We study the problem of finding an optimal kernel from a prescribed convex set of kernels K for learning a real-valued function by regularization. We establish for a wide variety of regularization functionals that this leads to a convex optimization problem and, for square loss regularization, we characterize the solution of this problem. We show that, although K may be an uncountable set, the ...

Recently, Y.Q. Bai, M. El Ghami and C. Roos [3] introduced a new class of so-called eligible kernel functions which are defined by some simple conditions. The authors designed primal-dual interiorpoint methods for linear optimization (LO) based on eligible kernel functions and simplified the analysis of these methods considerably. In this paper we consider the semidefinite optimization (SDO) pr...

Let X be a random variable taking values in a function space F, and let Y be a discrete random label with values 0 and 1. We investigate asymptotic properties of the moving window classification rule based on independent copies of the pair (X,Y ). Contrary to the finite dimensional case, it is shown that the moving window classifier is not universally consistent in the sense that its probabilit...

We propose one type of TOP (Tangent vector Of the Posterior log-odds) kernel and apply it to text categorization. In a number of categorization tasks including text categorization, negative examples are usually more common than positive examples and there may be several different types of negative examples. Therefore, we construct a TOP kernel, regarding the probabilistic model of negative exam...

It is proved that quadrature domains are ubiquitous in a very strong sense in the realm of smoothly bounded multiply connected domains in the plane. In fact, they are so dense that one might as well assume that any given smooth domain one is dealing with is a quadrature domain, and this allows access to a host of strong conditions on the classical kernel functions associated to the domain. Foll...

A smooth kernel estimator is proposed for multivariate cumulative distribution functions (cdf), extending the work of Yamato [H. Yamato, Uniform convergence of an estimator of a distribution function, Bull. Math. Statist. 15 (1973), pp. 69–78.] on univariate distribution function estimation. Under assumptions of strict stationarity and geometrically strong mixing, we establish that the proposed...

Exploring Complexity of Large Update Interior-Point Methods for ) k ( P* Linear Complementarity Problems Based on Kernel Function KEYVAN AMINI* M.REZA PEYGHAMI +,2 ∗ Department of Sciences, Razi University, Kermanshah, Iran + Department of Sciences, Khajeh Nasir Toosi (KNT) University of Technology, Tehran, Iran Abstract. Interior Point Methods not only are the most effective methods in practic...

We investigate the performance of conventional bandwidth estimators for non-parametric kernel density estimation on a number of representative pattern-recognition tasks, to gain a better understanding of the behaviour of these estimators in high-dimensional spaces. We show that there are several regularities in the relative performance of conventional kernel bandwidth estimators across differen...