Related papers: Discrete reproducing kernel Hilbert spaces: Sampli…
We introduce a complex-valued counterpart of the representer theorem in machine learning. We study several learning and minimization problems in reproducing kernel Hilbert spaces (RKHSs), with the aim of identifying appropriate input-output…
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…
Operator-Valued Kernels (OVKs) and associated vector-valued Reproducing Kernel Hilbert Spaces provide an elegant way to extend scalar kernel methods when the output space is a Hilbert space. Although primarily used in finite dimension for…
This paper proposes a method for constructing one-step prediction tubes for nonlinear systems using reproducing kernel Hilbert spaces. We approximate a bounded reproducing kernel Hilbert space (RKHS) hypothesis set by a finite-dimensional…
In this paper, we present an efficient algorithm for solving a class of chance constrained optimization under non-parametric uncertainty. Our algorithm is built on the possibility of representing arbitrary distributions as functions in…
A framework for coherent pattern extraction and prediction of observables of measure-preserving, ergodic dynamical systems with both atomic and continuous spectral components is developed. It is based on an approximation of the generator of…
In this work, we analyze the learnability of reproducing kernel Hilbert spaces (RKHS) under the $L^\infty$ norm, which is critical for understanding the performance of kernel methods and random feature models in safety- and…
This paper addresses the covariate shift problem in the context of nonparametric regression within reproducing kernel Hilbert spaces (RKHSs). Covariate shift arises in supervised learning when the input distributions of the training and…
We review definitions and properties of reproducing kernel Hilbert spaces attached to Gaussian variables and processes, with a view to applications in nonparametric Bayesian statistics using Gaussian priors. The rate of contraction of…
To help understand various reproducing kernels used in applied sciences, we investigate the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of feature maps of the corresponding reproducing kernels are…
In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial frequency domain (k-space), typically by time-consuming line-by-line scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data…
We study a reproducing kernel Hilbert space of functions defined on the positive integers and associated to the binomial coefficients. We introduce two transforms, which allow us to develop a related harmonic analysis in this Hilbert space.…
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 illustrate the effectiveness of reproducing kernel Hilbert space techniques in the study of composition operators. For weighted Hardy spaces on the unit disk, we characterize the composition operators whose adjoint is…
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…
We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…
Traditionally, kernel methods rely on the representer theorem which states that the solution to a learning problem is obtained as a linear combination of the data mapped into the reproducing kernel Hilbert space (RKHS). While elegant from…
We focus on kernel methods for set-valued inputs and their application to Bayesian set optimization, notably combinatorial optimization. We investigate two classes of set kernels that both rely on Reproducing Kernel Hilbert Space…
We propose a novel adaptive learning algorithm based on iterative orthogonal projections in the Cartesian product of multiple reproducing kernel Hilbert spaces (RKHSs). The task is estimating/tracking nonlinear functions which are supposed…
Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. The primary mathematical tool employed in these methods is the notion of the Reproducing Kernel Hilbert Space.…