This article develops a frequentist solution to the functional calibration problem, where value of parameter in computer model is allowed vary with control variables physical system. The need motivated by engineering applications using constant results significant mismatch between outputs from and experiment. Reproducing kernel Hilbert spaces (RKHS) are used optimal function, defined as relatio...

Abstract The aim of the paper is to create a link between theory reproducing kernel Hilbert spaces (RKHS) and notion unitary representation group or groupoid. More specifically, it demonstrated on one hand how construct positive definite an RKHS for given group(oid), other retrieve groupoid from defined that group(oid) with help Moore–Aronszajn theorem. constructed inspired by in terms convolut...

A reproducing kernel defines an embedding of a data point into an infinite dimensional reproducing kernel Hilbert space (RKHS). The norm in this space describes a distance, which we call the kernel distance. The random Fourier features (of Rahimi and Recht) describe an oblivious approximate mapping into finite dimensional Euclidean space that behaves similar to the RKHS. We show in this paper t...

Let B be a Banach space and (H, ‖ · ‖H) be a dense, imbedded subspace. For a ∈ B, its distance to the ball of H with radius R (denoted as I(a, R)) tends to zero when R tends to infinity. We are interested in the rate of this convergence. This approximation problem arose from the study of learning theory, where B is the L2 space and H is a reproducing kernel Hilbert space. The class of elements ...

The method of regularization with the Gaussian reproducing kernel is popular in the machine learning literature and successful in many practical applications. In this paper we consider the periodic version of the Gaussian kernel regularization. We show in the white noise model setting, that in function spaces of very smooth functions, such as the infinite-order Sobolev space and the space of an...