We present an embedding of stochastic optimal control problems, of the so called path integral form, into reproducing kernel Hilbert spaces. Using consistent, sample based estimates of the embedding leads to a model-free, non-parametric approach for calculation of an approximate solution to the control problem. This formulation admits a decomposition of the problem into an invariant and task de...

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...

In this paper we introduce a generalization of the classical L2(R)-based Sobolev spaces with the help of a vector differential operator P which consists of finitely or countably many differential operators Pn which themselves are linear combinations of distributional derivatives. We find that certain proper full-space Green functions G with respect to L = P∗TP are positive definite functions. H...

A semiparametric model is a class of statistical models, which are characterized by a finite dimensional parameter and an infinite dimensional parameter. Asymptotic variance of estimator of the finite dimensional parameter is minimized when semiparametric efficient estimation is implemented. However, the efficient estimation is not possible for some models. We suggest a general method to carry ...

Variable selection is popular in high-dimensional data analysis to identify the truly informative variables. Many variable selection methods have been developed under various model assumptions. Whereas success has been widely reported in literature, their performances largely depend on validity of the assumed models, such as the linear or additive models. This article introduces a model-free va...

The present study proposes a new radial basis function which is derived based on an idea of mapping data into a high dimensional feature space which is known as Reproducing Kernel Hilbert Space (RKHS) and then performing Radial Basis Function (RBF) network in the feature space. Orthogonal Least Squares (OLS) method is employed to select a suitable set of centers (regressors) from a large set of...

A mean function in reproducing kernel Hilbert space, or a kernel mean, is an important part of many applications ranging from kernel principal component analysis to Hilbert-space embedding of distributions. Given finite samples, an empirical average is the standard estimate for the true kernel mean. We show that this estimator can be improved via a well-known phenomenon in statistics called Ste...