling sparsely and irregularly sampled functional data when…

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…

Despite their many appealing properties, kernel methods are heavily affected by the curse of dimensionality. For instance, in the case of inner product kernels in $\mathbb{R}^d$, the Reproducing Kernel Hilbert Space (RKHS) norm is often…

This paper introduces algorithms to select/design kernels in Gaussian process regression/kriging surrogate modeling techniques. We adopt the setting of kernel method solutions in ad hoc functional spaces, namely Reproducing Kernel Hilbert…

Kernel-based methods offer a powerful and flexible mathematical framework for addressing histopolation problems. In histopolation, the available input data does not consist of pointwise function samples but of averages taken over intervals…

We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework encompasses two key classes: (i) compact kernels, which…

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…

In $\mathbb R^d$, it is well-known that cumulants provide an alternative to moments that can achieve the same goals with numerous benefits such as lower variance estimators. In this paper we extend cumulants to reproducing kernel Hilbert…

Kernel mean embedding (KME) is a powerful tool to analyze probability measures for data, where the measures are conventionally embedded into a reproducing kernel Hilbert space (RKHS). In this paper, we generalize KME to that of von…

This article presents a general framework for the transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces (RKHSs),…

We present a general framework to learn functions in tensor product reproducing kernel Hilbert spaces (TP-RKHSs). The methodology is based on a novel representer theorem suitable for existing as well as new spectral penalties for tensors.…

Optimal experimental design seeks to determine the most informative allocation of experiments to infer an unknown statistical quantity. In this work, we investigate the optimal design of experiments for {\em estimation of linear functionals…

Substring kernels are classical tools for representing biological sequences or text. However, when large amounts of annotated data are available, models that allow end-to-end training such as neural networks are often preferred. Links…

In this paper, we develop a generalized theory of convolutional signal processing and neural networks for Reproducing Kernel Hilbert Spaces (RKHS). Leveraging the theory of algebraic signal processing (ASP), we show that any RKHS allows the…

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…

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…