Related papers: Reproducing kernel Hilbert space methods for model…
Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…
We consider conditions on a given system $\mathcal{F}$ of vectors in Hilbert space $\mathcal{H}$, forming a frame, which turn $\mathcal{H}$ into a reproducing kernel Hilbert space. It is assumed that the vectors in $\mathcal{F}$ are…
Hilbertian kernel methods and their positive semidefinite kernels have been extensively used in various fields of applied mathematics and machine learning, owing to their several equivalent characterizations. We here unveil an analogy with…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
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…
Based on direct integrals, a framework allowing to integrate a parametrised family of reproducing kernels with respect to some measure on the parameter space is developed. By pointwise integration, one obtains again a reproducing kernel…
We use a classical characterisation to prove that functions which are bounded away from zero cannot be elements of reproducing kernel Hilbert spaces whose reproducing kernels decays to zero in a suitable way. The result is used to study…
In Bayesian multilevel models, the data are structured in interconnected groups, and their posteriors borrow information from one another due to prior dependence between latent parameters. However, little is known about the behaviour of the…
We use some results from the theory of Reproducing Kernel Hilbert Spaces to show that the reachable space of the heat equation for a finite rod with either one or two Dirichlet boundary controls is a RKHS of analytic functions on a square,…
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…
We develop sampling formulas for high-dimensional functions in reproducing kernel Hilbert spaces, where we rely on irregular samples that are taken at determining sequences of data points. We place particular emphasis on sampling formulas…
The distribution regression problem encompasses many important statistics and machine learning tasks, and arises in a large range of applications. Among various existing approaches to tackle this problem, kernel methods have become a method…
Imputation and propensity score weighting are two popular techniques for handling missing data. We address these problems using the regularized M-estimation techniques in the reproducing kernel Hilbert space. Specifically, we first use the…
The reproducing kernel Hilbert space (RKHS) embedding method is a recently introduced estimation approach that seeks to identify the unknown or uncertain function in the governing equations of a nonlinear set of ordinary differential…
We introduce a vector differential operator $\mathbf{P}$ and a vector boundary operator $\mathbf{B}$ to derive a reproducing kernel along with its associated Hilbert space which is shown to be embedded in a classical Sobolev space. This…
This paper addresses the problem of regression to reconstruct functions, which are observed with superimposed errors at random locations. We address the problem in reproducing kernel Hilbert spaces. It is demonstrated that the estimator,…
Non-linear systems of differential equations have attracted the interest in fields like system biology, ecology or biochemistry, due to their flexibility and their ability to describe dynamical systems. Despite the importance of such models…
The aim of this thesis is to analyze and renovate few main-stream models on inflation derivatives. In the first chapter of the thesis, concepts of financial instruments and fundamental terms are introduced, such as coupon bond,…
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…
The paper studies sub and super-replication price bounds for contingent claims defined on general trajectory based market models. No prior probabilistic or topological assumptions are placed on the trajectory space, trading is assumed to…