We study a smoothness regularization method for functional linear regression and provide a unified treatment for both the prediction and estimation problems. By developing a tool on simultaneous diagonalization of two positive definite kernels, we obtain shaper results on the minimax rates of convergence and show that smoothness regularized estimators achieve the optimal rates of convergence fo...

Reproducing kernel Hilbert space (RKHS) methods provide a unified context for solving a wide variety of statistical modelling and function estimation problems. We consider two such problems: We are given a training set [yi, ti, i = 1, em leader, n], where yi is the response for the ith subject, and ti is a vector of attributes for this subject. The value of y(i) is a label that indicates which ...

A reproducing-kernel Hilbert space approach to image interpolation is introduced. In particular, the reproducing kernels of Sobolev spaces are shown to be exponential functions. These functions, in turn, give rise to alternative interpolation kernels that outperform presently available designs. Both theoretical and experimental results are presented.

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...

We present a novel online learning paradigm for nonlinear function estimation based on iterative orthogonal projections in an L space reflecting the stochastic property of input signals. An online algorithm is built upon the fact that any finite dimensional subspace has a reproducing kernel, which is given in terms of the Gram matrix of its basis. The basis used in the present study involves mu...

Voice activity detection (VAD) is used to detect whether the acoustic signal belongs to speech or non-speech clusters based on the statistical distribution of the acoustic features. Traditional VAD algorithms are applied in a linear transformed space without any constraint relating to the special characteristics speech or noise. As a result, the VAD algorithms are not robust to noise interferen...

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 paper presents an online support vector machine (SVM) that uses the stochastic meta-descent (SMD) algorithm to adapt its step size automatically. We formulate the online learning problem as a stochastic gradient descent in reproducing kernel Hilbert space (RKHS) and translate SMD to the nonparametric setting, where its gradient trace parameter is no longer a coefficient vector but an eleme...

We propose denotational semantics for a language of probabilistic arithmetic expressions based on reproducing kernel Hilbert spaces (RKHS). The RKHS approach has numerous practical advantages, but from a semantics point of view the most important is ability to provide convergence guarantees on approximate evaluations of expressions. We present preliminary results on convergence bounds, adapting...

We consider reproducing kernels K : ⌦ ⇥ ⌦ ! R in multiscale series expansion form, i.e., kernels of the form K (x, y) = P ` 2N`P j2I`` ,j (x) `,j (y) with weightsànd structurally simple basis functions`,i. Here, we deal with basis functions such as polynomials or frame systems, where, for`2 N, the index set I ` is finite or countable. We derive relations between approximation properties of spac...