Infinite-dimensional stochastic transforms and reproducing kernel Hilbert space
نویسندگان
چکیده
By way of concrete presentations, we construct two infinite-dimensional transforms at the crossroads Gaussian fields and reproducing kernel Hilbert spaces (RKHS), thus leading to a new Fourier transform in general setting processes. Our results serve unify existing tools from analysis.
منابع مشابه
Reproducing Kernel Space Hilbert Method for Solving Generalized Burgers Equation
In this paper, we present a new method for solving Reproducing Kernel Space (RKS) theory, and iterative algorithm for solving Generalized Burgers Equation (GBE) is presented. The analytical solution is shown in a series in a RKS, and the approximate solution u(x,t) is constructed by truncating the series. The convergence of u(x,t) to the analytical solution is also proved.
متن کاملReproducing Kernel Hilbert Space vs. Frame Estimates
We consider conditions on a given system F of vectors in Hilbert space H, forming a frame, which turn H into a reproducing kernel Hilbert space. It is assumed that the vectors in F are functions on some set Ω. We then identify conditions on these functions which automatically give H the structure of a reproducing kernel Hilbert space of functions on Ω. We further give an explicit formula for th...
متن کاملSubspace Regression in Reproducing Kernel Hilbert Space
We focus on three methods for finding a suitable subspace for regression in a reproducing kernel Hilbert space: kernel principal component analysis, kernel partial least squares and kernel canonical correlation analysis and we demonstrate how this fits within a more general context of subspace regression. For the kernel partial least squares case a least squares support vector machine style der...
متن کاملPolicy Search in Reproducing Kernel Hilbert Space
Modeling policies in reproducing kernel Hilbert space (RKHS) renders policy gradient reinforcement learning algorithms non-parametric. As a result, the policies become very flexible and have a rich representational potential without a predefined set of features. However, their performances might be either non-covariant under reparameterization of the chosen kernel, or very sensitive to step-siz...
متن کاملSubspace classifier in reproducing kernel Hilbert space
To improve the performance of subspace classi er, it is e ective to reduce the dimensionality of the intersections between subspaces. For this purpose, the feature space is mapped implicitly to a high dimensional reproducing kernel Hilbert space and the subspace classi er is applied in this space. As a result of Hiragana recognition experiment, our classi er outperformed the conventional subspa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Sampling theory, signal processing, and data analysis
سال: 2023
ISSN: ['2730-5724', '1530-6429', '2730-5716']
DOI: https://doi.org/10.1007/s43670-023-00051-z